The empty world - a view from the free volume concept and Eyring's rate process theory

The many-body problem is a common issue, irrespective of the scale of entities under consideration. From electrons to atoms, small molecules like simple inorganic or organic structures, large molecules like proteins or polymers, nanometer- or micrometer-sized particles, granular matter, and even galaxies, the precise determination or estimation of geometrical locations and momentum energy of individual entities, and interaction forces between these millions of entities, is impossible but unfortunately important for understanding the collective physical properties like mechanical and electrical characteristics of the whole system. Despite foreseeable difficulties and complexities, attempts to estimate "interparticle" forces have never stopped using traditional Newtonian models, quantum mechanical approaches, and density functional theory. In this review, a simple approach integrating the free volume and Eyring's rate process theory is summarized and its application across a wide range of scales from electrons to the universe is presented in a unified manner. The focus is on comparisons between theoretical predictions and experimental results.

Interplay of valley, layer and band topology towards interacting quantum phases in moiré bilayer graphene

In Bernal-stacked bilayer graphene (BBG), the Landau levels give rise to an intimate connection between valley and layer degrees of freedom. Adding a moiré superlattice potential enriches the BBG physics with the formation of topological minibands - potentially leading to tunable exotic quantum transport. Here, we present magnetotransport measurements of a high-quality bilayer graphene-hexagonal boron nitride (hBN) heterostructure. The zero-degree alignment generates a strong moiré superlattice potential for the electrons in BBG and the resulting Landau fan diagram of longitudinal and Hall resistance displays a Hofstadter butterfly pattern with a high level of detail. We demonstrate that the intricate relationship between valley and layer degrees of freedom controls the topology of moiré-induced bands, significantly influencing the energetics of interacting quantum phases in the BBG superlattice. We further observe signatures of field-induced correlated insulators, helical edge states and clear quantizations of interaction-driven topological quantum phases, such as symmetry broken Chern insulators.

Electrical noise spectroscopy of magnons in a quantum Hall ferromagnet

Collective spin-wave excitations, magnons, are promising quasi-particles for next-generation spintronics devices, including platforms for information transfer. In a quantum Hall ferromagnets, detection of these charge-neutral excitations relies on the conversion of magnons into electrical signals in the form of excess electrons and holes, but if the excess electron and holes are equal, detecting an electrical signal is challenging. In this work, we overcome this shortcoming by measuring the electrical noise generated by magnons. We use the symmetry-broken quantum Hall ferromagnet of the zeroth Landau level in graphene to launch magnons. Absorption of these magnons creates excess noise above the Zeeman energy and remains finite even when the average electrical signal is zero. Moreover, we formulate a theoretical model in which the noise is produced by equilibration between edge channels and propagating magnons. Our model also allows us to pinpoint the regime of ballistic magnon transport in our device.

Large Polaron Condensation in a Pseudo-Bilayer Quantum Hall Composite

There is much interest regarding the "coupled ferroelectricity and superconductivity" in the two-dimensional material, bilayer Td-MoTe2; however, the value and the type of electric polarization are unknown. The device structure and the measurement method show that the measured material is the composite of the pseudo-bilayer quantum Hall system, with a thickness of about thirty-six nanometers. The derived dielectric hysteresis loops and the calculated electronic structure reveal that the condensed large polarons are responsible for the reverse ferroelectricity and the coupled superconductivity. The maximum value of polaron-type electric polarization is ~12 nC/μm2 or 1.2 × 104 μc/cm2.

Energy Gap of the Even-Denominator Fractional Quantum Hall State in Bilayer Graphene

Bernal bilayer graphene hosts even-denominator fractional quantum Hall states thought to be described by a Pfaffian wave function with non-Abelian quasiparticle excitations. Here, we report the quantitative determination of fractional quantum Hall energy gaps in bilayer graphene using both thermally activated transport and by direct measurement of the chemical potential. We find a transport activation gap of 5.1 K at B=12  T for a half filled N=1 Landau level, consistent with density matrix renormalization group calculations for the Pfaffian state. However, the measured thermodynamic gap of 11.6 K is smaller than theoretical expectations for the clean limit by approximately a factor of 2. We analyze the chemical potential data near fractional filling within a simplified model of a Wigner crystal of fractional quasiparticles with long-wavelength disorder, explaining this discrepancy. Our results quantitatively establish bilayer graphene as a robust platform for probing the non-Abelian anyons expected to arise as the elementary excitations of the even-denominator state.

Intra-Zero-Energy Landau Level Crossings in Bilayer Graphene at High Electric Fields

The highly tunable band structure of the zero-energy Landau level (zLL) of bilayer graphene makes it an ideal platform for engineering novel quantum states. However, the zero-energy Landau level at high electric fields has remained largely unexplored. Here we present magnetotransport measurements of bilayer graphene in high transverse electric fields. We observe previously undetected Landau level crossings at filling factors ν = -2, 1, and 3 at high electric fields. These crossings provide constraints for theoretical models of the zero-energy Landau level and show that the orbital, valley, and spin character of the quantum Hall states at high electric fields is very different from low electric fields. At high E, new transitions between states at ν = -2 with different orbital and spin polarization can be controlled by the gate bias, while the transitions between ν = 0 → 1 and ν = 2 → 3 show anomalous behavior.

Unconventional correlated insulator in CrOCl-interfaced Bernal bilayer graphene

The realization of graphene gapped states with large on/off ratios over wide doping ranges remains challenging. Here, we investigate heterostructures based on Bernal-stacked bilayer graphene (BLG) atop few-layered CrOCl, exhibiting an over-1-GΩ-resistance insulating state in a widely accessible gate voltage range. The insulating state could be switched into a metallic state with an on/off ratio up to 107 by applying an in-plane electric field, heating, or gating. We tentatively associate the observed behavior to the formation of a surface state in CrOCl under vertical electric fields, promoting electron-electron (e-e) interactions in BLG via long-range Coulomb coupling. Consequently, at the charge neutrality point, a crossover from single particle insulating behavior to an unconventional correlated insulator is enabled, below an onset temperature. We demonstrate the application of the insulating state for the realization of a logic inverter operating at low temperatures. Our findings pave the way for future engineering of quantum electronic states based on interfacial charge coupling.

Quantum Hall phase in graphene engineered by interfacial charge coupling

The quantum Hall effect can be substantially affected by interfacial coupling between the host two-dimensional electron gases and the substrate, and has been predicted to give rise to exotic topological states. Yet the understanding of the underlying physics and the controllable engineering of this interaction remains challenging. Here we demonstrate the observation of an unusual quantum Hall effect, which differs markedly from that of the known picture, in graphene samples in contact with an antiferromagnetic insulator CrOCl equipped with dual gates. Two distinct quantum Hall phases are developed, with the Landau levels in monolayer graphene remaining intact at the conventional phase, but largely distorted for the interfacial-coupling phase. The latter quantum Hall phase is even present close to the absence of a magnetic field, with the consequential Landau quantization following a parabolic relation between the displacement field and the magnetic field. This characteristic prevails up to 100 K in a wide effective doping range from 0 to 10¹³ cm^-2.

Hexagonal Boron Nitride on III–V Compounds: A Review of the Synthesis and Applications

Since the successful separation of graphene from its bulk counterpart, two-dimensional (2D) layered materials have become the focus of research for their exceptional properties. The layered hexagonal boron nitride (h-BN), for instance, offers good lubricity, electrical insulation, corrosion resistance, and chemical stability. In recent years, the wide-band-gap layered h-BN has been recognized for its broad application prospects in neutron detection and quantum information processing. In addition, it has become very important in the field of 2D crystals and van der Waals heterostructures due to its versatility as a substrate, encapsulation layer, and a tunneling barrier layer for various device applications. However, due to the poor adhesion between h-BN and substrate and its high preparation temperature, it is very difficult to prepare large-area and denseh-BN films. Therefore, the controllable synthesis of h-BN films has been the focus of research in recent years. In this paper, the preparation methods and applications of h-BN films on III–V compounds are systematically summarized, and the prospects are discussed.

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.

Observation of ballistic upstream modes at fractional quantum Hall edges of graphene

The presence of "upstream" modes, moving against the direction of charge current flow in the fractional quantum Hall (FQH) phases, is critical for the emergence of renormalized modes with exotic quantum statistics. Detection of excess noise at the edge is a smoking gun for the presence of upstream modes. Here, we report noise measurements at the edges of FQH states realized in dual graphite-gated bilayer graphene devices. A noiseless dc current is injected at one of the edge contacts, and the noise generated at contacts at length, L = 4 μm and 10 μm away along the upstream direction is studied. For integer and particle-like FQH states, no detectable noise is measured. By contrast, for "hole-conjugate" FQH states, we detect a strong noise proportional to the injected current, unambiguously proving the existence of upstream modes. The noise magnitude remains independent of length, which matches our theoretical analysis demonstrating the ballistic nature of upstream energy transport, quite distinct from the diffusive propagation reported earlier in GaAs-based systems.

Direct Visualization of Native Defects in Graphite and Their Effect on the Electronic Properties of Bernal-Stacked Bilayer Graphene

Graphite crystals used to prepare graphene-based heterostructures are generally assumed to be defect free. We report here scanning tunneling microscopy results that show graphite commonly used to prepare graphene devices can contain a significant amount of native defects. Extensive scanning of the surface allows us to determine the concentration of native defects to be 6.6 × 10⁸ cm^-2. We further study the effects of these native defects on the electronic properties of Bernal-stacked bilayer graphene. We observe gate-dependent intravalley scattering and successfully compare our experimental results to T-matrix-based calculations, revealing a clear carrier density dependence in the distribution of the scattering vectors. We also present a technique for evaluating the spatial distribution of short-scale scattering. Finally, we present a theoretical analysis based on the Boltzmann transport equation that predicts that the dilute native defects identified in our study are an important extrinsic source of scattering, ultimately setting the charge carrier mobility at low temperatures.

Limits of Applicability of the Composite Fermion Model

The popular model of composite fermions, proposed in order to rationalize FQHE, were insufficient in view of recent experimental observations in graphene monolayer and bilayer, in higher Landau levels in GaAs and in so-called enigmatic FQHE states in the lowest Landau level of GaAs. The specific FQHE hierarchy in double Hall systems of GaAs 2DES and graphene also cannot be explained in the framework of composite fermions. We identify the limits of the usability of the composite fermion model by means of topological methods, which elucidate the phenomenological assumptions in composite fermion structure and admit further development of FQHE understanding. We demonstrate how to generalize these ideas in order to explain experimentally observed FQHE phenomena, going beyond the explanation ability of the conventional composite fermion model.

Electronic and thermal transport in novel carbon-based bilayer with tetragonal rings: a combined study using first-principles and machine learning approach

In this article, the structural, electronic and thermal transport characteristics of bilayer tetragonal graphene (TG) are systematically explored with a combination of first-principles calculations and machine-learning interatomic potential approaches. Optimized ground state geometry of the bilayer TG structure is predicted and examined by employing various stability criteria. Electronic bandstructure analysis confirmed that bilayer TG exhibits a metallic band structure similar to the monolayer T-graphene structure. Thermal transport characteristics of the bilayer TG structure are explored by analysing thermal conductivity, the Seebeck coefficient, and electrical conductivity. The electronic part of the thermal conductivity shows linearly increasing behaviour with temperature, however the lattice part exhibits the opposite character. The lattice thermal conductivity part is investigated in terms of the three phonon scattering rates and weighted phase space. On the other hand, the Seebeck coefficient goes through a transition from negative to positive values with increasing temperature. The Wiedemann-Franz law regarding electrical transport of the bilayer TG is verified and confirms the universal Lorentz number. Specific heat of the bilayer TG structure follows the Debye model at low temperature and constant behaviour at high temperature. Moreover, the Debye temperature of the bilayer TG structure is verified by ab initio calculations as well as fitting the specific heat data using the Debye model.

Vanishing Thermal Equilibration for Hole-Conjugate Fractional Quantum Hall States in Graphene

Transport through edge channels is responsible for conduction in quantum Hall (QH) phases. Robust quantized values of charge and thermal conductances dictated by bulk topology appear when equilibration processes become dominant. We report on measurements of electrical and thermal conductances of integer and fractional QH phases, realized in hexagonal boron nitride encapsulated graphite-gated bilayer graphene devices for both electron and hole doped sides with different valley and orbital symmetries. Remarkably, for complex edges at filling factors ν=5/3 and 8/3, closely related to the paradigmatic hole-conjugate ν=2/3 phase, we find quantized thermal conductance whose values (3κ_{0}T and 4κ_{0}T, respectively where κ_{0}T is the thermal conductance quantum) are markedly inconsistent with the values dictated by topology (1κ_{0}T and 2κ_{0}T, respectively). The measured thermal conductance values remain insensitive to different symmetries, suggesting its universal nature. Our findings are supported by a theoretical analysis, which indicates that, whereas electrical equilibration at the edge is established over a finite length scale, the thermal equilibration length diverges for strong electrostatic interaction. Our results elucidate the subtle nature of crossover from coherent, mesoscopic to topology-dominated transport.

Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields

Recent topology classification of 2D electron states induced by different homotopy classes of mappings of the planar Brillouin zone into Bloch space can be supplemented by a homotopy classification of various phases of multi-electron homotopy patterns induced by Coulomb interaction between electrons. The general classification of such type is presented. It explains the topologically protected correlations responsible for integer and fractional Hall effects in 2D multi-electron systems in the presence of perpendicular quantizing magnetic field or Berry field, the latter in topological Chern insulators. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to local binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants and illustrated by experimental observations in GaAs 2DES, graphene monolayer, and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to the local crystal field, local disorder, and variation of the electron interaction strength. The nonzero interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems.

Enhanced Exciton-Exciton Collisions in an Ultraflat Monolayer MoSe2 Prepared through Deterministic Flattening

Squeezing bubbles and impurities out of interlayer spaces by applying force through a few-layer graphene capping layer leads to van der Waals heterostructures with the ultraflat structure free from random electrostatic potential arising from charged impurities. Without the graphene capping layer, a squeezing process with an AFM tip induces applied-force-dependent charges of Δn ∼ 2 × 10¹² cm^-2 μN^-1, resulting in the significant intensity of trions in photoluminescence spectra of MoSe₂ at low temperature. We found that a hBN/MoSe₂/hBN prepared with the "graphene-capping-assisted AFM nano-squeezing method" shows a strong excitonic emission with negligible trion peak, and the residual line width of the exciton peak is only 2.2 meV, which is comparable to the homogeneous limit. Furthermore, in this high-quality sample, we found that the formation of biexciton occurs even at extremely low excitation power (Φ_ph ∼ 2.3 × 10¹⁹ cm^-2 s^-1) due to the enhanced collisions between excitons.

Homotopy Phases of FQHE with Long-Range Quantum Entanglement in Monolayer and Bilayer Hall Systems

Correlated phases in Hall systems have topological character. Multilayer configurations of planar electron systems create the opportunity to change topological phases on demand using macroscopic factors, such as vertical voltage. We present an analysis of such phenomena in close relation to recent experiments with multilayer Hall setups including GaAs and graphene multi-layers. The consequences of the blocking or not of the inter-layer electron tunneling in stacked Hall configurations are analyzed and presented in detail. Multilayer Hall systems are thus tunable topological composite nanomaterials, in the case of graphene-stacked systems by both intra- and inter-layer voltage.

Quantum Hall Effect Measurement of Spin-Orbit Coupling Strengths in Ultraclean Bilayer Graphene/WSe2 Heterostructures

We study proximity-induced spin-orbit coupling (SOC) in bilayer graphene/few-layer WSe₂ heterostructure devices. Contact mode atomic force microscopy (AFM) cleaning yields ultraclean interfaces and high-mobility devices. In a perpendicular magnetic field, we measure the quantum Hall effect to determine the Landau level structure in the presence of out-of-plane Ising and in-plane Rashba SOC. A distinct Landau level crossing pattern emerges when tuning the charge density and displacement field independently with dual gates, originating from a layer-selective SOC proximity effect. Analyzing the Landau level crossings and measured inter-Landau level energy gaps yields the proximity-induced SOC energy scale. The Ising SOC is ∼2.2 meV, 100 times higher than the intrinsic SOC in graphene, whereas its sign is consistent with theories predicting a dependence of SOC on interlayer twist angle. The Rashba SOC is ∼15 meV. Finally, we infer the magnetic field dependence of the inter-Landau level Coulomb interactions. These ultraclean bilayer graphene/WSe₂ heterostructures provide a high mobility system with the potential to realize novel topological electronic states and manipulate spins in nanostructures.

Fractional and Symmetry-Broken Chern Insulators in Tunable Moiré Superlattices

We study dual-gated graphene bilayer/hBN moiré superlattices. Under zero magnetic field, we observe additional resistance peaks as the charge density varies. The peaks' resistivities vary approximately quadratically with an applied perpendicular displacement field D. Data fit to a continuum model yield a bilayer/hBN interaction energy scale ∼30 ± 10 meV. Under a perpendicular magnetic field, we observe Hofstadter butterfly spectra as well as symmetry-broken and fractional Chern insulator states. Their topology and lattice symmetry breaking is D-tunable, enabling the realization of new topological states in this system.

Quantum parity Hall effect in Bernal-stacked trilayer graphene

The quantum Hall effect has recently been generalized from transport of conserved charges to include transport of other approximately conserved-state variables, including spin and valley, via spin- or valley-polarized boundary states with different chiralities. Here, we report a class of quantum Hall effect in Bernal- or ABA-stacked trilayer graphene (TLG), the quantum parity Hall (QPH) effect, in which boundary channels are distinguished by even or odd parity under the system's mirror reflection symmetry. At the charge neutrality point, the longitudinal conductance [Formula: see text] is first quantized to [Formula: see text] at a small perpendicular magnetic field [Formula: see text], establishing the presence of four edge channels. As [Formula: see text] increases, [Formula: see text] first decreases to [Formula: see text], indicating spin-polarized counterpropagating edge states, and then, to approximately zero. These behaviors arise from level crossings between even- and odd-parity bulk Landau levels driven by exchange interactions with the underlying Fermi sea, which favor an ordinary insulator ground state in the strong [Formula: see text] limit and a spin-polarized state at intermediate fields. The transitions between spin-polarized and -unpolarized states can be tuned by varying Zeeman energy. Our findings demonstrate a topological phase that is protected by a gate-controllable symmetry and sensitive to Coulomb interactions.

Tuning spin-orbit coupling in 2D materials for spintronics: a topical review

Atomically-thin 2D materials have opened up new opportunities in the past decade in realizing novel electronic device concepts, owing to their unusual electronic properties. The recent progress made in the aspect of utilizing additional degrees of freedom of the electrons such as spin and valley suggests that 2D materials have a significant potential in replacing current electronic-charge-based semiconductor technology with spintronics and valleytronics. For spintronics, spin-orbit coupling plays a key role in manipulating the electrons' spin degree of freedom to encode and process information, and there are a host of recent studies exploring this facet of 2D materials. We review the recent advances in tuning spin-orbit coupling of 2D materials which are of notable importance to the progression of spintronics.

Tunneling Spectroscopy of Quantum Hall States in Bilayer Graphene p-n Junctions

We report tunneling transport in spatially controlled networks of quantum Hall (QH) edge states in bilayer graphene. By manipulating the separation, location, and spatial span of QH edge states via gate-defined electrostatics, we observe resonant tunneling between copropagating QH states across incompressible strips. Employing spectroscopic tunneling measurements and an analytical model, we characterize the energy gap, width, density of states, and compressibility of the QH edge states with high precision and sensitivity within the same device. The capability to engineer the QH edge network also provides an opportunity to build future quantum electronic devices with electrostatic manipulation of QH edge states, supported by rich underlying physics.

High-Quality Electrostatically Defined Hall Bars in Monolayer Graphene

Realizing graphene's promise as an atomically thin and tunable platform for fundamental studies and future applications in quantum transport requires the ability to electrostatically define the geometry of the structure and control the carrier concentration, without compromising the quality of the system. Here, we demonstrate the working principle of a new generation of high-quality gate-defined graphene samples, where the challenge of doing so in a gapless semiconductor is overcome by using the ν = 0 insulating state, which emerges at modest applied magnetic fields. In order to verify that the quality of our devices is not compromised, we compare the electronic transport response of different sample geometries, paying close attention to fragile quantum states, such as the fractional quantum Hall states that are highly susceptible to disorder. The ability to define local depletion regions without compromising device quality establishes a new approach toward structuring graphene-based quantum transport devices.

Interface States in Bilayer Graphene Encapsulated by Hexagonal Boron Nitride

The threshold voltages at the onset of conduction for electron and hole branches can provide information on band gap values or interface states in a gap. We measured conductivity of bilayer graphene encapsulated by hexagonal boron nitride as a function of back and top gates, where another bilayer graphene is used as a top gate. From the measured conductivity the transport gap values were extracted assuming zero interface trap states, and they are close to the theoretically expected gap values. From a little discrepancy an average density of interface states per energy within a band gap ( D_it) is also estimated. The data clearly show that D_it decreases as a bilayer graphene band gap increases rather than being constant. Despite the decreasing trend of D_it, interestingly the total interface states within a gap increases linearly as a band gap increases. This is because of ∼2 × 10¹⁰ cm^-2 interface states localized at band edges even without a band gap, and other gap states are equally spread over the gap.

Quantitative Transport Measurements of Fractional Quantum Hall Energy Gaps in Edgeless Graphene Devices

Owing to their wide tunability, multiple internal degrees of freedom, and low disorder, graphene heterostructures are emerging as a promising experimental platform for fractional quantum Hall (FQH) studies. Here, we report FQH thermal activation gap measurements in dual graphite-gated monolayer graphene devices fabricated in an edgeless Corbino geometry. In devices with substrate-induced sublattice splitting, we find a tunable crossover between single- and multicomponent FQH states in the zero energy Landau level. Activation gaps in the single-component regime show excellent agreement with numerical calculations using a single broadening parameter Γ≈7.2  K. In the first excited Landau level, in contrast, FQH gaps are strongly influenced by Landau level mixing, and we observe an unexpected valley-ordered state at integer filling ν=-4.

Extremely flat band in bilayer graphene

We propose a novel mechanism of flat band formation based on the relative biasing of only one sublattice against other sublattices in a honeycomb lattice bilayer. The mechanism allows modification of the band dispersion from parabolic to "Mexican hat"-like through the formation of a flattened band. The mechanism is well applicable for bilayer graphene-both doped and undoped. By angle-resolved photoemission from bilayer graphene on SiC, we demonstrate the possibility of realizing this extremely flattened band (< 2-meV dispersion), which extends two-dimensionally in a k-space area around the K ¯ point and results in a disk-like constant energy cut. We argue that our two-dimensional flat band model and the experimental results have the potential to contribute to achieving superconductivity of graphene- or graphite-based systems at elevated temperatures.

Electrically Inert h-BN/Bilayer Graphene Interface in All-Two-Dimensional Heterostructure Field Effect Transistors

Bilayer graphene field effect transistors (BLG-FETs), unlike conventional semiconductors, are greatly sensitive to potential fluctuations because of the charged impurities in high- k gate stacks because the potential difference between two layers induced by the external perpendicular electrical filed is the physical origin behind the band gap opening. The assembly of BLG with layered h-BN insulators into a van der Waals heterostructure has been widely recognized to achieve the superior electrical transport properties. However, the carrier response properties at the h-BN/BLG heterointerface, which control the device performance, have not yet been revealed because of the inevitably large parasitic capacitance. In this study, the significant reduction of potential fluctuations to ∼1 meV is achieved in an all-two-dimensional heterostructure BLG-FET on a quartz substrate, which results in the suppression of the off-current to the measurement limit at a small band gap of ∼90 meV at 20 K. By capacitance measurement, we demonstrate that the electron trap/detrap response at such heterointerface is suppressed to undetectable level in the measurement frequency range. The electrically inert van der Waals heterointerface paves the way for the realization of future BLG electronics applications.

Landau Level Diagram and the Continuous Rotational Symmetry Breaking in Trilayer Graphene

The sequence of the zeroth Landau levels (LLs) between filling factors ν=-6 to 6 in ABA-stacked trilayer graphene (TLG) is unknown because it depends sensitively on the nonuniform charge distribution on the three layers of ABA-stacked TLG. Using the sensitivity of quantum Hall data on the electric field and magnetic field, in an ultraclean ABA-stacked TLG sample, we quantitatively estimate the nonuniformity of the electric field and determine the sequence of the zeroth LLs. We also observe anticrossings between some LLs differing by 3 in LL index, which result from the breaking of the continuous rotational to C_{3} symmetry by the trigonal warping.

Manifestation of plasmonic response in the detection of sub-terahertz radiation by graphene-based devices

We report on the sub-terahertz (THz) (129-450 GHz) photoresponse of devices based on single layer graphene and graphene nanoribbons with asymmetric source and drain (vanadium and gold) contacts. Vanadium forms a barrier at the graphene interface, while gold forms an Ohmic contact. We find that at low temperatures (77 K) the detector responsivity rises with the increasing frequency of the incident sub-THz radiation. We interpret this result as a manifestation of a plasmonic effect in the devices with the relatively long plasmonic wavelengths. Graphene nanoribbon devices display a similar pattern, albeit with a lower responsivity.

A review of the quantum Hall effects in MgZnO/ZnO heterostructures

This review visits recent experimental efforts on high mobility two-dimensional electron systems (2DES) hosted at the Mg _x Zn[Formula: see text]O/ZnO heterointerface. We begin with the growth of these samples, and highlight the key characteristics of ozone-assisted molecular beam epitaxy required for their production. The transport characteristics of these structures are found to rival that of traditional semiconductor material systems, as signified by the high electron mobility ([Formula: see text] cm² Vs^-1) and rich quantum Hall features. Owing to a large effective mass and small dielectric constant, interaction effects are an order of magnitude stronger in comparison with the well studied GaAs-based 2DES. The strong correlation physics results in robust Fermi-liquid renormalization of the effective mass and spin susceptibility of carriers, which in turn dictates the parameter space for the quantum Hall effect. Finally, we explore the quantum Hall effect with a particular emphasis on the spin degree of freedom of carriers, and how their large spin splitting allows control of the ground states encountered at ultra-low temperatures within the fractional quantum Hall regime. We discuss in detail the physics of even-denominator fractional quantum Hall states, whose observation and underlying character remain elusive and exotic.

Gate-Controlled Transmission of Quantum Hall Edge States in Bilayer Graphene

The edge states of the quantum Hall and fractional quantum Hall effect of a two-dimensional electron gas carry key information of the bulk excitations. Here we demonstrate gate-controlled transmission of edge states in bilayer graphene through a potential barrier with tunable height. The backscattering rate is continuously varied from 0 to close to 1, with fractional quantized values corresponding to the sequential complete backscattering of individual modes. Our experiments demonstrate the feasibility to controllably manipulate edge states in bilayer graphene, thus opening the door to more complex experiments.

Effective Landau Level Diagram of Bilayer Graphene

The E=0 octet of bilayer graphene in the filling factor range of -4<ν<4 is a fertile playground for many-body phenomena, yet a Landau level diagram is missing due to strong interactions and competing quantum degrees of freedom. We combine measurements and modeling to construct an empirical and quantitative spectrum. The single-particlelike diagram incorporates interaction effects effectively and provides a unified framework to understand the occupation sequence, gap energies, and phase transitions observed in the octet. It serves as a new starting point for more sophisticated calculations and experiments.

Numerical Study of Quantum Hall Bilayers at Total Filling ν_{T}=1: A New Phase at Intermediate Layer Distances

We study the phase diagram of quantum Hall bilayer systems with total filing ν_{T}=1/2+1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1<d/l_{B}<1.8 (l_{B} is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers and (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Furthermore, from our finite-size study, the energy cost of transferring one electron between the layers shows an even-odd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling ν_{T}=1.

Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene

The high magnetic field electronic structure of bilayer graphene is enhanced by the spin, valley isospin, and an accidental orbital degeneracy, leading to a complex phase diagram of broken symmetry states. Here, we present a technique for measuring the layer-resolved charge density, from which we directly determine the valley and orbital polarization within the zero energy Landau level. Layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital order, including previously unobserved orbitally polarized states stabilized by skew interlayer hopping. We fit our data to a model that captures both single-particle and interaction-induced anisotropies, providing a complete picture of this correlated electron system. The resulting roadmap to symmetry breaking paves the way for deterministic engineering of fractional quantum Hall states, while our layer-resolved technique is readily extendable to other two-dimensional materials where layer polarization maps to the valley or spin quantum numbers.

The phase diagram of bilayer graphene at high magnetic fields has been an outstanding question, with orders possibly between multiple internal quantum degrees of freedom. Here, Hunt et al. report the measurement of the valley and orbital order, allowing them to directly reconstruct the phase diagram.

Anomalous Dirac point transport due to extended defects in bilayer graphene

Charge transport at the Dirac point in bilayer graphene exhibits two dramatically different transport states, insulating and metallic, that occur in apparently otherwise indistinguishable experimental samples. We demonstrate that the existence of these two transport states has its origin in an interplay between evanescent modes, that dominate charge transport near the Dirac point, and disordered configurations of extended defects in the form of partial dislocations. In a large ensemble of bilayer systems with randomly positioned partial dislocations, the distribution of conductivities is found to be strongly peaked at both the insulating and metallic limits. We argue that this distribution form, that occurs only at the Dirac point, lies at the heart of the observation of both metallic and insulating states in bilayer graphene.

In seemingly indistinguishable bilayer graphene samples, two distinct transport regimes, insulating and metallic, have been identified experimentally. Here, the authors demonstrate that these two states originate from the interplay between extended defects and evanescent modes at the Dirac point.

Unconventional fractional quantum Hall effect in bilayer graphene

Recent experimental progress in Hall measurements in bilayer graphene in the so-called open-face configuration of boron nitride encapsulated samples, together with the earlier technique of suspended samples, allows for precise observation of the fractional quantum Hall effect (FQHE) in all 4 subbands of the Lowest Landau level (with n = 0 and n = 1) and in the next LL subbands (with n = 2) in the bilayer system. Many newly observed FQHE features do not agree with a conventional model of composite fermions and reveal a different hierarchy in comparison to monolayer graphene or GaAs 2DEG. We explain the peculiarity of the FQHE hierarchy in the bilayer system in the framework of a topological approach, which includes the composite fermion model as its special case. Inclusion of a topological effect caused by the hopping of electrons between the two sheets in the bilayer system allowed for an explanation of the FQHE hierarchy in the graphene bilayer in satisfactory accordance with the experimental observations.

Thermal Transport Signatures of Broken-Symmetry Phases in Graphene

In the half filled zero-energy Landau level of bilayer graphene, competing phases with spontaneously broken symmetries and an intriguing quantum critical behavior have been predicted. Here we investigate signatures of these broken-symmetry phases in thermal transport measurements. To this end, we calculate the spectrum of spin and valley waves in the ν=0 quantum Hall state of bilayer graphene. The presence of Goldstone modes enables heat transport even at low temperatures, which can serve as compelling evidence for spontaneous symmetry breaking. By varying external electric and magnetic fields, it is possible to determine the nature of the symmetry breaking. Temperature-dependent measurements may yield additional information about gapped modes.

Layer Polarizability and Easy-Axis Quantum Hall Ferromagnetism in Bilayer Graphene

We report magnetotransport measurements of graphene bilayers at large perpendicular electric displacement fields, up to ∼1.5 V/nm, where we observe crossings between Landau levels with different orbital quantum numbers. The displacement fields at the studied crossings are primarily determined by energy shifts originating from the Landau level layer polarizability or polarization. Despite decreasing Landau level spacing with energy, successive crossings occur at larger displacement fields, resulting from decreasing polarizability with orbital quantum number. For particular crossings we observe resistivity hysteresis in displacement field, indicating the presence of a first-order transition between states exhibiting easy-axis quantum Hall ferromagnetism.

Graphene bubbles and their role in graphene quantum transport

Graphene bubbles are often formed when graphene and other layered two-dimensional materials are vertically stacked as van der Waals heterostructures. Here, we investigate how graphene bubbles and their related disorder impact the quantum transport behavior of graphene in the absence and presence of external magnetic fields. By combining experimental observations and numerical simulations, we find that the disorder induced by the graphene bubbles is mainly from p-type dopants and the charge transport in pristine graphene can be severely influenced by the presence of bubbles via long- and short-range scattering even with a small bubble-coverage of 2% and below. Upon bubble density increase, we observe an overall decrease in carrier mobility, and the appearance of a second Dirac point on the electron carrier side. At high magnetic fields, the disorder from graphene bubbles primarily impacts the quantization of the lowest Landau level, resulting in quantum Hall features associated with a new Dirac cone at high charge carrier density.

Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers

We study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum l=+1 are energetically favored for filling ν=1/2+1/2 and 1/4+1/4. The degeneracy between states with ±l is lifted by the interlayer density-current interaction arising from the interplay of the long-range Coulomb interaction and the Chern-Simons term in the HLR theory.

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene

According to electronic structure theory, bilayer graphene is expected to have anomalous electronic properties when it has long-period moiré patterns produced by small misalignments between its individual layer honeycomb lattices. We have realized bilayer graphene moiré crystals with accurately controlled twist angles smaller than 1° and studied their properties using scanning probe microscopy and electron transport. We observe conductivity minima at charge neutrality, satellite gaps that appear at anomalous carrier densities for twist angles smaller than 1°, and tunneling densities-of-states that are strongly dependent on carrier density. These features are robust up to large transverse electric fields. In perpendicular magnetic fields, we observe the emergence of a Hofstadter butterfly in the energy spectrum, with fourfold degenerate Landau levels, and broken symmetry quantum Hall states at filling factors ±1, 2, 3. These observations demonstrate that at small twist angles, the electronic properties of bilayer graphene moiré crystals are strongly altered by electron-electron interactions.

Robust fractional quantum Hall effect in the N=2 Landau level in bilayer graphene

The fractional quantum Hall effect is a canonical example of electron-electron interactions producing new ground states in many-body systems. Most fractional quantum Hall studies have focussed on the lowest Landau level, whose fractional states are successfully explained by the composite fermion model. In the widely studied GaAs-based system, the composite fermion picture is thought to become unstable for the N≥2 Landau level, where competing many-body phases have been observed. Here we report magneto-resistance measurements of fractional quantum Hall states in the N=2 Landau level (filling factors 4<|ν|<8) in bilayer graphene. In contrast with recent observations of particle-hole asymmetry in the N=0/N=1 Landau levels of bilayer graphene, the fractional quantum Hall states we observe in the N=2 Landau level obey particle-hole symmetry within the fully symmetry-broken Landau level. Possible alternative ground states other than the composite fermions are discussed.

Broken-Symmetry Quantum Hall States in Twisted Bilayer Graphene

Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley, providing eight-fold degeneracy in the low energy states. We have investigated broken-symmetry quantum Hall (QH) states and their transitions due to the interplay of the relative strength of valley, spin and layer polarizations in twisted bilayer graphene. The energy gaps of the broken-symmetry QH states show an electron-hole asymmetric behaviour, and their dependence on the induced displacement field are opposite between even and odd filling factor states. These results strongly suggest that the QH states with broken valley and spin symmetries for individual layer become hybridized via interlayer tunnelling, and the hierarchy of the QH states is sensitive to both magnetic field and displacement field due to charge imbalance between layers.

Wafer-Scale Single-Crystalline AB-Stacked Bilayer Graphene

Single-crystalline artificial AB-stacked bilayer graphene is formed by aligned transfer of two single-crystalline monolayers on a wafer-scale. The obtained bilayer has a well-defined interface and is electronically equivalent to exfoliated or direct-grown AB-stacked bilayers.

Tunable Symmetries of Integer and Fractional Quantum Hall Phases in Heterostructures with Multiple Dirac Bands

The copresence of multiple Dirac bands in few-layer graphene leads to a rich phase diagram in the quantum Hall regime. Using transport measurements, we map the phase diagram of BN-encapsulated ABA-stacked trilayer graphene as a function charge density n, magnetic field B, and interlayer displacement field D, and observe transitions among states with different spin, valley, orbital, and parity polarizations. Such a rich pattern arises from crossings between Landau levels from different subbands, which reflect the evolving symmetries that are tunable in situ. At D=0, we observe fractional quantum Hall (FQH) states at filling factors 2/3 and -11/3. Unlike those in bilayer graphene, these FQH states are destabilized by a small interlayer potential that hybridizes the different Dirac bands.