Interactions and Magnetotransport through Spin-Valley Coupled Landau Levels in Monolayer MoS_{2}

Even-integer quantum Hall effect in an oxide caused by a hidden Rashba effect

In the presence of a high magnetic field, quantum Hall systems usually host both even- and odd-integer quantized states because of lifted band degeneracies. Selective control of these quantized states is challenging but essential to understand the exotic ground states and manipulate the spin textures. Here we demonstrate the quantum Hall effect in Bi2O2Se thin films. In magnetic fields as high as 50 T, we observe only even-integer quantum Hall states, but there is no sign of odd-integer states. However, when reducing the thickness of the epitaxial Bi2O2Se film to one unit cell, we observe both odd- and even-integer states in this Janus (asymmetric) film grown on SrTiO3. By means of a Rashba bilayer model based on the ab initio band structures of Bi2O2Se thin films, we can ascribe the only even-integer states in thicker films to the hidden Rasbha effect, where the local inversion-symmetry breaking in two sectors of the [Bi2O2]2+ layer yields opposite Rashba spin polarizations, which compensate with each other. In the one-unit-cell Bi2O2Se film grown on SrTiO3, the asymmetry introduced by the top surface and bottom interface induces a net polar field. The resulting global Rashba effect lifts the band degeneracies present in the symmetric case of thicker films.

Exchange Energy of the Ferromagnetic Electronic Ground State in a Monolayer Semiconductor

Mobile electrons in the semiconductor monolayer MoS_{2} form a ferromagnetic state at low temperature. The Fermi sea consists of two circles: one at the K point, the other at the K[over ˜] point, both with the same spin. Here, we present an optical experiment on gated MoS_{2} at low electron density in which excitons are injected with known spin and valley quantum numbers. The resulting trions are identified using a model which accounts for the injection process, the formation of antisymmetrized trion states, electron-hole scattering from one valley to the other, and recombination. The results are consistent with a complete spin polarization. From the splittings between different trion states, we measure the exchange energy Σ, the energy required to flip a single spin within the ferromagnetic state, as well as the intervalley Coulomb exchange energy J. We determine Σ=11.2  meV and J=5  meV at n=1.5×10^{12}  cm^{-2} and find that J depends strongly on the electron density n.

Transport Study of Charge-Carrier Scattering in Monolayer WSe_{2}

Employing flux-grown single crystal WSe_{2}, we report charge-carrier scattering behaviors measured in h-BN encapsulated monolayer field effect transistors. We observe a nonmonotonic change of transport mobility as a function of hole density in the degenerately doped sample, which can be explained by energy dependent scattering amplitude of strong defects calculated using the T-matrix approximation. Utilizing long mean-free path (>500  nm), we also demonstrate the high quality of our electronic devices by showing quantized conductance steps from an electrostatically defined quantum point contact, showing the potential for creating ultrahigh quality quantum optoelectronic devices based on atomically thin semiconductors.

Pressure tuning of minibands in MoS2/WSe2 heterostructures revealed by moiré phonons

Moiré superlattices of two-dimensional heterostructures arose as a new platform to investigate emergent behaviour in quantum solids with unprecedented tunability. To glean insights into the physics of these systems, it is paramount to discover new probes of the moiré potential and moiré minibands, as well as their dependence on external tuning parameters. Hydrostatic pressure is a powerful control parameter, since it allows to continuously and reversibly enhance the moiré potential. Here we use high pressure to tune the minibands in a rotationally aligned MoS2/WSe2 moiré heterostructure, and show that their evolution can be probed via moiré phonons. The latter are Raman-inactive phonons from the individual layers that are activated by the moiré potential. Moiré phonons manifest themselves as satellite Raman peaks arising exclusively from the heterostructure region, increasing in intensity and frequency under applied pressure. Further theoretical analysis reveals that their scattering rate is directly connected to the moiré potential strength. By comparing the experimental and calculated pressure-induced enhancement, we obtain numerical estimates for the moiré potential amplitude and its pressure dependence. The present work establishes moiré phonons as a sensitive probe of the moiré potential as well as the electronic structures of moiré systems.

Non-Destructive Low-Temperature Contacts to MoS2 Nanoribbon and Nanotube Quantum Dots

Molybdenum disulfide nanoribbons and nanotubes are quasi-1D semiconductors with strong spin-orbit interaction, a nanomaterial highly promising for quantum electronic applications. Here, it is demonstrated that a bismuth semimetal layer between the contact metal and this nanomaterial strongly improves the properties of the contacts. Two-point resistances on the order of 100 kΩ are observed at room temperature. At cryogenic temperature, Coulomb blockade is visible. The resulting stability diagrams indicate a marked absence of trap states at the contacts and the corresponding disorder, compared to previous devices that use low-work-function metals as contacts. Single-level quantum transport is observed at temperatures below 100 mK.

Mechanical Detection of the De Haas-van Alphen Effect in Graphene

In our work, we study the dynamics of a graphene Corbino disk supported by a gold mechanical resonator in the presence of a magnetic field. We demonstrate here that our graphene/gold mechanical structure exhibits a nontrivial resonance frequency dependence on the applied magnetic field, showing how this feature is indicative of the de Haas-van Alphen effect in the graphene Corbino disk. Relying on the mechanical resonances of the Au structure, our detection scheme is essentially independent of the material considered and can be applied for dHvA measurements on any conducting 2D material. In particular, the scheme is expected to be an important tool in studies of centrosymmetric transition metal dichalcogenide (TMD) crystals, shedding new light on hidden magnetization and interaction effects.

Effective Low-Energy Hamiltonians and Unconventional Landau-Level Spectrum of Monolayer C3N

We derive low-energy effective k·p Hamiltonians for monolayer C3N at the Γ and M points of the Brillouin zone, where the band edge in the conduction and valence band can be found. Our analysis of the electronic band symmetries helps to better understand several results of recent ab initio calculations for the optical properties of this material. We also calculate the Landau-level spectrum. We find that the Landau-level spectrum in the degenerate conduction bands at the Γ point acquires properties that are reminiscent of the corresponding results in bilayer graphene, but there are important differences as well. Moreover, because of the heavy effective mass, n-doped samples may host interesting electron-electron interaction effects.

Optical Detection of Long Electron Spin Transport Lengths in a Monolayer Semiconductor

Using a spatially resolved optical pump-probe experiment, we measure the lateral transport of spin-valley polarized electrons over very long distances (tens of micrometers) in a single WSe_{2} monolayer. By locally pumping the Fermi sea of 2D electrons to a high degree of spin-valley polarization (up to 75%) using circularly polarized light, the lateral diffusion of the electron polarization can be mapped out via the photoluminescence induced by a spatially separated and linearly polarized probe laser. Up to 25% spin-valley polarization is observed at pump-probe separations up to 20  μm. Characteristic spin-valley diffusion lengths of 18±3  μm are revealed at low temperatures. The dependence on temperature, pump helicity, pump intensity, and electron density highlight the key roles played by spin relaxation time and pumping efficiency on polarized electron transport in monolayer semiconductors possessing spin-valley locking.

Benchmarking Noise and Dephasing in Emerging Electrical Materials for Quantum Technologies

As quantum technologies develop, a specific class of electrically conducting materials is rapidly gaining interest because they not only form the core quantum-enabled elements in superconducting qubits, semiconductor nanostructures, or sensing devices, but also the peripheral circuitry. The phase coherence of the electronic wave function in these emerging materials will be crucial when incorporated in the quantum architecture. The loss of phase memory, or dephasing, occurs when a quantum system interacts with the fluctuations in the local electromagnetic environment, which manifests in "noise" in the electrical conductivity. Hence, characterizing these materials and devices therefrom, for quantum applications, requires evaluation of both dephasing and noise, although there are very few materials where these properties are investigated simultaneously. Here, the available data on magnetotransport and low-frequency fluctuations in electrical conductivity are reviewed to benchmark the dephasing and noise. The focus is on new materials that are of direct interest to quantum technologies. The physical processes causing dephasing and noise in these systems are elaborated, the impact of both intrinsic and extrinsic parameters from materials synthesis and devices realization are evaluated, and it is hoped that a clearer pathway to design and characterize both material and devices for quantum applications is thus provided.

The Low-Temperature Photocurrent Spectrum of Monolayer MoSe2: Excitonic Features and Gate Voltage Dependence

Two-dimensional transition metal dichalcogenides (2D-TMDs) are among the most promising materials for exploring and exploiting exciton transitions. Excitons in 2D-TMDs present remarkably long lifetimes, even at room temperature. The spectral response of exciton transitions in 2D-TMDs has been thoroughly characterized over the past decade by means of photoluminescence spectroscopy, transmittance spectroscopy, and related techniques; however, the spectral dependence of their electronic response is still not fully characterized. In this work, we investigate the electronic response of exciton transitions in monolayer MoSe2 via low-temperature photocurrent spectroscopy. We identify the spectral features associated with the main exciton and trion transitions, with spectral bandwidths down to 15 meV. We also investigate the effect of the Fermi level on the position and intensity of excitonic spectral features, observing a very strong modulation of the photocurrent, which even undergoes a change in sign when the Fermi level crosses the charge neutrality point. Our results demonstrate the unexploited potential of low-temperature photocurrent spectroscopy for studying excitons in low-dimensional materials, and provide new insight into excitonic transitions in 1L-MoSe2.

Signature of Spin-Resolved Quantum Point Contact in p-Type Trilayer WSe2 van der Waals Heterostructure

In this study, an electrostatically induced quantum confinement structure, so-called quantum point contact, has been realized in a p-type trilayer tungsten diselenide-based van der Waals heterostructure with modified van der Waals contact method with degenerately doped transition metal dichalcogenide crystals. Clear quantized conductance and pinch-off state through the one-dimensional confinement were observed by dual-gating of split gate electrodes and top gate. Conductance plateaus were observed at a step of e²/h in addition to quarter plateaus such as 0.25 × 2e²/h at a finite bias voltage condition indicating the signature of intrinsic spin-polarized quantum point contact.

Time-resolved ARPES Determination of a Quasi-Particle Band Gap and Hot Electron Dynamics in Monolayer MoS2

The electronic structure and dynamics of 2D transition metal dichalcogenide (TMD) monolayers provide important underpinnings both for understanding the many-body physics of electronic quasi-particles and for applications in advanced optoelectronic devices. However, extensive experimental investigations of semiconducting monolayer TMDs have yielded inconsistent results for a key parameter, the quasi-particle band gap (QBG), even for measurements carried out on the same layer and substrate combination. Here, we employ sensitive time- and angle-resolved photoelectron spectroscopy (trARPES) for a high-quality large-area MoS₂ monolayer to capture its momentum-resolved equilibrium and excited-state electronic structure in the weak-excitation limit. For monolayer MoS₂ on graphite, we obtain QBG values of ≈2.10 eV at 80 K and of ≈2.03 eV at 300 K, results well-corroborated by the scanning tunneling spectroscopy (STS) measurements on the same material.

Effect of the strain on spin-valley transport properties in MoS2 superlattice

The effect of the strain on the spin and valley dependent transport properties, including the conductance and polarization, through a monolayer MoS2 superlattice under Rashba spin-orbit coupling is theoretically investigated. It is found that the conductance strongly depends on the spin and valley degrees of freedom, and spin-inversion can be achieved by MoS2 superlattice. Also, the spin and valley dependent conductance in a monolayer MoS2 superlattice can be efficiently adjusted via strain and the number of the superlattice barriers. Moreover, it is demonstrated that both the magnitude and sign of the spin and valley polarization depend on the strain strength, the number of barriers, and electrostatic barrier height. Both full spin and valley polarized current (with 100% or - 100% efficiency) can be realized in a MoS2 superlattice under strain.

Superconducting Contacts to a Monolayer Semiconductor

We demonstrate superconducting vertical interconnect access (VIA) contacts to a monolayer of molybdenum disulfide (MoS2), a layered semiconductor with highly relevant electronic and optical properties. As a contact material we use MoRe, a superconductor with a high critical magnetic field and high critical temperature. The electron transport is mostly dominated by a single superconductor/normal conductor junction with a clear superconductor gap. In addition, we find MoS2 regions that are strongly coupled to the superconductor, resulting in resonant Andreev tunneling and junction-dependent gap characteristics, suggesting a superconducting proximity effect. Magnetoresistance measurements show that the bandstructure and the high intrinsic carrier mobility remain intact in the bulk of the MoS2. This type of VIA contact is applicable to a large variety of layered materials and superconducting contacts, opening up a path to monolayer semiconductors as a platform for superconducting hybrid devices.

Rashba valleys and quantum Hall states in few-layer black arsenic

Exciting phenomena may emerge in non-centrosymmetric two-dimensional electronic systems when spin-orbit coupling (SOC)¹ interplays dynamically with Coulomb interactions^2,3, band topology^4,5 and external modulating forces^6-8. Here we report synergetic effects between SOC and the Stark effect in centrosymmetric few-layer black arsenic, which manifest as particle-hole asymmetric Rashba valley formation and exotic quantum Hall states that are reversibly controlled by electrostatic gating. The unusual findings are rooted in the puckering square lattice of black arsenic, in which heavy 4p orbitals form a Brillouin zone-centred Γ valley with p_z symmetry, coexisting with doubly degenerate D valleys of p_x origin near the time-reversal-invariant momenta of the X points. When a perpendicular electric field breaks the structure inversion symmetry, strong Rashba SOC is activated for the p_x bands, which produces spin-valley-flavoured D^± valleys paired by time-reversal symmetry, whereas Rashba splitting of the Γ valley is constrained by the p_z symmetry. Intriguingly, the giant Stark effect shows the same p_x-orbital selectiveness, collectively shifting the valence band maximum of the D^± Rashba valleys to exceed the Γ Rashba top. Such an orchestrating effect allows us to realize gate-tunable Rashba valley manipulations for two-dimensional hole gases, hallmarked by unconventional even-to-odd transitions in quantum Hall states due to the formation of a flavour-dependent Landau level spectrum. For two-dimensional electron gases, the quantization of the Γ Rashba valley is characterized by peculiar density-dependent transitions in the band topology from trivial parabolic pockets to helical Dirac fermions.

Optical properties of excitons in two-dimensional transition metal dichalcogenide nanobubbles

Strain in two-dimensional transition metal dichalcogenide has led to localized states with exciting optical properties, in particular, in view of designing one photon sources. The naturally formed nanobubbles when the MoS₂ monolayer is deposited on an hBN substrate lead to a local reduction in the band gap due to strain developing in the nanobubble. The photogenerated particles are thus confined in the strain-induced potential. Using numerical diagonalization, we simulate the spectra of the confined exciton states, their oscillator strengths, and their radiative lifetimes. We show that a single state of the confined exciton is optically active, which suggests that the MoS₂/hBN nanobubbles are a good candidate for the realization of single-photon sources. Furthermore, our calculations show that the localized exciton gains in activation energy and radiative lifetime inside the nanobubble, the latter decreasing toward the one of free excitons when the nanobubble size increases.

Measurement of Conduction and Valence Bands g-Factors in a Transition Metal Dichalcogenide Monolayer

The electron valley and spin degree of freedom in monolayer transition-metal dichalcogenides can be manipulated in optical and transport measurements performed in magnetic fields. The key parameter for determining the Zeeman splitting, namely, the separate contribution of the electron and hole g factor, is inaccessible in most measurements. Here we present an original method that gives access to the respective contribution of the conduction and valence band to the measured Zeeman splitting. It exploits the optical selection rules of exciton complexes, in particular the ones involving intervalley phonons, avoiding strong renormalization effects that compromise single particle g-factor determination in transport experiments. These studies yield a direct determination of single band g factors. We measure g_{c1}=0.86±0.1, g_{c2}=3.84±0.1 for the bottom (top) conduction bands and g_{v}=6.1±0.1 for the valence band of monolayer WSe_{2}. These measurements are helpful for quantitative interpretation of optical and transport measurements performed in magnetic fields. In addition, the measured g factors are valuable input parameters for optimizing band structure calculations of these 2D materials.

Probing negatively charged and neutral excitons in MoS2/hBN and hBN/MoS2/hBN van der Waals heterostructures

High-quality van der Waals heterostructures assembled from hBN-encapsulated monolayer transition metal dichalcogenides enable observations of subtle optical and spin-valley properties whose identification was beyond the reach of structures exfoliated directly on standard SiO2/Si substrates. Here, we describe different van der Waals heterostructures based on uncapped single-layer MoS2 stacked onto hBN layers of different thicknesses and hBN-encapsulated monolayers. Depending on the doping level, they reveal the fine structure of excitonic complexes, i.e. neutral and charged excitons. In the emission spectra of a particular MoS2/hBN heterostructure without an hBN cap we resolve two trion peaks, T1 and T2, energetically split by about 10 meV, resembling the pair of singlet and triplet trion peaks (T S and T T ) in tungsten-based materials. The existence of these trion features suggests that monolayer MoS2 has a dark excitonic ground state, despite having a 'bright' single-particle arrangement of spin-polarized conduction bands. In addition, we show that the effective excitonic g-factor significantly depends on the electron concentration and reaches the lowest value of -2.47 for hBN-encapsulated structures, which reveals a nearly neutral doping regime. In the uncapped MoS2 structures, the excitonic g-factor varies from -1.15 to -1.39 depending on the thickness of the bottom hBN layer and decreases as a function of rising temperature.

Spontaneous Valley Polarization of Interacting Carriers in a Monolayer Semiconductor

We report magnetoabsorption spectroscopy of gated WSe_{2} monolayers in high magnetic fields up to 60 T. When doped with a 2D Fermi sea of mobile holes, well-resolved sequences of optical transitions are observed in both σ^{±} circular polarizations, which unambiguously and separately indicate the number of filled Landau levels (LLs) in both K and K^{'} valleys. This reveals the interaction-enhanced valley Zeeman energy, which is found to be highly tunable with hole density p. We exploit this tunability to align the LLs in K and K^{'}, and find that the 2D hole gas becomes unstable against small changes in LL filling and can spontaneously valley polarize. These results cannot be understood within a single-particle picture, highlighting the importance of exchange interactions in determining the ground state of 2D carriers in monolayer semiconductors.

Measurement of the spin-forbidden dark excitons in MoS2 and MoSe2 monolayers

Excitons with binding energies of a few hundreds of meV control the optical properties of transition metal dichalcogenide monolayers. Knowledge of the fine structure of these excitons is therefore essential to understand the optoelectronic properties of these 2D materials. Here we measure the exciton fine structure of MoS2 and MoSe2 monolayers encapsulated in boron nitride by magneto-photoluminescence spectroscopy in magnetic fields up to 30 T. The experiments performed in transverse magnetic field reveal a brightening of the spin-forbidden dark excitons in MoS2 monolayer: we find that the dark excitons appear at 14 meV below the bright ones. Measurements performed in tilted magnetic field provide a conceivable description of the neutral exciton fine structure. The experimental results are in agreement with a model taking into account the effect of the exchange interaction on both the bright and dark exciton states as well as the interaction with the magnetic field.

Quantum Hall effect of Weyl fermions in n-type semiconducting tellurene

Dirac and Weyl nodal materials can host low-energy relativistic quasiparticles. Under strong magnetic fields, the topological properties of Dirac/Weyl materials can directly be observed through quantum Hall states. However, most Dirac/Weyl nodes generically exist in semimetals without exploitable band gaps due to their accidental band-crossing origin. Here, we report the first experimental observation of Weyl fermions in a semiconductor. Tellurene, the two-dimensional form of tellurium, possesses a chiral crystal structure which induces unconventional Weyl nodes with a hedgehog-like radial spin texture near the conduction band edge. We synthesize high-quality n-type tellurene by a hydrothermal method with subsequent dielectric doping and detect a topologically non-trivial π Berry phase in quantum Hall sequences. Our work expands the spectrum of Weyl matter into semiconductors and offers a new platform to design novel quantum devices by marrying the advantages of topological materials to versatile semiconductors.

Odd- and even-denominator fractional quantum Hall states in monolayer WSe2

Monolayer semiconducting transition-metal dichalcogenides (TMDs) represent a unique class of two-dimensional (2D) electron systems. Their atomically thin structure facilitates gate tunability just like graphene does, but unlike graphene, TMDs have the advantage of a sizable band gap and strong spin-orbit coupling. Measurements under large magnetic fields have revealed an unusual Landau level (LL) structure^1-3, distinct from other 2D electron systems. However, owing to the limited sample quality and poor electrical contact, probing the lowest LLs has been challenging, and observation of electron correlations within the fractionally filled LL regime has not been possible. Here, through bulk electronic compressibility measurements, we investigate the LL structure of monolayer WSe₂ in the extreme quantum limit, and observe fractional quantum Hall states in the lowest three LLs. The odd-denominator fractional quantum Hall sequences demonstrate a systematic evolution with the LL orbital index, consistent with generic theoretical expectations. In addition, we observe an even-denominator state in the second LL that is expected to host non-Abelian statistics. Our results suggest that the 2D semiconductors can provide an experimental platform that closely resembles idealized theoretical models in the quantum Hall regime.

Scanning gate microscopy mapping of edge current and branched electron flow in a transition metal dichalcogenide nanoribbon and quantum point contact

We study scanning gate microscopy conductance mapping of a [Formula: see text] zigzag ribbon exploiting tight-binding and continuum models. We show that, even though the edge modes of a pristine nanoribbon are robust to backscattering on the potential induced by the tip, the conductance mapping reveals presence of both the edge modes and the quantized spin- and valley-current carrying modes. By inspecting the electron flow from a split gate quantum point contact (QPC) we find that the mapped current flow allows to determine the nature of the quantization in the QPC as spin-orbit coupling strength affects the number of branches in which the current exits the constriction. The radial conductance oscillation fringes found in the conductance mapping reveal the presence of two possible wavevectors for the charge carriers that correspond to spin and valley opposite modes. Finally, we show that disorder induced valley mixing leads to a beating pattern in the radial fringes.

First-Order Magnetic Phase Transition of Mobile Electrons in Monolayer MoS_{2}

Evidence is presented for a first-order magnetic phase transition in a gated two-dimensional semiconductor, monolayer-MoS_{2}. The phase boundary separates a ferromagnetic phase at low electron density and a paramagnetic phase at high electron density. Abrupt changes in the optical response signal an abrupt change in the magnetism. The magnetic order is thereby controlled via the voltage applied to the gate electrode of the device. Accompanying the change in magnetism is a large change in the electron effective mass.

Interface engineering of two-dimensional transition metal dichalcogenides towards next-generation electronic devices: recent advances and challenges

Over the past decade, two-dimensional (2D) transition metal dichalcogenides (TMDCs) have attracted tremendous research interest for future electronics owing to their atomically thin thickness, compelling properties and various potential applications. However, interface engineering including contact optimization and channel modulations for 2D TMDCs represents fundamental challenges in ultimate performance of ultrathin electronics. This article provides a comprehensive overview of the basic understanding of contacts and channel engineering of 2D TMDCs and emerging electronics benefiting from these varying approaches. In particular, we elucidate multifarious contact engineering approaches such as edge contact, phase engineering and metal transfer to suppress the Fermi level pinning effect at the metal/TMDC interface, various channel treatment avenues such as van der Waals heterostructures, surface charge transfer doping to modulate the device properties, and as well the novel electronics constructed by interface engineering such as diodes, circuits and memories. Finally, we conclude this review by addressing the current challenges facing 2D TMDCs towards next-generation electronics and offering our insights into future directions of this field.

Landau-Quantized Excitonic Absorption and Luminescence in a Monolayer Valley Semiconductor

We investigate Landau-quantized excitonic absorption and luminescence of monolayer WSe_{2} under magnetic field. We observe gate-dependent quantum oscillations in the bright exciton and trions (or exciton polarons) as well as the dark trions and their phonon replicas. Our results reveal spin- and valley-polarized Landau levels (LLs) with filling factors n=+0, +1 in the bottom conduction band and n=-0 to -6 in the top valence band, including the Berry-curvature-induced n=±0 LLs of massive Dirac fermions. The LL filling produces periodic plateaus in the exciton energy shift accompanied by sharp oscillations in the exciton absorption width and magnitude. This peculiar exciton behavior can be simulated by semiempirical calculations. The experimentally deduced g factors of the conduction band (g∼2.5) and valence band (g∼15) exceed those predicted in a single-particle model (g=1.5, 5.5, respectively). Such g-factor enhancement implies strong many-body interactions in gated monolayer WSe_{2}. The complex interplay between Landau quantization, excitonic effects, and many-body interactions makes monolayer WSe_{2} a promising platform to explore novel correlated quantum phenomena.

Introducing Electrode Contact by Controlled Micro-Alloying in Few-Layered GaTe Field Effect Transistors

Recently, gallium telluride (GaTe) has triggered much attention for its unique properties and offers excellent opportunities for nanoelectronics. Yet it is a challenge to bridge the semiconducting few-layered GaTe crystals with metallic electrodes for device applications. Here, we report a method on fabricating electrode contacts to few-layered GaTe field effect transistors (FETs) by controlled micro-alloying. The devices show linear I-V curves and on/off ratio of ∼10 4 on HfO 2 substrates. Kelvin probe force microscope (KPFM) and energy dispersion spectrum (EDS) are performed to characterize the electrode contacts, suggesting that the lowered Schottky barrier by the diffusion of Pd element into the GaTe conduction channel may play an important role. Our findings provide a strategy for the engineering of electrode contact for future device applications based on 2DLMs.

Band Filling and Cross Quantum Capacitance in Ion-Gated Semiconducting Transition Metal Dichalcogenide Monolayers

Ionic liquid gated field-effect transistors (FETs) based on semiconducting transition metal dichalcogenides (TMDs) are used to study a rich variety of extremely interesting physical phenomena, but important aspects of how charge carriers are accumulated in these systems are not understood. We address these issues by means of a systematic experimental study of transport in monolayer MoSe₂ and WSe₂ as a function of magnetic field and gate voltage, exploring accumulated densities of carriers ranging from approximately 10¹⁴ cm^-2 holes in the valence band to 4 × 10¹⁴ cm^-2 electrons in the conduction band. We identify the conditions when the chemical potential enters different valleys in the monolayer band structure (the K and Q valley in the conduction band and the two spin-split K-valleys in the valence band) and find that an independent electron picture describes the occupation of states well. Unexpectedly, however, the experiments show very large changes in the device capacitance when multiple valleys are occupied that are not at all compatible with the commonly expected quantum capacitance contribution of these systems, C_Q = e²/ (dμ/dn). A theoretical analysis of all terms responsible for the total capacitance shows that under general conditions a term is present besides the usual quantum capacitance, which becomes important for very small distances between the capacitor plates. This term, which we call cross quantum capacitance, originates from screening of the electric field generated by charges on one plate from charges sitting on the other plate. The effect is negligible in normal capacitors but large in ionic liquid FETs because of the atomic proximity between the ions in the gate and the accumulated charges on the TMD, and it accounts for all our experimental observations. Our findings therefore reveal an important contribution to the capacitance of physical systems that had been virtually entirely neglected until now.

Absence of Interlayer Tunnel Coupling of K-Valley Electrons in Bilayer MoS_{2}

In Bernal stacked bilayer graphene interlayer coupling significantly affects the electronic band structure compared to monolayer graphene. Here we present magnetotransport experiments on high-quality n-doped bilayer MoS_{2}. By measuring the evolution of the Landau levels as a function of electron density and applied magnetic field we are able to investigate the occupation of conduction band states, the interlayer coupling in pristine bilayer MoS_{2}, and how these effects are governed by electron-electron interactions. We find that the two layers of the bilayer MoS_{2} behave as two independent electronic systems where a twofold Landau level's degeneracy is observed for each MoS_{2} layer. At the onset of the population of the bottom MoS_{2} layer we observe a large negative compressibility caused by the exchange interaction. These observations, enabled by the high electronic quality of our samples, demonstrate weak interlayer tunnel coupling but strong interlayer electrostatic coupling in pristine bilayer MoS_{2}. The conclusions from the experiments may be relevant also to other transition metal dichalcogenide materials.

Revealing exciton masses and dielectric properties of monolayer semiconductors with high magnetic fields

In semiconductor physics, many essential optoelectronic material parameters can be experimentally revealed via optical spectroscopy in sufficiently large magnetic fields. For monolayer transition-metal dichalcogenide semiconductors, this field scale is substantial-tens of teslas or more-due to heavy carrier masses and huge exciton binding energies. Here we report absorption spectroscopy of monolayer [Formula: see text], and [Formula: see text] in very high magnetic fields to 91 T. We follow the diamagnetic shifts and valley Zeeman splittings of not only the exciton's [Formula: see text] ground state but also its excited [Formula: see text] Rydberg states. This provides a direct experimental measure of the effective (reduced) exciton masses and dielectric properties. Exciton binding energies, exciton radii, and free-particle bandgaps are also determined. The measured exciton masses are heavier than theoretically predicted, especially for Mo-based monolayers. These results provide essential and quantitative parameters for the rational design of opto-electronic van der Waals heterostructures incorporating 2D semiconductors.

Interaction-Induced Shubnikov-de Haas Oscillations in Optical Conductivity of Monolayer MoSe_{2}

We report polarization-resolved resonant reflection spectroscopy of a charge-tunable atomically thin valley semiconductor hosting tightly bound excitons coupled to a dilute system of fully spin- and valley-polarized holes in the presence of a strong magnetic field. We find that exciton-hole interactions manifest themselves in hole-density dependent, Shubnikov-de Haas-like oscillations in the energy and line broadening of the excitonic resonances. These oscillations are evidenced to be precisely correlated with the occupation of Landau levels, thus demonstrating that strong interactions between the excitons and Landau-quantized itinerant carriers enable optical investigation of quantum-Hall physics in transition metal dichalcogenides.

Disorder in van der Waals heterostructures of 2D materials

Realizing the full potential of any materials system requires understanding and controlling disorder, which can obscure intrinsic properties and hinder device performance. Here we examine both intrinsic and extrinsic disorder in two-dimensional (2D) materials, in particular graphene and transition metal dichalcogenides (TMDs). Minimizing disorder is crucial for realizing desired properties in 2D materials and improving device performance and repeatability for practical applications. We discuss the progress in disorder control for graphene and TMDs, as well as in van der Waals heterostructures realized by combining these materials with hexagonal boron nitride. Furthermore, we showcase how atomic defects or disorder can also be harnessed to provide useful electronic, optical, chemical and magnetic functions.

Spin-polarized electrons in monolayer MoS2

Coulomb interactions are crucial in determining the ground state of an ideal two-dimensional electron gas (2DEG) in the limit of low electron densities¹. In this regime, Coulomb interactions dominate over single-particle phase-space filling. In silicon and gallium arsenide, electrons are typically localized at these low densities. In contrast, in transition-metal dichalcogenides (TMDs), Coulomb correlations in a 2DEG can be anticipated at experimentally relevant electron densities. Here, we investigate a 2DEG in a gated monolayer of the TMD molybdenum disulfide². We measure the optical susceptibility, a probe of the 2DEG which is local, minimally invasive and spin selective³. In a magnetic field of 9.0 T and at electron concentrations up to n ≃ 5 × 10¹² cm^-2, we present evidence that the ground state is spin-polarized. Out of the four available conduction bands^4,5, only two are occupied. These two bands have the same spin but different valley quantum numbers. Our results suggest that only two bands are occupied even in the absence of a magnetic field. The spin polarization increases with decreasing 2DEG density, suggesting that Coulomb interactions are a key aspect of the symmetry breaking. We propose that exchange couplings align the spins⁶. The Bohr radius is so small⁷ that even electrons located far apart in phase-space interact with each other⁶.

Determining Interaction Enhanced Valley Susceptibility in Spin-Valley-Locked MoS2

Two-dimensional transition metal dichalcogenides (TMDCs) are recently emerged electronic systems with various novel properties, such as spin-valley locking, circular dichroism, valley Hall effect, and superconductivity. The reduced dimensionality and large effective masses further produce unconventional many-body interaction effects. Here we reveal strong interaction effects in the conduction band of MoS₂ by transport experiment. We study the massive Dirac electron Landau levels (LL) in high-quality MoS₂ samples with field-effect mobilities of 24 000 cm²/(V·s) at 1.2 K. We identify the valley-resolved LLs and low-lying polarized LLs using the Lifshitz-Kosevitch formula. By further tracing the LL crossings in the Landau fan diagram, we unambiguously determine the density-dependent valley susceptibility and the interaction enhanced g-factor from 12.7 to 23.6. Near integer ratios of Zeeman-to-cyclotron energies, we discover LL anticrossings due to the formation of quantum Hall Ising ferromagnets, the valley polarizations of which appear to be reversible by tuning the density or an in-plane magnetic field. Our results provide evidence for many-body interaction effects in the conduction band of MoS₂ and establish a fertile ground for exploring strongly correlated phenomena of massive Dirac electrons.