Ferroelectrics based on van der Waals semiconductors represent an emergent class of materials for disruptive technologies ranging from neuromorphic computing to low-power electronics. However, many theoretical predictions of their electronic properties have yet to be confirmed experimentally and exploited. Here, we use nanoscale angle-resolved photoemission electron spectroscopy and optical transmission in high magnetic fields to reveal the electronic band structure of the van der Waals ferroelectric indium selenide (α-In2Se3). This indirect bandgap semiconductor features a weakly dispersed valence band, which is shaped like an inverted Mexican hat. Its form changes following an irreversible structural phase transition of α-In2Se3 into β-In2Se3 via a thermal annealing in ultra-high vacuum. Density functional theory supports the experiments and reveals the critical contribution of spin orbit coupling to the form of the valence band. The measured band structure and its in situ manipulation offer opportunities for precise engineering of ferroelectrics and their functional properties beyond traditional semiconducting systems.

Abstract Graphene placed on hexagonal boron nitride (hBN) has received significant interest due to its excellent electrical performance and physics phenomena, such as superlattice Dirac points. Direct molecular beam epitaxy growth of graphene on hBN offers an alternative fabrication route for hBN/graphene devices. Here, we investigate the electronic transport of moiré field effect transistors (FETs) in which the conducting channel is monolayer graphene grown on hexagonal boron nitride by high temperature molecular beam epitaxy (HT-MBE). Alignment between hBN and HT-MBE graphene crystal lattices gives rise to a moiré-fringed hexagonal superlattice pattern. Its electronic band structure takes the form of a “Hofstadter butterfly”. When a strong magnetic field B is applied perpendicular to the graphene layer, the electrical conductance displays magneto-oscillations, periodic in B −1, over a wide range of gate voltages and temperatures up to 350 K. We attribute this behaviour to the quantisation of electronic charge and magnetic flux within each unit cell of the superlattice, which gives rise to so-called Brown-Zak oscillations, previously reported only in high-mobility exfoliated graphene. Thus, this HT-MBE graphene/hBN heterostructure provides a platform for observation of room temperature quantum effects and device applications.

Coulomb drag between adjacent electron and hole gases has attracted considerable attention, being studied in various two-dimensional systems, including semiconductor and graphene heterostructures. Here we report measurements of electron-hole drag in the Planckian plasma that develops in monolayer graphene in the vicinity of its Dirac point above liquid-nitrogen temperatures. The frequent electron-hole scattering forces minority carriers to move against the applied electric field due to the drag induced by majority carriers. This unidirectional transport of electrons and holes results in nominally negative mobility for the minority carriers. The electron-hole drag is found to be strongest near room temperature, despite being notably affected by phonon scattering. Our findings provide better understanding of the transport properties of charge-neutral graphene, reveal limits on its hydrodynamic description, and also offer insight into quantum-critical systems in general.

Insights into the fundamental properties of graphene’s Dirac-Weyl fermions have emerged from studies of electron tunnelling transistors in which an atomically thin layer of hexagonal boron nitride (hBN) is sandwiched between two layers of high purity graphene. Here, we show that when a single defect is present within the hBN tunnel barrier, it can inject electrons into the graphene layers and its sharply defined energy level acts as a high resolution spectroscopic probe of electron-electron interactions in graphene. We report a magnetic field dependent suppression of the tunnel current flowing through a single defect below temperatures of ~2 K. This is attributed to the formation of a magnetically-induced Coulomb gap in the spectral density of electrons tunnelling into graphene due to electron-electron interactions.

The quantum Hall effect is widely used for the investigation of fundamental phenomena, ranging from topological phases to composite fermions. In particular, the discovery of a room temperature resistance quantum in graphene is significant for compact resistance standards that can operate above cryogenic temperatures. However, this requires large magnetic fields that are accessible only in a few high magnetic field facilities. Here, we report on the quantum Hall effect in graphene encapsulated by the ferroelectric insulator CuInP 2 S 6 . Electrostatic gating of the graphene channel enables the Fermi energy to be tuned so that electrons in the localized states of the insulator are in equilibrium with the current-carrying, delocalized states of graphene. Due to the presence of strongly bound states in this hybrid system, a quantum Hall plateau is observed over a wide range of temperatures in relatively modest magnetic fields.

We use phenomenological modelling and detailed experimental studies of charge carrier transport to investigate the dependence of the electrical resistivity,ρ, on gate voltage,Vg, for a series of monolayer graphene field effect transistors with mobilities,μ, ranging between 5000 and 250 000 cm2V-1s-1at low-temperature. Our measurements over a wide range of temperatures from 4 to 400 K can be fitted by the universal relationμ=4/eδnmaxfor all devices, whereρmaxis the resistivity maximum at the neutrality point andδnis an 'uncertainty' in the bipolar carrier density, given by the full width at half maximum of the resistivity peak expressed in terms of carrier density,n. This relation is consistent with thermal broadening of the carrier distribution and the presence of the disordered potential landscape consisting of so-called electron-hole puddles near the Dirac point. To demonstrate its utility, we combine this relation with temperature-dependent linearised Boltzmann transport calculations that include the effect of optical phonon scattering. This approach demonstrates the similarity in the temperature-dependent behaviour of carriers in different types of single layer graphene transistors with widely differing carrier mobilities. It can also account for the relative stability, over a wide temperature range, of the measured carrier mobility of each device.

The quantum Hall effect is widely used for the investigation of fundamental phenomena, ranging from topological phases to composite fermions. In particular, the discovery of a room temperature resistance quantum in graphene is significant for compact resistance standards that can operate above cryogenic temperatures. However, this requires large magnetic fields that are accessible only in a few high magnetic field facilities. Here, we report on the quantum Hall effect in graphene encapsulated by the ferroelectric insulator CuInP2S6. Electrostatic gating of the graphene channel enables the Fermi energy to be tuned so that electrons in the localized states of the insulator are in equilibrium with the current-carrying, delocalized states of graphene. Due to the presence of strongly bound states in this hybrid system, a quantum Hall plateau can be achieved at room temperature in relatively modest magnetic fields. This phenomenon offers the prospect for the controlled manipulation of the quantum Hall effect at room temperature.

The light-matter interaction in bulk semiconductors is in the strong-coupling regime with hybrid eigenstates, the so-called exciton polaritons and phonon polaritons. In two-dimensional (2D) systems, the translational invariance is broken in the direction perpendicular to the plane of the 2D system. The light-matter interaction switches to the weak-coupling regime with a finite radiative lifetime of the matter excitations in 2D. Radiative phenomena have been extensively studied for 2D excitons in quantum wells and 2D crystals, but their counterpart has never been addressed for optical phonons in 2D. Here we present a parallel study of the exciton and phonon radiative linewidths in atomically thin layers of hexagonal boron nitride (h-BN), epitaxially grown on graphite. Reflectivity experiments are performed either in the deep ultraviolet for the excitonic resonance or in the midinfrared for the phononic one. A quantitative interpretation is implemented in the framework of a transfer matrix approach generalized to the case of monolayers with the inclusion of Breit-Wigner resonances of either excitonic or phononic nature. For the exciton we find a giant radiative broadening in comparison to other 2D crystals, with a value of similar to 25 meV related to the strong excitonic effects in h-BN. For the phonon we provide the first estimation of the radiative linewidth of a 2D phonon, with a value of similar to 0.2 meV in monolayer h-BN. Our results are found to be in good agreement with first-principles calculations. Our study unravels the existence of radiative states for optical phonons in 2D, with numerous perspectives for fundamental physics, optoelectronic applications in the midinfrared spectral range, and advanced thermal management, and h-BN is emerging as a model system in this novel topic.

Monolayers of hexagonal boron nitride (hBN) are grown on graphite substrates using high-temperature molecular beam epitaxy (HT-MBE). The hBN monolayers are observed to grow predominantly from step edges on the graphite surface and exhibit a strong dependence of the morphology, including the dominant crystallographic edge, of the hBN monolayers, on the growth temperature, as well as systematic variations in growth rate and coverage, and significant differences in the growth at monolayer and multilayer graphite steps. At graphite monolayer steps hBN grows laterally across the surface on the lower terrace, but hBN growth on the upper side of the graphite step is more limited and is nucleated by three-dimensional clusters. Multilayer graphite steps exhibit a much higher density of non-planar hBN aggregates and growth on both the upper and lower terraces occurs. The results show that the hBN monolayer growth edge type, hBN island shape and the presence of hBN aggregates can be controlled in HT-MBE, with the highest quality layers grown at a substrate temperature of about 1390 °C. Sequential HT-MBE growth of hBN, graphene (G) and a second cycle of hBN growth results in the formation of monolayer thick lateral hBN–G–hBN heterostructures, in which a strip of G is embedded between monolayers of hBN.

Oscillatory magnetoresistance measurements on graphene have revealed a wealth of novel physics. These phenomena are typically studied at low currents. At high currents, electrons are driven far from equilibrium with the atomic lattice vibrations so that their kinetic energy can exceed the thermal energy of the phonons. Here, we report three non-equilibrium phenomena in monolayer graphene at high currents: (i) a “Doppler-like” shift and splitting of the frequencies of the transverse acoustic (TA) phonons emitted when the electrons undergo inter -Landau level (LL) transitions; (ii) an intra -LL Mach effect with the emission of TA phonons when the electrons approach supersonic speed, and (iii) the onset of elastic inter-LL transitions at a critical carrier drift velocity, analogous to the superfluid Landau velocity. All three quantum phenomena can be unified in a single resonance equation. They offer avenues for research on out-of-equilibrium phenomena in other two-dimensional fermion systems.

The ${\mathrm{SnSe}}_{2(1\ensuremath{-}x)}{\mathrm{S}}_{2x}$ alloy is a van der Waals semiconductor with versatile, tunable electronic properties and prospects for future applications ranging from electronics to thermoelectrics and superconductivity. Its band structure and carrier effective masses underlie the quantum behavior of charge carriers and hold great promise in future technologies. However, experimental measurement of these properties remains a challenging task. Here magnetotransmission spectroscopy of ${\mathrm{SnSe}}_{2(1\ensuremath{-}x)}{\mathrm{S}}_{2x}$ thin films at pulsed magnetic fields $B$ of up to 150 T reveals a large electron-hole reduced cyclotron mass ${\ensuremath{\mu}}^{*}g$ 0.454 ${m}_{e}$ (${m}_{e}$ is the free electron mass). This finding is supported by first-principle calculations of the band structure and by semiclassical Boltzmann transport theory, which predict a pronounced anisotropy of the carrier effective masses and electrical conductivity over two orthogonal directions (namely in the layer plane and out-of-plane) with a different anisotropy for electrons and holes. These properties are unique and important features of this class of compounds and are critical for understanding and using the tunable band structure of ${\mathrm{SnSe}}_{2(1\ensuremath{-}x)}{\mathrm{S}}_{2x}$ in fundamental and applied research.

The design of advanced functional materials with customized properties often requires the use of an alloy. This approach has been used for decades, but only recently to create van der Waals (vdW) alloys for applications in electronics, optoelectronics, and thermoelectrics. A route to engineering their physical properties is by mixing isoelectronic elements, as done for the SnSe 2(1− x ) S 2 x alloy. Here, by experiment and first‐principles modeling, it is shown that the value of x can be adjusted over a wide range, indicating good miscibility of the SnS 2 and SnSe 2 compounds. The x ‐dependence of the indirect bandgap energy from E ind = 1.20 eV for SnSe 2 to E ind = 2.14 eV for SnS 2 , corresponds to a large bowing coefficient b ≈ 1 eV, arising from volume deformation and charge exchange effects due to the different sizes and orbital energies of the S‐ and Se‐atoms. This also causes composition‐dependent phonon energy modes, electron–phonon interaction, and temperature dependence of E ind . The alloys are exfoliable into thin layers with properties that depend on the composition, but only weakly on the layer thickness. This work shows that the electronic and vibrational properties of the SnSe 2(1− x ) S 2 x alloy and its thin layers provide a versatile platform for development and exploitation.

Two-dimensional (2D) van der Waals (vdW) crystals have attracted considerable interest for digital electronics beyond Si-based complementary metal oxide semiconductor technologies. Despite the transformative success of Si-based devices, there are limits to their miniaturization and functionalities. Here we realize a resonant tunnelling transistor (RTT) based on a 2D InSe layer sandwiched between two multilayered graphene (MLG) electrodes. In the RTT the energy of the quantum-confined 2D subbands of InSe can be tuned by the thickness of the InSe layer. By applying a voltage across the two MLG electrodes, which serve as the source and drain electrodes to the InSe, the chemical potential in the source can be tuned in and out of resonance with a given 2D subband, leading to multiple regions of negative differential conductance that can be additionally tuned by electrostatic gating. This work demonstrates the potential of InSe and InSe-based RTTs for applications in quantum electronics.

Integration of graphene and hexagonal boron nitride (hBN) into lateral heterostructures has drawn focus due to the ability to broadly engineer the material properties. Hybrid monolayers with tuneable bandgaps have been reported, while the interface itself possesses unique electronic and magnetic qualities. Herein, we demonstrate lateral heteroepitaxial growth of graphene and hBN by sequential growth using high-temperature molecular beam epitaxy (MBE) on highly oriented pyrolytic graphite (HOPG). We find, using scanning probe microscopy, that graphene growth nucleates at hBN step edges and grows across the surface to form nanoribbons with a controlled width that is highly uniform across the surface. The graphene nanoribbons grow conformally from the armchair edges of hexagonal hBN islands forming multiply connected regions with the growth front alternating from armchair to zigzag in regions nucleated close to the vertices of hexagonal hBN islands. Images with lattice resolution confirm a lateral epitaxial alignment between the hBN and graphene nanoribbons, while the presence of a moire pattern within the ribbons indicates that some strain relief occurs at the lateral heterojunction. These results demonstrate that high temperature MBE is a viable route towards integrating graphene and hBN in lateral heterostructures.

Recent progress in the synthesis of high stability inorganic perovskite nanocrystals (NCs) has led to their increasing use in broadband photodetectors. These NCs are of particular interest for the UV range as they have the potential to extend the wavelength range of photodetectors based on traditional materials. Here we demonstrate a defect-assisted high photoconductive gain in graphene transistors decorated with all-inorganic cesium lead halide perovskite NCs. The photoconductive gain in the UV-vis wavelength range arises from the charge transfer between the NCs and graphene and enables observation of high photoconductive gain of 10(6) A/W. This is accompanied by a giant hysteresis of the graphene resistance that is strongly dependent on electrostatic gating and temperature. Our data are well described by a phenomenological macroscopic model of the charge transfer from bound states in the NCs into the graphene layer, providing a useful tool for the design of high-photoresponsivity perovskite/graphene transistors.

Hexagonal boron nitride is a large band-gap insulating material which complements the electronic and optical properties of graphene and the transition metal dichalcogenides. However, the intrinsic optical properties of monolayer boron nitride remain largely unexplored. In particular, the theoretically expected crossover to a direct-gap in the limit of the single monolayer is presently not confirmed experimentally. Here, in contrast to the technique of exfoliating few-layer 2D hexagonal boron nitride, we exploit the scalable approach of high-temperature molecular beam epitaxy to grow high-quality monolayer boron nitride on graphite substrates. We combine deep-ultraviolet photoluminescence and reflectance spectroscopy with atomic force microscopy to reveal the presence of a direct gap of energy 6.1 eV in the single atomic layers, thus confirming a crossover to direct gap in the monolayer limit.

Van der Waals materials and their heterostructures offer a versatile platform for studying a variety of quantum transport phenomena due to their unique crystalline properties and the exceptional ability in tuning their electronic spectrum. However, most experiments are limited to devices that have lateral dimensions of only a few micrometres. Here, we perform magnetotransport measurements on graphene/hexagonal boron-nitride Hall bars and show that wider devices reveal additional quantum effects. In devices wider than ten micrometres we observe distinct magnetoresistance oscillations that are caused by resonant scattering of Landau-quantised Dirac electrons by acoustic phonons in graphene. The study allows us to accurately determine graphene’s low energy phonon dispersion curves and shows that transverse acoustic modes cause most of phonon scattering. Our work highlights the crucial importance of device width when probing quantum effects and also demonstrates a precise, spectroscopic method for studying electron-phonon interactions in van der Waals heterostructures.

Recently observed magnetophonon resonances in the magnetoresistance of graphene are investigated using the Kubo formalism. This analysis provides a quantitative fit to the experimental data over a wide range of carrier densities. It demonstrates the predominance of carrier scattering by low energy transverse acoustic (TA) mode phonons: the magnetophonon resonance amplitude is significantly stronger for the TA modes than for the longitudinal acoustic (LA) modes. We demonstrate that the LA and TA phonon speeds and the electron-phonon coupling strengths determined from the magnetophonon resonance measurements also provide an excellent fit to the measured dependence of the resistivity at zero magnetic field over a temperature range of 4-150 K. A semiclassical description of magnetophonon resonance in graphene is shown to provide a simple physical explanation for the dependence of the magneto-oscillation period on carrier density. The correspondence between the quantum calculation and the semiclassical model is discussed.

In this work we present our recent results on the high-temperature plasma-assisted molecular beam epitaxy (PA-MBE) of hBN monolayers with atomically controlled thicknesses for 2D applications and on the growth of significantly thicker hBN layers for potential DUV applications. We also report our recent results on the high-temperature PA-MBE growth of hBN layers using a high-efficiency RF plasma source with high active nitrogen fluxes. Our results demonstrate that PA-MBE growth on highly oriented pyrolytic graphite (HOPG) substrates at temperatures ~1390°C can achieve mono- and few-layer thick hBN with a control of the hBN coverage and atomically flat hBN surfaces which is essential for 2D applications of hBN layers. The hBN monolayer coverage can be reproducible controlled by the PA-MBE growth temperature, time and B:N flux ratios. Significantly thicker hBN layers have been achieved at higher B:N flux ratios. We observed a gradual increase of the hBN thickness by decreasing the growth temperature from 1390°C to 1080°C. However, by decreasing the MBE growth temperature below 1250°C, we observe a rapid degradation of the optical properties of hBN layers. Therefore, high-temperature PA-MBE, above 1250°C, is a viable approach for the growth of high-quality hBN layers for 2D and DUV applications.

The transfer of electronic charge across the interface of two van der Waals crystals can underpin the operation of a new class of functional devices. Among van der Waals semiconductors, an exciting and rapidly growing development involves the “post‐transition” metal chalcogenide InSe. Here, field effect phototransistors are reported where single layer graphene is capped with n‐type InSe. These device structures combine the photosensitivity of InSe with the unique electrical properties of graphene. It is shown that the light‐induced transfer of charge between InSe and graphene offers an effective method to increase or decrease the carrier density in graphene, causing a change in its resistance that is gate‐controllable and only weakly dependent on temperature. The charge transfer at the InSe/graphene interface is probed by Hall effect and photoconductivity measurmentes and it is demonstrated that light can induce a sign reversal of the quantum Hall voltage and photovoltaic effects in the graphene layer. These findings demonstrate the potential of light‐induced charge transfer in gate‐tunable InSe/graphene phototransistors for optoelectronics and quantum metrology.