Two-dimensional hexagonal semiconductors beyond graphene

The discovery of graphene by Novoselov, Geim et al [1] not only led to the emergence and the development of an extremely promising scientific area as 'a rapidly rising star on the horizon of materials science and condensed matter physics' and revealed 'a cornucopia of new physics and potential applications' [2], but also stimulated the development of a wider scientific area—that of the research and applications of two-dimensional hexagonal semiconductor (THS) materials beyond graphene, such as phosphorene [3–5], silicene [6, 7], hexagonal boron nitride (h-BN) [8, 9], transition metal dichalcogenide (TMDC) [10–12] and their van der Waals heterostructures [13, 14].

Some year ago Xu et al [15] published a comprehensive review in graphene-like two-dimensional materials. Since that time a significant progress has been achieved in the research and applications of this particular type of THSs. The purpose of present work is to review scientific results obtained after the submission of the article [15].

A review on recent advances in the research and applications of phosphorene and silicene is the content of section 2. Also in recent years the research and applications of TMDCs were very active, a large number of experimental works on these interesting and extremely promising two-dimensional hexagonal semiconducting materials were carried out. Their results are summarized in section 3. The content of section 4 is a review on van der Waals heterostructures of various two-dimensional hexagonal semiconducting materials (including graphene). The conclusion and discussion are presented in section 5.

In a very interesting and important article [3] Reich remarked that although graphene possesses enticing electrical properties allowing electrons to flow freely across its surface, it lacks a natural bandgap that could be used to swith this flow on and off. This deficiency reduces graphene's usefulness as a replacement for the semiconductor switches in computer circuits. Phosphorene, an atom—thick layer of elemental phosphorus that does have a natural bandgap could be an alternative to overcome above-mentioned deficiency of graphene, and at the same time, might be also useful for developing flexible electronics. From phosphorene layers Churchill and Jarillo-Herrero fabricated transistor devices [4], while Chen, Zhang et al fabricated field-effect transistors (FETs) [5].

Strain-induced gap in black phosphorus (BP) was studied by Castro Neto et al [16]. Using density functional theory and tight-binding models the authors predicted the band structure of single-layer BP and the effect of strain. Having determined the localized orbital composition of the individual bands from first principle, the authors used the system symmetry to write down the effective low-energy Hamiltonian at the point. From numerical calculations and arguments based on the crystal structure of the material the authors showed that the deformation in the direction normal to the plane can be used to change the gap size and induce a semiconductor-metal transition.

A computational study on semiconducting layered blue phosphorus was carried out by Tománek et al [17]. The authors investigated a previously unknown phase of phosphorus that shares it layered structure and high stability with the BP allotrope. They found the in-plane hexagonal structure and bulk layer stacking of this structure, and called it 'blue phosphorus'. Unlike graphite and BP, blue phosphorus displays a wide fundamental bandgap. Moreover, it should be easily exfoliated to form a quasi-two-dimensional structure suitable for electronic applications.

In [18] Tománek et al demonstrated the phase coexistence and metal-insulator transition in few-layer phosphorene by using a computational study. Based on ab initio density functional calculations the authors proposed γ − P and δ − P as two additional stable structural phases of layered phosphorus besides the layered α − P (black) and β − P (blue) phosphorus allotropes. Monolayers of some of these allotropes have a wide bandgap, whereas others, including γ − P, show a metal-insulator transition caused by in-layer strain or changing the number of layers. An unforeseen benefit was the possibility to connect different structural phases at no energy cost. This becomes particularly valuable in assembling heterostructures with well-defined metallic and semiconducting regions in one continuous layer.

Electron–phonon coupling in two-dimensional silicene and germanene was studied by Chou et al [19]. Following work in graphene the authors performed the first principles calculations of electron–phonon coupling in low-buckled monolayer silicene and germanene. Despite the similar honeycomb atomic arrangement and linear band dispersion, the electron–phonon coupling matrix element squares of the Γ − E_g and K–A₁ modes in silicene are only about 50% of those in graphene. However, the smaller Fermi velocity in silicene compensates for this reduction by providing a larger joint electronic density of states near the Dirac point, giving rise to comparable phonon linewidths. The authors predicted that Kohn anomalies associated with these two optical modes are significant in silicene. In addition, the electron–phonon coupling induced frequency shift and linewidth of the Raman-active Γ − E_g mode in silicene were calculated as a function of doping. The results are comparable to those in graphene, indicating a similar nonadiabatic dynamic origin.

In [20] Yang et al investigated layer-controlled bandgap and anisotropic excitons in few-layer BP. The authors observed the quasiparticle bandgap, excitons and highly anisotropic optical responses of few-layer BP. It was shown that this material exhibits unique many-electron effects, and its electronic structure is dispersive essentially along one dimension, leading to particularly enhanced self-energy corrections and excitonic effects. Additionally, within a wide energy range, including infrared light and a part of visible light, few-layer BP absorbs light polarized along the armchair direction, and is transparent to light polarized along the zigzag direction, making them potentially viable linear polarizers for applications. Finally, the numbers of phosphorene layers included in the stack controls the material's bandgap, optical absorption spectrum, and anisotropic polarization energy window across a wide range.

Scaling laws for the bandgap and optical response of phosphorene nanoribbons (PNRs) were establishe by Yang and Tran [21]. The authors studied electronic structure and optical absorption spectra of monolayer PNRs by using first-principles simulations. The bandgap of PNRs is strongly enhanced by quantum confinement. However, differently orientated PNRs exhibit distinct scalling laws for the bandgap versus the ribbon width. The bandgaps of armchair PNRs scale as 1/W², while zigzag PNRs exhibit a 1/W behavior. These distinct scaling laws reflect a significant implication of the band dispersion of phosphorene: electrons and holes behave as nonrelativistic particles along the zigzag direction but resemble relativistic particles along the armchair direction. This unexpected merging of nonrelativistic and relativistic properties in a single material may produce novel electrical and magnetotransport properties of few-layer BP and its ribbon structure. Finally, the respective PNRs host electrons and holes with markedly different effective masses and optical absorption spectra, which are suitable for a wide range of applications.

In [22] Castro Neto, Özyil Maz et al investigated electric field effect in ultrathin BP. The authors demonstrated few-layer BP field effect devices a Si/SiO₂ and measured charge carrier mobility in a four probe configuration as well as drain current modulation modulation in a two point configuration. The authors found room temperature mobilities up to 300 cm² V⁻¹ s⁻¹ and drain current modulation of over 10³. At low temperature the ON/OFF ratio exceeded 10⁵, and the device exhibited both electron and hole conduction. Using atomic force microscope the authors observed significant surface roughening of thin BP crystals over the course of 1 h after exfoliation.

A superior gas sensor based on phosphorene was proposed by Kou et al [23]. Using first principles calculations the authors studied the adsorption of CO, CO₂, NH₃, NO and NO₂ gas molecules on a monolayer of phosphorene and predicted superior sensing performance of phosphorene rivaling or even surpassing that of other 2D materials. The authors determined the optimal adsorption positions of these molecules on phosphorene and identified molecular doping, that is, charge transfer between the molecules and phosphorene, as the driving mechanism for the high adsorption strength. Further the authors calculated the current–voltage (I − V) relation using nonequilibrium Green's function formalism. The transport features showed large (1–2 order of magnitude) anisotropy along different (armchair or zigzag) directions, which is consistent with the anisotropic band structure of phosphorene. Remarkably, the I−V relation exhibits distinct responses with a marked change of the I−V relation along either the armchair or the zigzag directions depending on the type of molecules. Such selectivity and sensitivity to adsorption make phosphorene a superior gas sensor that promises widely ranging applications.

The anisotropic electrical conductance of few-layer BP can be generated by strain-engineering. In [24] Yang et al applied first principles calculations to demonstrate that the anisotropic electronic mobility can be controlled by using simple strain conditions. With the appropriate biaxial or uniaxial strain (4%–6%) the preferred conducting direction can rotate by 90°. This will be useful for exploring unusual quantum Hall effects and exotic electronic and mechanical applications based on phosphorene.

Few-layer BP is a high-mobility layered semiconductor with a direct bandgap strongly depending on the number of layers, from 0.35 eV (bulk) to 2.0 eV (single layer). Therefore BP is an appealing candidate for tunable photodetection from the visible to the infrared part of the spectrum. The fast and broadband photoresponse of few-layer BP FETs was demonstrated by Buscema, Castellanos-Gomez et al [25]. The authors studied the photoresponse of FETs fabricated from few-layer BP (3–8 nm thick) as a function of excitation wavelength, power, and frequency. In the dark state, the BP FETs could be tuned both in hole and electron doping regimes allowing for ambipolar operation. The authors measured mobilities in the order of 100 cm² V⁻¹ s⁻¹ and a current ON/OFF ratio large than 10³. Upon illumination, the BP FETs showed a response to excitation wavelengths from the visible region up to 940 nm and a rise time of about 1 ms, demonstrating broadband and fast detection. The responsivity reached 4.8 mA W⁻¹, and it could be drastically enhanced by engineering a detector based on a p–n function. The ambipolar behavior coupled to the fast and broadband photodetection makes few-layer BP a promising two-dimensional material for photodetection across the visible and near-infrared part of the electromagnetic spectrum.

Strain and orientation modulated bandgaps and effective masses in PNRs were investigated by Guo et al [26]. The authors applied the density functional theory to study passivated PNRs, armchair nanoribbon (a-PNR), diagonal nanoribbon (d-PNR) and zigzag nanoribon (z-PNR). It was shown that z-PNRs demonstrate the greatest quantum size effect, tuning the bandgap from 1.4 to 2.6 eV when the width is reduced from 26 to 6 Å. Strain effectively tunes charge carrier of electron effective mass at +8% strain for a-PNRs or a hole effective mass at +3% strain for z-PNRs, differentiating the ${{m}}_{{h}}^{* }/{{m}}_{{e}}^{* }$ ratio by an order of magnitude in each case. Straining of d-PNRs results in a direct to indirect band gap transition at either −7% or +5% strain and therein creates degenerate energy valleys with potential applications for valleys with potential applications for valleytronics and/or photocatalysis.

In [27] Das et al investigated the tunable transport gap in phosphorene. The authors experimentally demonstrated that the transport gap of phosphorene can be tuned monotonically from ∼0.3 to ∼1.0 eV when the flake thickness is scaled down from bulk to a single layer. As a consequence, the ON current, the OFF current, and the current ON/OFF ratio of phosphorene FETs were found to be significantly impacted by the layer thickness. The transport gap was determined from the transfer characteristics of phosphorene FETs using a robus technique. By scaling the thickness of the gate oxide, the authors were also able to demonstrate enhanced ambipolar conduction in monolayer and few-layer phosphorene FETs. The asymmetry of electron and hole current was found to be dependent on the layer thickness that can be explained by dynamic changes of the metal Fermi level with the energy band of phosphorene depending on the layer number. The authors also extracted the Schottky barrier height for both the electron and the hole injection as a function of the layer thickness. Finally, the authors discussed the dependence of the hole mobility of phosphorene on temperature and carrier concentration.

Enhanced thermoelectric efficiency via orthogonal electrical and thermal conductance in phosphorene was investigated by Yang et al [28]. Thermoelectric devices that utilize the Seebeck effect to convert heat flow into electrical energy are highly desirable for the development of portable, solid state, passively powered electronic systems. The conversion efficiencies of such devices are quantified by the dimension less thermoelectric figure of merit (ZT), which is proportional to the ratio of a device's electrical conductance to its thermal conductance. By applying first-principles and model calculations the authors demonstrated that phosphorene possesses a spatially anisotropic electrical conductance and its lattice thermal conductance exhibits a pronounced special-anisotropy as well. The prominent electrical and thermal conducting directions are orthogonal to one another, enhancing the ratio of these conductances. As a result, ZT may reach the criterion for commercial deployment along the armchair direction of phosphorence at T = 500 K and is close to 1 even at room temperature. Ultimately, phosphorene hopefully stands out as an environmentally sound thermoelectric material with unprecedented qualities. Intrinsically, it is a mechanically flexible materials that converts heat energy with high efficiency at low temperature (∼300 K).

The electronic bandgap and edge reconstruction in phosphorene materials were investigated by Meunier, Pan et al [29]. The authors considered atomic scale electronic variation related to strain-induced honeycomb structure of freshly cleaved BP using a high-resolution scanning tunneling spectroscopy (STS) to survey the light (x) and heavy (y) effective mass directions. Through a combination of STS measurements and first-principles calculations, a model for edge reconstruction was also determined.

Special properties of phosphorene were investigate by Ye et al [30]. The authors showed that single-layer phosphorene is flexible, stable and can be mechanically exfoliated. Unlike graphene, phosphorene has an inherent, direct and appreciate bandgap. By using ab initio calculations the authors indicated that the bandgap of phosphorene is direct, depends on the number of layers and the in-layer strain, and is significantly large than the bulk value of 0.31–0.36 eV. The observed photoluminescence (PL) peak of single-layer phosphorene in the visible optical range also confirmed that the bandgap is larger than that of the bulk system. The transport studies indicated a hole mobility that reflects the structural anisotropy of phosphorene. At room temperature the prepared few-layer phosphorene FET with 0.1 μm channel length displayed a high ON-current of 194 mA mm⁻¹, a high hole field-effect mobility of 286 cm² V⁻¹ s⁻¹, and ON/OFF ratio up to 10⁴.

The PL and Raman spectroscopy in few-layer phosphorene were investigated by Lu et al [31]. In this work few-layer phosphorus flakes were fabricated using mechanical exfoliation techniques. The flakes were identified by optical contrast in a microscope. Regions with different colors correspond to phosphorene flakes with different thicknesses. All Raman and PL measurements were carried out in a confocal microscopy setup, which has a 532 nm solid state green laser for excitation. The authors used PL system with two liquid nitrogen cooled detectors which can detect photons with wavelengths ranging from 200 to 1650 nm. Measured PL spectra in few-layer phosphorene were highly dependent on number of layers. Strong peaks at 961, 1268, 1413 and 1558 nm were observed in two-, three-, four- and five-layered phosphorene, respectively, which correspond to energy values of 1.29, 0.98, 0.88 and 0.80 eV, respectively. The measured PL peaks are attributed to the nature of excitons, which represent lower bounds on the fundamental bandgap value in few-layer phosphorene. Thus the energy positions of PL peak increase rapidly, in the consistency with the results of the theoretical calculations of the authors. The strong PL in few-layer phosphorene arises from direct electronic transitions with high radiative recombination rate.

The measured Raman peaks at 359, 437 and 466 cm⁻¹ are attributed to the Ag¹, B_2g, and Ag² phonon modes in the crystalline few-layer phosphorene flakes. The decrease of temperature led to their blue shift. The highly angle-dependent Raman spectra from phosphorene flakes enabled the authors quickly determine their crystalline orientation without TEM or SEM.

The ambipolar phosphorene FET with record high electron mobility was demonstrated by Das et al [32]. By tuning the work function of the contact metal and scaling the thickness of the gate oxide the authors showed that electron transport can indeed be realized in phosphorene. The authors obtained record high electron field-effect mobility of ∼38 cm V⁻¹ s⁻¹ and hole field-effect mobility of ∼172 cm V⁻¹ s⁻¹ in phosphorene. The contact resistance values of the Schottky barrier were also extracted and its effects on the device performance were discussed.

Previously silicene has been theoretically predicted as a buckled honeycomb arrangement of Si atoms with an electronic dispersion resembling that of relativistic Dirac fermions in graphene. Le Lay et al [6] provided compelling evidence, from both structural and electronic properties, for the synthesis of epitaxial silicene sheets on a silver (111) substrate, through the combination of scanning tunneling microscopy and angular-resolved photoemission spectroscopy in conjunction with calculations based on density functional theory. Another evidence for Dirac fermions in a honeycomb lattice based on silicon was shown by Wu et al [33]. The authors performed scanning tunneling microscopy studies on the atomic and electronic properties of silicene on Ag (111). Pronounced quasiparticle interference patterns, originating from both the intervalley and intravalley scatterings were observed. From these patterns, in conjunction with theoretical calculations, the authors derived a linear energy–momentum dispersion and a large Fermi velocity, which proved the existence of Dirac fermion in silicene. One more experimental evidence for epitaxial silicene was demonstrated by Yamada-Takamura et al [34]. The authors showed that two-dimensional epitaxial silicene formed diboride thin films grown on Si wafer through surface segregation on zirconium. A particular buckling of silicene induced by epitaxial relationship with surface led to a direct electronic bandgap at the Γ-point. These results demonstrated that the buckling and thus electronic properties of silicene were modified by epitaxial strain.

Although until now the theoretical calculations of the electronic structures of phosphorene and silicene [35–45] still did not reach final confirmed results, there was a significant progress in the applications of this new type of two-dimensional semiconductors. For example, in [46] Xu et al investigated electrical transport and optoelectronic properties of FETs fabricated from few-layer BP crystal down to a few nanometers. The authors explored the anisotropic nature and photocurrent generation mechanisms in BP FETs though spatial-, polarization-, gate-, and bias-dependent photocurrent measurements. Obtained results revealed that the photocurrent signals at BP-electrode junctions are mainly attributed to the photovoltaic effect in the OFF-sate and photothermoelectric effect in the ON-state, and their anisotropic feature primarily results from the directional-dependent absorption of BP crystals.

Very recently Molle, Akinwande et al [7] successfully fabricated silicene FET corrobogating theoretical expectations regarding its ambipolar Dirac fermion transport with a measured room-temperature mobility of 100 cm² V⁻¹ s⁻¹ attributed to acoustic phonon-limited transport and grain boundary scattering. These results were enabled by a growth-transfer-fabrication process that the authors have devised. This approach addresses a major challenge for material preservation of silicene during transfer and device fabrication and is applicable to other air-sensitive two-dimensional materials. Silicene's allotropic affinity with bulk silicon and its low-temperature synthesis compared with graphene or alternative two-dimensional semiconductors suggest more direct integration with ubiquitous semiconductor technology.

Subsequently Xu, Xia et al [47] observed highly anisotropic and robust excitons in monolayer BP. Although BP has emerged as a promising new two-dimensional material due to its widely tunable and direct bandgap, high carrier mobility and remarkable in-plane anisotropic electrical, optical and phonon properties, current progress of the research on this material is primarily limited to its thin-film form. In above-mentioned work the authors revealed highly anisotropic and strongly bound excitons in monolayer BP using polarization-resolved PL measurements at room temperature. The authors showed that, regardless of the excitation laser polarization, the emitted light from the monolayer is linearly polarized along the light effective mass direction and centers around 1.3 eV, a clear signature of emission from highly anisotropic bright excitons. Moreover, PL excitation spectroscopy suggest a quasiparticle bandgap of 2.2 eV, from which the authors estimated an exciton binding energy of ∼0.9 eV, consistent with theoretical results based on first principles. The experimental observation of highly anisotropic, bright excitons with large binding energy not only opened avenues for the explorations of many-electron physics in this unusual two-dimensional material, but also suggested its promising future in optoelectronic devices.

In the experimental work [48] Martel et al applied in situ Raman and transmission electron spectroscopies to study the photoexcitation and quantum confinement effects in exfoliated BP. Phosphorene thin layers are exfoliated from lamellar crystal of phosphorus atoms. However, probing the properties of phosphorene thin layer has been challenged by the fast degradation of phosphorene thin layers on exposure to ambient conditions. Therefore a procedure carried out in a glove box was used to prepare phosphorene thin layer in their pristine states for further studies on the effect of layer thickness on the Raman modes. Controlled experiments in ambient conditions were shown to lower the Ag¹/Ag² intensity ratio for ultrathin layers, a signature of oxidation.

3.1. Research on general properties of thin layers of TMDCs

3.2. Research on thin layers of MoS₂ and MoSe₂

3.3. Research on thin layers of WS₂, WSe₂ and TiS₂

For the fabrication of electronic, optoelectronic and photonic devices from THSs the formation of multilayer heterostructures owing to the van der Waals interaction between them plays a crucial role. The present section is a review of the research on this topic.

Haigh, Gorbashev et al [13] indicated that by stacking various two-dimensional atomic crystals on top each other, it is possible to create multilayer heterostructures and devices with designed electronics properties. However, various adsorbates become trapped between layer during their assembly, and this is not only affects the formation of a true artificial layerd crystal upheld by van der Waals interaction, creating instead a laminate glued together by contamination. TEM showed that graphene and boron nitride monolayers, the two best characterized two-dimensional crystals, are densely covered with hydrocarbons (even after thermal annealing in high vacuum) and exhibit only small clean patches suitable for atomic resolution imaging. This observation seems detrimental for any realistic prospect of creating van der Waals materials and heterostructures with atomically sharp interface. The authors employed cross-sectional TEM to take a side view of several graphene-boron nitride heterostrucstures. The authors found that the trapped hydrocarbons segregate into isolated pockets, leaving the interfaces atomically clean. Moreover, the authors observed a clear correlation between interface roughness and the electronic quality of encapsulate graphene.

A general discussion on van der Waals heterostructures was presented by Geim and Grigorieva [14], noting that isolated atomic planes can also be reassembled into designer heterostructures created layer by layer in a precisely chosen sequence. The authors reviewed this emerging research area and identified possible future directions with steady improvement in fabrication techniques and using graphene' springboard, van der Waals heterostructures should develop into a large field of their own.

Jarillo-Herrero, Ashoori et al [94] studied Dirac fermion and Hofstadter band structure engineering in a van der Waals heterostructure. The authors desmonstrated band structure engineering in a van der Waals heterostructure composed of a monolayer graphene flake coupled to a rotationally aligned hexagonal boron nitride substrate. The spatially varying interlayer atomic registry results in both a local breaking of the carbon sublattice symmetry and a long-range moiré superlattice potential in the graphene. In the prepared samples this interplay between short- and long-wavelength effects resulted in a band structure described by isolated superlattice minibands and an unexpectedly large band gap at charge neutrality. This picture was confirmed by the observation of fractional quantum Hall states at ±5/3 filling and features associated with the Hofstadter butterfly at ultrahigh magnetic fields.

A comprehensive commentary on progress, challenges and opportunities in two-dimensional materials beyond graphene was presented by Goldberger et al [95]. The authors reviewed the state-of-the art of two-dimensional materials beyond different classes of two-dimensional materials and discussed various strategies to prepare single-layer, few-layer and multilayer assembly materials in solution, on substrates and on the wafer scale. Additionally the authors presented an experimental guide for identifying and characterizing single-layer-thick materials as well as outlining emerging techniques that yield both local and global informations. The authors described the differences that occur in the electronic structure between the bulk and the single layer, and discussed various methods of tuning their electronic properties by manipulating the surface. Finally, the authors highlighted the properties and advantages of single-, few- and many-layer two-dimensional materials in FETs, spin- and valley-tronics, thermoelectrics, and topological insulators, among many other applications.

Lateral heterojunctions within monolayer MoSe₂−WSe₂ semiconductors were investigated by Wu, Sanchez et al [96]. The authors demonstrated that high-quality in-plane heterojunctions can be grown between monolayer semiconductors MoSe₂ and WSe₂. The junctions grown by lateral heteroepitaxy using physical vapor transport were visible in an optical microscope and showed enhanced PL. Atomically resolved TEM revealed that their structure is an undistorted honeycomb lattice in which substitution of one transition metal by another occurs across the interface. The growth of such lateral junctions will allow new device functionalities, such as in-plane transistors and diodes, to be integrated within a single atomically layer.

Vertical and in-plane heterostructures from WS₂/MoS₂ monolayers were fabricated and investigated by Zhou, Ajayan et al [97]. Layer-by-layer stacking or lateral interfacing of atomic monolayers has opened up unprecedented opportunities to engineer two-dimensional heteromaterials. Fabrication of such artificial heterostructures with atomically clean and sharp interfaces, however, was challenging. In the present work the authors report a one-step strategy for the creation of high-quality vertically stacked as well as in-plane interconnected heterostructures of WS₂/MoS₂ via control of the growth temperature. Vertically stacked bilayers with WS₂ epitaxially grown on top of the MoS₂ monolayer were formed with preferred stacking order at high temperature. A strong interlayer excitonic transition was observed due to the type II band alignment and to the clean interface of these bilayers. Vapor growth at low temperature, on the other hand, led to lateral epitaxy of WS₂ on MoS₂ edges, creating seamless and atomically sharp in-plane heterostructures that generated strong localized PL enhancement and intrinsic p–n junctions. Thus the fabrication of heterostructures from monolayers, using simple and scalable growth, paved the way for for the creation of unprecedented two-dimensional materials with exciting properties.

Photoinduced doping in heterostructures of graphene and boron nitride was performed by Wang et al [98]. The design of the stacks of layered materials in which adjacent layers interact by van der Waals forces has enabled the combination of various two-dimensional crystals with different electrical, optical and mechanical properties as well as the emergence of novel physical phenomena and device functionality. In the present work the authors reported photoinduced doping in van der Waals heterostructures consisting of graphene and boron nitride layers. It enabled flexible and repeatable writing and erasing of charge doping in grapheme with visible light. The authors demonstrated that this photoinduced doping maintains the high carrier mobility of the graphene/boron nitride heterostructure, thus resembling the modulation doping technique used in semiconductor heterojunctions, and can be used to generate spatially varying doping profiles such as p–n junctions. The authors showed that this photoinduced doping arises from microscopically coupled optical and electrical responses of graphene/boron nitride heterostructures, including optical excitation of defect transitions in boron nitride, electrical transport in graphene, and charge transfer between boron nitride and graphene.

Atomically thin p–n junctions with van der Waals heterointerfaces were investigated by Kim et al [99]. In conventional p–n junctions, regions depleted of free charge carriers are formed on either side of the function, generating built-in potentials associated with uncompensated dopant atoms. Carrier transport across the junction occurs by diffusion and drift processes influenced by the spatial extent of this depletion region. With the advent of atomically thin van der Waals materials and their heterostructures, it is now possible to realize p–n junctions at the ultimate thickness limit. Van der Waals junctions composed of p- and n-type semiconductors-each just one unit cell thick-are predicted to exhibit completely different transport characteristics than bulk heterojunctions. In the present work the authors reported the characterization of the electronic and optoelectronic properties of atomically thin p–n heterojunctions fabricated using van der Waals assembly of TMDCs. The authors observed gate-tunable diode-like current rectification and a photovoltaic response across the p–n interface, and found that the tunneling-assisted interlayer recombination of the majority carriers was responsible for the tenability of the electronic and optoelectronic processes. Sandwiching an atomic p–n junction between graphene layers enhanced the collection of the photoexcited carriers. The atomically scaled van der Waals p–n heterostructures presented in this work constituted the ultimate functional unit for nanoscale electronic and optoelectronic devices.

Ultrafast charge transfer in atomically thin MoS₂/WS₂ heterostructures was studied by Wang et al [12]. Van der Waals heterostructures have recently emerged as a new class of materials, where quantum coupling between stacked atomically thin two-dimensional layers, including graphene, hexagonal-boron nitride and TMDCs give rise to fascinating new phenomena. TMDC heterostructures are particularly exciting for novel optoelectronic and photovoltaic applications, because two-dimensional TMDC monolayers can have an optical bandgap in the near-infrared to visible spectral rang and exhibit extremely strong light–matter interactions. Theory predicted that many stacked TMDC heterostructures form type II semiconductor heterojunctions that facilitate efficient electron–hole separation for light detecting and harvesting. In the present work the ultrafast charge transfer in photoexcited MoS₂/WS₂ heterostructures was experimentally observed by using both PL mapping and femto-second pump-probe spectroscopy. The authors showed that hole transfer from MoS₂ layer to WS₂ layer took place within 50 fs after optical excitation, a remarkable rate for van der Waals coupled two-dimensional layers. Such ultrafast charge transfer in van der Waals heterostructures can enable novel two-dimensional devices for optoelectronics and light harvesting.

Twist-controlled resonant tunneling in graphene/boron nitride/graphene heterostructures was investigated by Novoselov et al [100]. Recent development in the technology of van der Waals heterostructures fabricated from two-dimensional atomic crystals have already led to the observation of new physical phenomena, such as the metal-insulator transition and Coulomb drag, and to the realization of functional devices such as tunnel diodes, tunnel transistors and photovoltaic sensors. An unprecedented degree of control of the electronic properties was available not only by means of the selection of materials in the stack, but also through the additional fine-tunning achievable by adjusting the built in strain and relative orientation of the component layers. In the present work the authors demonstrated how careful aligment of the crystallographic orientation of two graphene electrodes separated by a layer of hexagonal boron nitride in a transistor device can achieve resonant tunneling with the conservation of electron energy, momentum and, potentially, chirality. The authors showed how the resonance peak and negative differential conductance in the device characteristics induce a tunable radiofrequency oscillator current that has potential for future high-frequency technology.

In [101] Lee, Hone et al preformed multi-terminal transport measurements of MoS₂ using a van der Waals heterostructure device platform. Atomically thin two-dimensional semiconductors such as MoS₂ hold great promise for electrical, optical and mechanical devices and display novel physical phenomena. However, the electron mobility of mono-and few-layer MoS₂ has so far been substantially below theoretically predicted limits, which has hampered efforts to observe its intrinsic quantum transport behaviors. Potential sources of disorder and scattering include defects such as sulfur vacancies in the MoS₂ itself as well as extrinsic sources such as charged impurities and remote optical phonons from oxide dielectrics. To reduce extrinsic scattering, the authors have developed a van der Waals heterostructure device platform where MoS₂ layers were fully encapsulated within hexagonal boron nitride and electrically contacted in a multi-terminal geometry using gate-tunable graphene electrodes. Magneto-transport measurement showed dramatic improvement in performance, including a record-high Hall mobility reaching 34 000 cm² V⁻¹ s⁻¹ for six-layer MoS₂ at low temperature. The authors also observed Shubnikov–de Haas oscillations in high-mobility monolayer and few-layer MoS₂. Modeling of potential scattering sources and quantum lifetime analysis indicated that a combination of short-range and long-range interfacial scattering limited the low-temperature mobility of MoS₂.

A phosphorene-graphene hybrid material was used by Cui et al [102] as a high-capacity anode for sodium-ion batteries. Sodium-ion batteries have recently attracted significant attention as an alternative to lithium-ion batteries because sodium sources do not present the geopolitical issue that lithium sources might. Although recent reports on cathode materials for sodium-ion batteries have demonstrated performance comparable to their lithium-ion counterparts, the major scientific challenge for a competitive sodium-ion battery technology was to develop viable anode materials. In the present work the author showed that a hybrid material composed of a few phosphorene layers sandwiched between graphene layers possessed a specific capacity of 2.440 mA h g⁻¹ at a current density of 0.05 A g⁻¹ and an 83% capacity retention after 100 cycles while operating between 0 and 1.5 V. Using in situ TEM and ex situ x-ray diffraction technique, the authors explained the large capacity of fabricated anode through a dual mechanism of intercalation of sodium ions along the x-axis of the phosphorene layers followed by the formation of a Na₃P alloy. The presence of graphene layers in the hybrid material as a mechanical backbone and an electrical highway ensuired that a suitable elastic buffer space accomodated the anisotropic expansion of phosphorene layers along the y and z directions for stable cycling aperation.

Another graphene-hexagonal boron nitride heterostructure to be used as a tunable hyperbolic metamaterial was studied by Basov et al [103]. Hexagonal boron nitride (h-BN) is a natural hyperbolic material in which the dielectric constants are the same in the bassal plane (ε^t = ε^x = ε^y) but have opposite signs (ε^tε^z < 0) in the normal plane. Owing to this property, finite-thickness slabs of h-BN act as multimode waveguide for the propagation of hyperbolic phonon polariton modes that originate from the coupling between photons and electric dipoles in phonons. However, control of these hyperbolic phonon polariton modes has remained challenging, mostly because their electrodynamic properties are dictated by the crystal lattice of h-BN. Using direct nano-infrared imaging, the authors showed that these hyperbolic polaritons can be effectively modulated in a van der Waals heterostructure composed of monolayer graphene on h-BN. Tunability originated from the hybridization of surface plasmon polaritons in graphene with hyperbolic phonon polaritons in h-BN, so that the eigenmodes of the graphene/h-BN heterostructure are hyperbolic plasmon–phonon polaritons. The hyperbolic plasmon–phonon polaritons in graphene/h-BN suffer little from Ohmic losses, making their propagation length 1.5–2.0 times greater than that off hyperbolic phonon polaritons in h-BN. Therefore, graphene/h-BN can be classified as an electromagnetic metamalterial as the resulting properties of these devices are not present in its constituent elements alone.

The band offset and the negative compressibility in graphene- MoS₂ heterostructures were observed by Tutuc et al [104]. The authors used electron transport to characterize monolayer graphene-multilayer MoS₂ heterostructure. Prepared samples showed ambipolar characteristics and conductivity saturation on the electron branch that signaled the onset of MoS₂ conduction band population. Surprisingly, the carrier density in graphene decreased with gate bias once MoS₂ was populated, demonstrating negative compressibility in MoS₂. The authors quantitatively interpreted the results of measurements by accounting for disorder and using the random phase approximation for the exchange and correlation energies of both Dirac and parabolic-band two-dimensional electron gases. This interpretation allowed the authors to extract the energetic offset between the conduction band edge of MoS₂ and the Dirac point of graphene.

In [105] Das, Sumant et al reported on 10 atomic layer thick, high mobility, transparent thin film transistors (TFTs) with ambipolar device characteristics fabricated on both a conventional silicon platform as well as on a flexible substrate. Monolayer graphene was used as metal electrodes, 3–4 atomic layers of h-BN were used as the gate dielectric, and finally bilayers of WSe₂ were used as the semiconducting channel material for the TFTs. The field-effect carrier mobility was extracted to be 45 cm² V⁻¹ s⁻¹, which exceeded the mobility values of start-of-the art amorphous silicon based TFTs by ∼100 times. The active device stack of WSe₂-h-BN-graphene was found to be more than 88% transparent over the entire visible spectrum, and the device characteristics were unaltered for in-plane mechanical strain of up to 2%. The device demonstrated remarkable temperature stability over 77–400 K. Low contact resistance value of 1.4 kΩ μm, substhreshold slope of 90 mV/decade current ON/OFF ratio of 10⁷, and the presence of both electron and hole conduction were observed in all prepared two-dimensional TFTs. These characteristics are extremely desirable, but they were rarely reported in previous works on organic as well as inrrganic TFTs. For large-scale two-dimensional electronics was developed by Wang, Palacios et al [106]. The authors demonstrated a novel technology for constructing large-scale electronics systems based on graphene/MoS₂ heterostructures grown by chemical vapor deposition, and fabricated high-performance devices and circuits based on these heterostructures, where MoS₂ was used as the transistor channels and graphene as contact electrode and circuit interconnects. The authors provided a systematic comparison of graphene/MoS₂ heterojunction contact to more traditional MoS₂-metal junctions, as well as a theoretical investigation, using density functional theory. The tenability of the graphene work function with electrostatic doping significantly improved the Ohmic contact to MoS₂. These high-performance large-scale devices and circuits paved the way for practical flexible transparent electronics.

Hybride surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures were investigated by Atwater et al [107]. Infrared transmission measurements revealed the hybridization of graphene plasmons and the phonons in a monolayer hexagonal boron nitride (h-BN) sheet. Frequency-wave vector dispersion relations of the electromagnetically coupled graphene plasmon/h-BN phonon modes were derived from measurements of nanoresonators with the widths varying from 30 to 300 nm. It was shown that the graphene plasmon mode was split into two optical modes that displayed an anticrossing behavior near the energy of the h-BN optical phonon at 1370 cm⁻¹. The authors explained this behavior as a classical electromagnetic strong-coupling with the highly confined near fields of the graphene plasmons allowing for hybridization with the phonons of the atomically thin h-BN layer to create two clearly separated new surface-phonon-plasmon-polariton modes.

The electronic states at the graphene-hexagonal boron nitride zigzag (ZZ) interface were investigated by Liljeroth et al [108]. The authors proposed the ZZ-terminated, atomically sharp interfaces between graphene and hexagonal boron nitride (h-BN) as experimentally realizable, chemically stable model systems for graphene ZZ edges. Combining scanning tunneling microscopy and numerical methods, the authors explored the structure of graphene/h-BN interfaces and showed them to host localized electron states similar to those on the pristine graphene ZZ edge.

In [109] Loh et al studied lattice relaxation at the interface of graphene and hexagonal boron nitride. Heteroepitaxy of two-dimensional crystals such as h-BN on graphene can occur at the edge of an existing heterointerface. Understanding strain relaxation at such two-dimensional laterally fused interface is useful in fabricating heterointerfaces with a high degree of atomic coherency and structural stability. The authors used in situ scanning tunneling microscopy to study the heteroepitaxy of h-BN on graphene edges on a Ru surface with the aim of understanding the propagation od interfacial strain. The authors found that defect-free, pseudomorphic growth of h-BN on a graphene edge 'substrate' occurred only for a short distance (<1.29 nm) perpendicular to the interface, beyond which misfit dislocations occurred to reduce the elastic strain energy. Boundary states originating from a coherent zigzag-linked graphene/h-BN boundary were observed to greatly enhance the local conductivity, thus affording a new avenue to construct one-dimensional transport channel in graphene/h-BN hybrid interface.

In [110] Beschoten et al determined spin lifetimes in single-and few-layer graphene/h-BN hetersotructures at room temperature. The authors demonstrated a new fabrication method of graphene spin-valve devices that yielded enhanced spin and charge transport properties by improving both the electrode-to-graphene and graphene-to substrate interface. First the authors prepared CO/MgO spin injection electrodes onto Si⁺⁺/SiO₂. Thereafter the authors mechanically transferred a graphene/h-BN heterostructure onto the prepatterned electrodes, and showed that room temperature spin transport in single-, bi- and tri-layer graphene devices exhibited nanosecond spin lifetimes with spin diffusion lengths reaching 10 μm combined with carrier mobilities exceeding 20 000 cm² V⁻¹ s⁻¹.

The coupling of orbital magnetic moments to the valley degree of freedom in graphene van der Waals heterostructures was investigated by Grujić et al [111]. In honeycomb Dirac systems with broken inversion symmetry, orbital magnetic moments couple to the valley degree of freedom due to the topology of the band structure, leading to valley-selective optical dichroism On the other hand, in Dirac systems with prominent spin–orbit coupling, similar orbital magnetic moments emerge as well. These moments are coupled to spin, but otherwise have the same functional form as the moments stemming from spatial inversion breaking. After reviewing the basic properties of these moments, which are relevant for a whole set of newly discovered materials, such as silicene and germanene, the authors studied the particular impact that these moments have on graphene nanoegineered barriers with artificially enhanced spin–orbit coupling. The authors examined transmission properties of such barriers in the presence of a magnetic field. The orbital moments were found to manifest in transport characteristics through spin-dependent transmission and conductance, making them directly accessible in experiments. Moreover, the Zeeman-type effects appeared without explicitly incorporating the Zeeman term in the model, i.e., by using minimal coupling and Peierls substitution in continuum and the tight-binding methods, respectively.

Interlayer hybridization and Dirac relativistic carriers in graphene/MoS₂ van der Waals heterostructures were directly observed by Batzill et al [112]. Artificial heterostructures assembled from van der Waals materials promise to combine materials without traditional restriction in heterostructure-growth such as lattice matching conditions and atom interdiffusion. Simple stacking of van der Waals with diverse properties would thus enable the fabrication of novel materials or device structures with atomically precise interfaces. Because covalent bonding in these layered materials is limited to molecular planes and the interactions between planes are very weak, only small changes in the electronic structure are expected by stacking these materials on top of each other. In the present work the authors prepared interfaces between CVD-grown graphene and MoS₂, and reported the direct measurement of electronic structure of such a van der Waals heterostructure by angle-resolved photoemission spectroscopy. While the Dirac cone of graphene remained intact and no significant charge transfer doping was detected, the authors observed formation of bandgaps in the π-band of graphene away from the Fermi level due to hybridization with states from MoS₂ substrate.

Tunable light–matter interaction and the role of hyperbolicity in graphene/h-BN heterostructure was investigated by Fang et al [113]. In this work the authors examined theoretically the mind-infrared optical properties of graphene/h-BN heterostructures derived from their coupled plasmon–phonon modes. The authors found that the graphene plasmon couples differently with the phonons of two reststrahlen bands, owing to their different hyperbolicity. This also leads to distinctively different interactions between an external quantum emitter and the plasmon–phonon modes in the two bands, leading to substantial modification of its spectrum. The coupling to graphene plasmon allows for additional gate tenability in the Purcel factor and narrow dips in its emission spectra.

In [114] Kim et al carried out electrical and optical characterization of graphene/MoS₂ heterostructures. The few-layer MoS₂ devices with metal electrode at one end and monolayer graphene electrode at the other end showed nonlinearity in drain current with drain voltage sweep due to asymmetrical Schottky barrier height at the contacts and were modulated with an external gate field. The doping effect of MoS₂ on graphene was observed ad double Dirac points in the transfer characteristics of the graphene FET with a few-layer MoS₂ overlapping the middle part of the channel, whereas the underlapping of graphene had negligible effect on MoS₂ FET characteristics, which showed typical n-type behavior. The heterostructure also exhibited a strongest optical response for 520 nm wavelength which decreased with higher wavelengths. Another distinct feature observed in the heterostructure was the peak in the photocurrent around zero gate voltage. Thin peak was distinguished from conventional MoS₂ FET, which showed a continuos increase in photocurrent with black gate voltage. These results offered significant insight and further enhance in the understanding of the graphene/MoS₂ heterostructure.

Quantum transport detected by strong proximity interaction at a graphene/WS₂ van der Waals interface was studied by O'Farrell, Özyilmaz et al [115]. Magneto transport measurements demonstrated that graphene in a van der Waals hetrostructure is a sensitive probe of quantum transport in an adjacent WS₂ layer via strong Coulomb interactions. The authors observed a large low-field magnetoresistance and a −lnT temperature dependence of the resistance. In plane magnetic field resistance indicated that the origin is orbital and non classical. The authors demonstrated a strong electron–hole asymmetry in the mobility and coherence length of graphene demonstrating the presence of localized Coulomb interactions with ionized donors in the WS₂ substrate, which ultimately led to screening as the Fermi level of graphene was tuned toward the conduction band of WS₂. The authors concluded that graphene coupled to quantum localization processes in WS₂ via the Coulomb interaction. These results showed that theoretical descriptions of the van der Waals interface should not ignore localized strong localizations.

In this review we have presented fascinating achievements of basic research and applications of most important THSs beyond grapheme such as phosphorene, silicene and TMDCs MoS₂, MoSe₂, WS₂, WSe₂. We have seen that the basic research on these new materials led to the discovery of a new degree of freedom in the band structure of these materials—the valley degree of freedom, leading to the emergence of a new high technology—the valleytronics. On the basis of van de Waals heterostructures composed of various pairs of THSs many electronic optoelectronic, photonic, plasmonic and valleytronic devices were fabricated.

Thus the contents of the basic as well as applied researches on THSs are indeed very rich and extremely promising. On the basis of above presented scientific results we can now apply the famous statement of Richard Feynmann at Caltech more than a half of century ago and say that 'there is still plenty of room in two dimensions'.

The authors would like to express their deep gratitude to Vietnam Academy of Science and Technology for the support and encouragement.