Spectral Asymmetry Induces a Re-Entrant Quantum Hall Effect in a Topological Insulator

The band inversion of topological materials in three spatial dimensions is intimately connected to the parity anomaly of 2D massless Dirac fermions, known from quantum field theory. At finite magnetic fields, the parity anomaly reveals itself as a non-zero spectral asymmetry, i.e., an imbalance between the number of conduction and valence band Landau levels, due to the unpaired zero Landau level. This work reports the realization of this 2D Dirac physics at a single surface of the 3D topological insulator (Hg,Mn)Te. An unconventional re-entrant sequence of quantized Hall plateaus in the measured Hall resistance can be directly related to the occurrence of spectral asymmetry in a single topological surface state. The effect should be observable in any topological insulator where the transport is dominated by a single Dirac surface state.

Nonlinear Landau Fan Diagram for Graphene Electrons Exposed to a Moiré Potential

Due to Landau quantization, the conductance of two-dimensional electrons exposed to a perpendicular magnetic field exhibits oscillations that generate a fan of linear trajectories when plotted in the parameter space spanned by density and field. This fan looks identical, irrespective of the dispersion and field dependence of the Landau level energy. This is no surprise because the position of conductance minima depends solely on the level degeneracy that is linear in flux. The fractal energy spectrum that emerges within each Landau band when electrons are also exposed to a two-dimensional superlattice potential produces numerous additional oscillations, but they also create just linear fans for identical reasons. Here, we report conductance oscillations of graphene electrons exposed to a moiré potential that defy this general rule and form nonlinear trajectories in the density-field plane. We attribute this anomalous behavior to the simultaneous occupation of multiple minibands and magnetic breakdown-induced open orbits.

Electrical Detection of Ultrastrong Coherent Interaction between Terahertz Fields and Electrons Using Quantum Point Contacts

Light-matter interaction in the ultrastrong coupling regime is attracting considerable attention owing to its applications to coherent control of material properties by a vacuum fluctuation field. However, electrical access to such an ultrastrongly coupled system is very challenging. In this work, we have fabricated a gate-defined quantum point contact (QPC) near the gap of a terahertz (THz) split-ring resonator (SRR) fabricated on a GaAs two-dimensional (2D) electron system. By illuminating the system with external THz radiation, the QPC shows a photocurrent spectrum which exhibits significant anticrossing that arises from coupling between the cyclotron resonance of the 2D electrons and the SRR. The observed photocurrent signal can be explained by energy-selective transmission/reflection of the quantum Hall edge channels at the QPC. Furthermore, at the same gate voltage and magnetic field conditions under which the anticrossing signal was observed, the QPC exhibits anomalous conductance modulation even in the dark environment.

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.

Nondegenerate Integer Quantum Hall Effect from Topological Surface States in Ag2Te Nanoplates

The quantum Hall effect is one of the exclusive properties displayed by Dirac Fermions in topological insulators, which propagates along the chiral edge state and gives rise to quantized electron transport. However, the quantum Hall effect formed by the nondegenerate Dirac surface states has been elusive so far. Here, we demonstrate the nondegenerate integer quantum Hall effect from the topological surface states in three-dimensional (3D) topological insulator β-Ag2Te nanostructures. Surface-state dominant conductance renders quantum Hall conductance plateaus with a step of e2/h, along with typical thermopower behaviors of two-dimensional (2D) massless Dirac electrons. The 2D nature of the topological surface states is proven by the electrical and thermal transport responses under tilted magnetic fields. Moreover, the degeneracy of the surface states is removed by structure inversion asymmetry (SIA). The evidenced SIA-induced nondegenerate integer quantum Hall effect in low-symmetry β-Ag2Te has implications for both fundamental study and the realization of topological magneto-electric effects.

Orbitally Controlled Quantum Hall States in Decoupled Two-Bilayer Graphene Sheets

The authors report on integer and fractional quantum Hall states in a stack of two twisted Bernal bilayer graphene sheets. By exploiting the momentum mismatch in reciprocal space, the single-particle tunneling between both bilayers is suppressed. Since the bilayers are spatially separated by only 0.34 nm, the stack benefits from strong interlayer Coulombic interactions. These interactions can cause the formation of a Bose-Einstein condensate. Indeed, such a condensate is observed for half-filling in each bilayer sheet. However, only when the partially filled levels have orbital index 1. It is absent for partially filled levels with orbital index 0. This discrepancy is tentatively attributed to the role of skyrmion/anti-skyrmion pair excitations and the dependence of the energy of these excitations on the orbital index. The application of asymmetric top and bottom gate voltages enables to influence the orbital nature of the electronic states of the graphene bilayers at the chemical potential and to navigate in orbital mixed space. The latter hosts an even denominator fractional quantum Hall state at total filling of -3/2. These observations suggest a unique edge reconstruction involving both electrons and chiral p-wave composite fermions.

Edge Channel Transmission through a Quantum Point Contact in the Two-Dimensional Topological Insulator Cadmium Arsenide

Cadmium arsenide (Cd₃As₂) thin films feature a two-dimensional topological insulator (2D TI) phase for certain thicknesses, which theoretically hosts a set of counterpropagating helical edge statesA bar has been added to each symbol of the high-symmetry points of Cu(100) and Cu(111). The bar indicates the surface projected Brillouin zone. that are characteristic of a quantum spin Hall (QSH) insulator. In devices containing electrostatically defined junctions and for magnetic fields below a critical value, chiral edge modes of the quantum Hall effect can coexist with QSH-like edge modes. In this work, we use a quantum point contact (QPC) device to characterize edge modes in the 2D TI phase of Cd₃As₂ and to understand how they can be controllably transmitted, which is important for use in future quantum interference devices. We investigate equilibration among both types of modes and find non-spin-selective equilibration. We also demonstrate the effect of the magnetic field on suppressing equilibration. We discuss the potential role of QSH-like modes in a transmission pathway that precludes full pinch-off.

Thermoelectric Properties of the Corbino Disk in Graphene

Thermopower and the Lorentz number for an edge-free (Corbino) graphene disk in the quantum Hall regime is calculated within the Landauer-Büttiker formalism. By varying the electrochemical potential, we find that amplitude of the Seebeck coefficient follows a modified Goldsmid-Sharp relation, with the energy gap defined by the interval between the zero and the first Landau levels in bulk graphene. An analogous relation for the Lorentz number is also determined. Thus, these thermoelectric properties are solely defined by the magnetic field, the temperature, the Fermi velocity in graphene, and fundamental constants including the electron charge, the Planck and Boltzmann constants, being independent of the geometric dimensions of the system. This suggests that the Corbino disk in graphene may operate as a thermoelectric thermometer, allowing to measure small temperature differences between two reservoirs, if the mean temperature magnetic field are known.

Unconventional Flat Chern Bands and 2e Charges in Skyrmionic Moiré Superlattices

The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic structures in the form of the skyrmion lattice. In particular, we discover a scenario for generating |C| = 2 dispersionless electronic bands when the skyrmion periodicity and the moiré periodicity match. Following the Wilczek argument, the statistics of the charge-carrying excitations in this case is bosonic, characterized by electronic charge Q = 2e, which is even in units of electron charge e. The skyrmion coupling strength triggering the topological phase transition is realistic, with its lower bound estimated as 4 meV. The Hofstadter butterfly spectrum results in an unexpected quantum Hall conductance sequence ±2e2h,±4e2h,... for TBG with the skyrmion order.

Quantum-Hall physics and three dimensions

The discovery of the quantum Hall effect (QHE) in 1980 marked a turning point in condensed matter physics: given appropriate experimental conditions, the Hall conductivityσxyof a two-dimensional electron system is exactly quantized. But what happens to the QHE in three dimensions (3D)? Experiments over the past 40 years showed that some of the remarkable physics of the QHE, in particular plateau-like Hall conductivitiesσxyaccompanied by minima in the longitudinal resistivityρxx, can also be found in 3D materials. However, since typicallyρxxremains finite and a quantitative relation betweenσxyand the conductance quantume2/hcould not be established, the role of quantum Hall physics in 3D remains unsettled. Following a recent series of exciting experiments, the QHE in 3D has now returned to the center stage. Here, we summarize the leap in understanding of 3D matter in magnetic fields emerging from these experiments.

Chiral Transport of Hot Carriers in Graphene in the Quantum Hall Regime

Photocurrent (PC) measurements can reveal the relaxation dynamics of photoexcited hot carriers beyond the linear response of conventional transport experiments, a regime important for carrier multiplication. Here, we study the relaxation of carriers in graphene in the quantum Hall regime by accurately measuring the PC signal and modeling the data using optical Bloch equations. Our results lead to a unified understanding of the relaxation processes in graphene over different magnetic field strength regimes, which is governed by the interplay of Coulomb interactions and interactions with acoustic and optical phonons. Our data provide clear indications of a sizable carrier multiplication. Moreover, the oscillation pattern and the saturation behavior of PC are manifestations of not only the chiral transport properties of carriers in the quantum Hall regime but also the chirality change at the Dirac point, a characteristic feature of a relativistic quantum Hall effect.

High-Temperature Quantum Hall Effect in Graphite-Gated Graphene Heterostructure Devices with High Carrier Mobility

Since the discovery of the quantum Hall effect in 1980, it has attracted intense interest in condensed matter physics and has led to a new type of metrological standard by utilizing the resistance quantum. Graphene, a true two-dimensional electron gas material, has demonstrated the half-integer quantum Hall effect and composite-fermion fractional quantum Hall effect due to its unique massless Dirac fermions and ultra-high carrier mobility. Here, we use a monolayer graphene encapsulated with hexagonal boron nitride and few-layer graphite to fabricate micrometer-scale graphene Hall devices. The application of a graphite gate electrode significantly screens the phonon scattering from a conventional SiO₂/Si substrate, and thus enhances the carrier mobility of graphene. At a low temperature, the carrier mobility of graphene devices can reach 3 × 10⁵ cm²/V·s, and at room temperature, the carrier mobility can still exceed 1 × 10⁵ cm²/V·s, which is very helpful for the development of high-temperature quantum Hall effects under moderate magnetic fields. At a low temperature of 1.6 K, a series of half-integer quantum Hall plateaus are well-observed in graphene with a magnetic field of 1 T. More importantly, the ν = ±2 quantum Hall plateau clearly persists up to 150 K with only a few-tesla magnetic field. These findings show that graphite-gated high-mobility graphene devices hold great potential for high-sensitivity Hall sensors and resistance metrology standards for the new Système International d'unités.

Optical Sensing of Fractional Quantum Hall Effect in Graphene

Graphene and its heterostructures provide a unique and versatile playground for explorations of strongly correlated electronic phases, ranging from unconventional fractional quantum Hall (FQH) states in a monolayer system to a plethora of superconducting and insulating states in twisted bilayers. However, the access to those fascinating phases has been thus far entirely restricted to transport techniques, due to the lack of a robust energy bandgap that makes graphene hard to access optically. Here we demonstrate an all-optical, noninvasive spectroscopic tool for probing electronic correlations in graphene using excited Rydberg excitons in an adjacent transition metal dichalcogenide monolayer. These excitons are highly susceptible to the compressibility of graphene electrons, allowing us to detect the formation of odd-denominator FQH states at high magnetic fields. Owing to its submicron spatial resolution, the technique we demonstrate circumvents spatial inhomogeneities and paves the way for optical studies of correlated states in optically inactive atomically thin materials.

Phase diagram of superconductivity in the integer quantum Hall regime

An interplay between pairing and topological orders has been predicted to give rise to superconducting states supporting exotic emergent particles, such as Majorana particles obeying non-Abelian braid statistics. We consider a system of spin polarized electrons on a Hofstadter lattice with nearest-neighbor attractive interaction and solve the mean-field Bogoliubov-de Gennes equations in a self-consistent fashion, leading to gauge-invariant observables and a rich phase diagram as a function of the chemical potential, the magnetic field, and the interaction. As the strength of the attractive interaction is increased, the system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully gapped in the bulk but has topological chiral edge current, characterizing a topologically nontrivial state. This is followed by a vortex phase in which the vortices carrying Majorana modes form a lattice; the spectrum contains a low-energy Majorana band arising from the coupling between neighboring vortex-core Majorana modes but does not have chiral edge currents. For some parameters, a dimer vortex lattice occurs with no Majorana band. The experimental feasibility and the observable consequences of skyrmions as well as Majorana modes are indicated.

Quantum transport in CVD graphene synthesized with liquid carbon precursor

Large-area high-quality graphene enabled by chemical vapor deposition (CVD) can possibly pave the path for advanced flexible electronics and spintronics. CVD-grown method utilizing liquid carbon precursor has recently been demonstrated as an appealing choice for mass graphene production, thanks to its low cost and safe operation. However, the quality of the graphene film has been the major obstacle for the implementation of the liquid-precursor-based CVD method. Here we report the growth of centimeter-scale easily-transferable single-layer graphene (SLG) using acetone as a liquid carbon precursor. The dry-transfer technique was used to prepare the graphene device. The typical mobility of the dry-transferred SLG device is as high as 12 500 cm²V^-1s^-1at room temperature. Thanks to the high quality of the device, the robust quantum Hall effect can survive up to room temperature. The excellent device quality also enables us to observe the Shubnikov-de Haas oscillation in the low magnetic field regime and systemically study the leading scattering mechanism. We extracted both the transport scattering timeτ_tand the quantum scattering timeτ_qover a wide range of carrier density. The ratio of the scattering times suggests that the charged-impurity resided near the surface of the graphene restricted the device performance.

Spontaneous Gully-Polarized Quantum Hall States in ABA Trilayer Graphene

Bernal-stacked multilayer graphene is a versatile platform to explore quantum transport phenomena and interaction physics due to its exceptional tunability via electrostatic gating. For instance, upon applying a perpendicular electric field, its band structure exhibits several off-center Dirac points (so-called Dirac gullies) in each valley. Here, the formation of Dirac gullies and the interaction-induced breakdown of gully coherence is explored via magnetotransport measurements in high-quality Bernal-stacked (ABA) trilayer graphene. At zero magnetic field, multiple Lifshitz transitions indicating the formation of Dirac gullies are identified. In the quantum Hall regime, the emergence of Dirac gullies is evident as an increase in Landau level degeneracy. When tuning both electric and magnetic fields, electron-electron interactions can be controllably enhanced until, beyond critical electric and magnetic fields, the gully degeneracy is eventually lifted. The arising correlated ground state is consistent with a previously predicted nematic phase that spontaneously breaks the rotational gully symmetry.

Quantum Hall Effect across Graphene Grain Boundary

Charge carrier scattering at grain boundaries (GBs) in a chemical vapor deposition (CVD) graphene reduces the carrier mobility and degrades the performance of the graphene device, which is expected to affect the quantum Hall effect (QHE). This study investigated the influence of individual GBs on the QH state at different stitching angles of the GB in a monolayer CVD graphene. The measured voltage probes of the equipotential line in the QH state showed that the longitudinal resistance (R_xx) was affected by the scattering of the GB only in the low carrier concentration region, and the standard QHE of a monolayer graphene was observed regardless of the stitching angle of the GB. In addition, a controlled device with an added metal bar placed in the middle of the Hall bar configuration was introduced. Despite the fact that the equipotential lines in the controlled device were broken by the additional metal bar, only the R_xx was affected by nonzero resistance, whereas the Hall resistance (R_xy) revealed the well-quantized plateaus in the QH state. Thus, our study clarifies the effect of individual GBs on the QH states of graphenes.

Massive and Topological Surface States in Tensile-Strained HgTe

Magneto-transport measurements on gated high-mobility heterostructures containing a 60 nm layer of tensile-strained HgTe, a three-dimensional topological insulator, show well-developed Hall quantization from surface states both in the n- as well as in the p-type regime. While the n-type behavior is due to transport in the topological surface state of the material, we find from 8-orbital k·p calculations that the p-type transport results from massive Volkov-Pankratov states. Their formation prevents the Dirac point and thus the p-conducting topological surface state from being accessible in transport experiments. This interpretation is supported by low-field magneto-transport experiments demonstrating the coexistence of n-conducting topological surface states and p-conducting Volkov-Pankratov states at the relevant gate voltages.

Andreev Reflections in NbN/Graphene Junctions under Large Magnetic Fields

Hybrid superconductor/graphene (SC/g) junctions are excellent candidates for investigating correlations between Cooper pairs and quantum Hall (QH) edge modes. Experimental studies are challenging as Andreev reflections are extremely sensitive to junction disorder, and high magnetic fields are required to form QH edge states. We fabricated low-resistance SC/g interfaces, composed of graphene edge contacted with NbN with a barrier strength of Z ≈ 0.4, that remain superconducting under magnetic fields larger than 18 T. We establish the role of graphene's Dirac band structure on zero-field Andreev reflections and demonstrate dynamic tunability of the Andreev reflection spectrum by moving the boundary between specular and retro Andreev reflections with parallel magnetic fields. Through the application of perpendicular magnetic fields, we observe an oscillatory suppression of the 2-probe conductance in the ν = 4 Landau level attributed to the reduced efficiency of Andreev processes at the NbN/g interface, consistent with theoretical predictions.

Bilayer Quantum Hall States in an n-Type Wide Tellurium Quantum Well

Tellurium (Te) is a narrow bandgap semiconductor with a unique chiral crystal structure. The topological nature of electrons in the Te conduction band can be studied by realizing n-type doping using atomic layer deposition (ALD) technique on two-dimensional (2D) Te film. In this work, we fabricated and measured the double-gated n-type Te Hall-bar devices, which can operate as two separate or coupled electron layers controlled by the top gate and back gate. Profound Shubnikov-de Haas (SdH) oscillations are observed in both top and bottom electron layers. Landau level hybridization between two layers, compound and charge-transferable bilayer quantum Hall states at filling factor ν = 4, 6, and 8, are analyzed. Our work opens the door for the study of Weyl physics in coupled bilayer systems of 2D materials.

Fractional charge and fractional statistics in the quantum Hall effects

Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.

Odd Integer Quantum Hall States with Interlayer Coherence in Twisted Bilayer Graphene

We report on the quantum Hall effect in two stacked graphene layers rotated by 2°. The tunneling strength among the layers can be varied from very weak to strong via the mechanism of magnetic breakdown when tuning the density. Odd-integer quantum Hall physics is not anticipated in the regime of suppressed tunneling for balanced layer densities, yet it is observed. We interpret this as a signature of Coulomb interaction induced interlayer coherence and Bose-Einstein condensation of excitons that form at half filling of each layer. A density imbalance gives rise to reentrant behavior due to a phase transition from the interlayer coherent state to incompressible behavior caused by simultaneous condensation of both layers in different quantum Hall states. With increasing overall density, magnetic breakdown gains the upper hand. As a consequence of the enhanced interlayer tunneling, the interlayer coherent state and the phase transition vanish.

The Material Efforts for Quantized Hall Devices Based on Topological Insulators

A topological insulator (TI) is a kind of novel material hosting a topological band structure and plenty of exotic topological quantum effects. Achieving quantized electrical transport, including the quantum Hall effect (QHE) and the quantum anomalous Hall effect (QAHE), is an important aspect of realizing quantum devices based on TI materials. Intense efforts are made in this field, in which the most essential research is based on the optimization of realistic TI materials. Herein, the TI material development process is reviewed, focusing on the realization of quantized transport. Especially, for QHE, the strategies to increase the surface transport ratio and decrease the threshold magnetic field of QHE are examined. For QAHE, the evolution history of magnetic TIs is introduced, and the recently discovered magnetic TI candidates with intrinsic magnetizations are discussed in detail. Moreover, future research perspectives on these novel topological quantum effects are also evaluated.

30°-Twisted Bilayer Graphene Quasicrystals from Chemical Vapor Deposition

The artificial stacking of atomically thin crystals suffers from intrinsic limitations in terms of control and reproducibility of the relative orientation of exfoliated flakes. This drawback is particularly severe when the properties of the system critically depends on the twist angle, as in the case of the dodecagonal quasicrystal formed by two graphene layers rotated by 30°. Here we show that large-area 30°-rotated bilayer graphene can be grown deterministically by chemical vapor deposition on Cu, eliminating the need of artificial assembly. The quasicrystals are easily transferred to arbitrary substrates and integrated in high-quality hexagonal boron nitride-encapsulated heterostructures, which we process into dual-gated devices exhibiting carrier mobility up to 10⁵ cm²/(V s). From low-temperature magnetotransport, we find that the graphene quasicrystals effectively behave as uncoupled graphene layers, showing 8-fold degenerate quantum Hall states. This result indicates that the Dirac cones replica detected by previous photoemission experiments do not contribute to the electrical transport.

Bubble-Free Transfer Technique for High-Quality Graphene/Hexagonal Boron Nitride van der Waals Heterostructures

Bubbles at the interface of two-dimensional layered materials in van der Waals heterostructures cause deterioration in the quality of materials, thereby limiting the size and design of devices. In this paper, we report a simple all-dry transfer technique, with which the bubble formation can be avoided. As a key factor in the technique, a contact angle between a picked-up flake on a viscoelastic polymer stamp and another flake on a substrate was introduced by protrusion at the stamp surface. Using this technique, we demonstrated the fabrication of high-quality devices on the basis of graphene/hexagonal boron nitride heterostructures with a large bubble-free region. Additionally, the technique can be used to remove unnecessary flakes on a substrate under an optical microscopic scale. Most importantly, it improves the yield and throughput for the fabrication process of high-quality van der Waals heterostructure-based devices.

Landau Levels of Topologically-Protected Surface States Probed by Dual-Gated Quantum Capacitance

Spectroscopy of discrete Landau levels (LLs) in bulk-insulating three-dimensional topological insulators (3D TIs) in perpendicular magnetic field characterizes the Dirac nature of their surface states. Despite a number of studies demonstrating the quantum Hall effect (QHE) of topological surface states, quantitative evaluation of the LL energies, which serve as fundamental electronic quantities for study of the quantum states, is still limited. In this work, we explore the density of states of LLs by measuring quantum capacitance (C_Q) in a truly bulk insulating 3D TI via a van der Waals heterostructure configuration. By applying dual-gate voltages, we access the individual surface states' LLs and extract their chemical potentials to quantify the LL spacings of each surface. We evaluate the LLs' energies at two distinguished QH states, namely, dissipationless (ν = ±1) and dissipative (ν = 0) states in the 3D TI.

Giant magnetic field from moiré induced Berry phase in homobilayer semiconductors

When quasiparticles move in condensed matters, the texture of their internal quantum structure as a function of position and momentum can give rise to Berry phases that have profound effects on the material's properties. Seminal examples include the anomalous Hall and spin Hall effects from the momentum-space Berry phases in homogeneous crystals. Here, we explore a conjugate form of the electron Berry phase arising from the moiré pattern: the texture of atomic configurations in real space. In homobilayer transition metal dichalcogenides, we show that the real-space Berry phase from moiré patterns manifests as a periodic magnetic field with magnitudes of up to hundreds of Tesla. This quantity distinguishes moiré patterns from different origins, which can have an identical potential landscape, but opposite quantized magnetic flux per supercell. For low-energy carriers, the homobilayer moirés realize topological flux lattices for the quantum-spin Hall effect. An interlayer bias can continuously tune the spatial profile of the moiré magnetic field, whereas the flux per supercell is a topological quantity that can only have a quantized jump observable at a moderate bias. We also reveal the important role of the non-Abelian Berry phase in shaping the energy landscape in small moiré patterns. Our work points to new possibilities to access ultra-high magnetic fields that can be tailored to the nanoscale by electrical and mechanical controls.

Development of gateless quantum Hall checkerboard p-n junction devices

Measurements of fractional multiples of the ν = 2 plateau quantized Hall resistance (R H ≈ 12906 Ω) were enabled by the utilization of multiple current terminals on millimetre-scale graphene p-n junction devices fabricated with interfaces along both lateral directions. These quantum Hall resistance checkerboard devices have been demonstrated to match quantized resistance outputs numerically calculated with the LTspice circuit simulator. From the devices' functionality, more complex embodiments of the quantum Hall resistance checkerboard were simulated to highlight the parameter space within which these devices could operate. Moreover, these measurements suggest that the scalability of p-n junction fabrication on millimetre or centimetre scales is feasible with regards to graphene device manufacturing by using the far more efficient process of standard ultraviolet lithography.

Analytical determination of atypical quantized resistances in graphene p-n junctions

A mathematical approach is introduced for predicting quantized resistances in graphene p-n junction devices that utilize more than a single entry and exit point for electron flow. Depending on the configuration of an arbitrary number of terminals, electrical measurements yield nonconventional, fractional multiples of the typical quantized Hall resistance at the v = 2 plateau (R H ≈ 12906 Ω) and take the form:a b R H . This theoretical formulation is independent of material, and applications to other material systems that exhibit quantum Hall behaviors are to be expected. Furthermore, this formulation is supported with experimental data from graphene devices with multiple source and drain terminals.

Analysing quantized resistance behaviour in graphene Corbino p-n junction devices

Just a few of the promising applications of graphene Corbino pnJ devices include two-dimensional Dirac fermion microscopes, custom programmable quantized resistors, and mesoscopic valley filters. In some cases, device scalability is crucial, as seen in fields like resistance metrology, where graphene devices are required to accommodate currents of the order 100 μA to be compatible with existing infrastructure. However, fabrication of these devices still poses many difficulties. In this work, unusual quantized resistances are observed in epitaxial graphene Corbino p-n junction devices held at the ν = 2 plateau (R H ≈ 12906 Ω) and agree with numerical simulations performed with the LTspice circuit simulator. The formulae describing experimental and simulated data are empirically derived for generalized placement of up to three current terminals and accurately reflects observed partial edge channel cancellation. These results support the use of ultraviolet lithography as a way to scale up graphene-based devices with suitably narrow junctions that could be applied in a variety of subfields.

Superconducting Contact Geometries for Next-Generation Quantized Hall Resistance Standards

Precision quantum Hall resistance measurements can be greatly improved when implementing new electrical contact geometries made from superconducting NbTiN. The sample designs described here minimize undesired resistances at contacts and interconnections, enabling further enhancement of device size and complexity when pursuing next-generation quantized Hall resistance devices.

Reliable Postprocessing Improvement of van der Waals Heterostructures

The successful assembly of heterostructures consisting of several layers of different 2D materials in arbitrary order by exploiting van der Waals forces has truly been a game changer in the field of low-dimensional physics. For instance, the encapsulation of graphene or MoS₂ between atomically flat hexagonal boron nitride (hBN) layers with strong affinity and graphitic gates that screen charge impurity disorder provided access to a plethora of interesting physical phenomena by drastically boosting the device quality. The encapsulation is accompanied by a self-cleansing effect at the interfaces. The otherwise predominant charged impurity disorder is minimized, and random strain fluctuations ultimately constitute the main source of residual disorder. Despite these advances, the fabricated heterostructures still vary notably in their performance. Although some achieve record mobilities, others only possess mediocre quality. Here, we report a reliable method to improve fully completed van der Waals heterostructure devices with a straightforward postprocessing surface treatment based on thermal annealing and contact mode atomic force microscopy (AFM). The impact is demonstrated by comparing magnetotransport measurements before and after the AFM treatment on one and the same device as well as on a larger set of treated and untreated devices to collect device statistics. Both the low-temperature properties and the room temperature electrical characteristics, as relevant for applications, improve on average substantially. We surmise that the main beneficial effect arises from reducing nanometer scale corrugations at the interfaces, that is, the detrimental impact of random strain fluctuations.

Quantum-Hall to Insulator Transition in Ultra-Low-Carrier-Density Topological Insulator Films and a Hidden Phase of the Zeroth Landau Level

A key feature of the topological surface state under a magnetic field is the presence of the zeroth Landau level at the zero energy. Nonetheless, it is challenging to probe the zeroth Landau level due to large electron-hole puddles smearing its energy landscape. Here, by developing ultra-low-carrier density topological insulator Sb₂ Te₃ films, an extreme quantum limit of the topological surface state is reached and a hidden phase at the zeroth Landau level is uncovered. First, an unexpected quantum-Hall-to-insulator-transition near the zeroth Landau level is discovered. Then, through a detailed scaling analysis, it is found that this quantum-Hall-to-insulator-transition belongs to a new universality class, implying that the insulating phase discovered here has a fundamentally different origin from those in nontopological systems.

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.

Electronic and Thermal Properties of Graphene and Recent Advances in Graphene Based Electronics Applications

Recently, graphene has been extensively researched in fundamental science and engineering fields and has been developed for various electronic applications in emerging technologies owing to its outstanding material properties, including superior electronic, thermal, optical and mechanical properties. Thus, graphene has enabled substantial progress in the development of the current electronic systems. Here, we introduce the most important electronic and thermal properties of graphene, including its high conductivity, quantum Hall effect, Dirac fermions, high Seebeck coefficient and thermoelectric effects. We also present up-to-date graphene-based applications: optical devices, electronic and thermal sensors, and energy management systems. These applications pave the way for advanced biomedical engineering, reliable human therapy, and environmental protection. In this review, we show that the development of graphene suggests substantial improvements in current electronic technologies and applications in healthcare systems.

Two-Dimensional Quantum Transport in Free-Standing InSb Nanosheets

Low-dimensional narrow band gap III-V compound semiconductors, such as InAs and InSb, have attracted much attention as one of promising platforms for studying Majorana zero modes and non-Abelian statistics relevant for topological quantum computation. So far, most of experimental studies were performed on hybrid devices based on one-dimensional semiconductor nanowires. In order to build complex topological circuits toward scalable quantum computing, exploring high-mobility two-dimensional (2D) III-V compound electron system with strong spin-orbit coupling is highly desirable. Here, we study quantum transport in high-mobility InSb nanosheet grown by molecular-beam epitaxy. The observations of Shubnikov-de Hass oscillations and quantum Hall states, together with the angular dependence of magnetotransport measurements, provide the evidence for the 2D nature of electronic states in InSb nanosheet. The presence of strong spin-orbit coupling in the InSb nanosheet is verified by the low-field magnetotransport measurements, characterized by weak antilocalization effect. Finally, we demonstrate the realization of high-quality InSb nanosheet-superconductor junctions with transparent interface. Our results not only advance the study of 2D quantum transport but also open up opportunities for developing hybrid topological devices based on 2D semiconducting nanosheets with strong spin-orbit coupling.

The Quantum Hall Effect in the Era of the New SI

The quantum Hall effect (QHE), and devices reliant on it, will continue to serve as the foundation of the ohm while also expanding its territory into other SI derived units. The foundation, evolution, and significance of all of these devices exhibiting some form of the QHE will be described in the context of optimizing future electrical resistance standards. As the world adapts to using the quantum SI, it remains essential that the global metrology community pushes forth and continues to innovate and produce new technologies for disseminating the ohm and other electrical units.

Next-generation crossover-free quantum Hall arrays with superconducting interconnections

This work presents precision measurements of quantized Hall array resistance devices using superconducting, crossover-free, multiple interconnections as well as graphene split contacts. These new techniques successfully eliminate the accumulation of internal resistances and leakage currents that typically occur at interconnections and crossing leads between interconnected devices. As a result, a scalable quantized Hall resistance array is obtained with a nominal value that is as precise and stable as that from single-element quantized Hall resistance standards.

Imaging topology of Hofstadter ribbons

Physical systems with non-trivial topological order find direct applications in metrology (Klitzing et al 1980 Phys. Rev. Lett. 45 494-7) and promise future applications in quantum computing (Freedman 2001 Found. Comput. Math. 1 183-204; Kitaev 2003 Ann. Phys. 303 2-30). The quantum Hall effect derives from transverse conductance, quantized to unprecedented precision in accordance with the system's topology (Laughlin 1981 Phys. Rev. B 23 5632-33). At magnetic fields beyond the reach of current condensed matter experiment, around 10⁴ T, this conductance remains precisely quantized with values based on the topological order (Thouless et al 1982 Phys. Rev. Lett. 49 405-8). Hitherto, quantized conductance has only been measured in extended 2D systems. Here, we experimentally studied narrow 2D ribbons, just 3 or 5 sites wide along one direction, using ultracold neutral atoms where such large magnetic fields can be engineered (Jaksch and Zoller 2003 New J. Phys. 5 56; Miyake et al 2013 Phys. Rev. Lett. 111 185302; Aidelsburger et al 2013 Phys. Rev. Lett. 111 185301; Celi et al 2014 Phys. Rev. Lett. 112 043001; Stuhl etal 2015 Science 349 1514; Mancini et al 2015 Science 349 1510; An et al 2017 Sci. Adv. 3). We microscopically imaged the transverse spatial motion underlying the quantized Hall effect. Our measurements identify the topological Chern numbers with typical uncertainty of 5%, and show that although band topology is only properly defined in infinite systems, its signatures are striking even in nearly vanishingly thin systems.

Topological Insulator-Based van der Waals Heterostructures for Effective Control of Massless and Massive Dirac Fermions

Three dimensional (3D) topological insulators (TIs) are an important class of materials with applications in electronics, spintronics and quantum computing. With the recent development of truly bulk insulating 3D TIs, it has become possible to realize surface dominated phenomena in electrical transport measurements e.g. the quantum Hall (QH) effect of massless Dirac fermions in topological surface states (TSS). However, to realize more advanced devices and phenomena, there is a need for a platform to tune the TSS or modify them e.g. gap them by proximity with magnetic insulators, in a clean manner. Here we introduce van der Waals (vdW) heterostructures in the form of topological insulator/insulator/graphite to effectively control chemical potential of the TSS. Two types of gate dielectrics, normal insulator hexagonal boron nitride (hBN) and ferromagnetic insulator Cr₂Ge₂Te₆ (CGT) are utilized to tune charge density of TSS in the quaternary TI BiSbTeSe₂. hBN/graphite gating in the QH regime shows improved quantization of TSS by suppression of magnetoconductivity of massless Dirac fermions. CGT/graphite gating of massive Dirac fermions in the QH regime yields half-quantized Hall conductance steps and a measure of the Dirac gap. Our work shows the promise of the vdW platform in creating advanced high-quality TI-based devices.

Quantum Hall Effect in Electron-Doped Black Phosphorus Field-Effect Transistors

The advent of black phosphorus field-effect transistors (FETs) has brought new possibilities in the study of two-dimensional (2D) electron systems. In a black phosphorus FET, the gate induces highly anisotropic 2D electron and hole gases. Although the 2D hole gas in black phosphorus has reached high carrier mobilities that led to the observation of the integer quantum Hall effect, the improvement in the sample quality of the 2D electron gas (2DEG) has however been only moderate; quantum Hall effect remained elusive. Here, we obtain high quality black phosphorus 2DEG by defining the 2DEG region with a prepatterned graphite local gate. The graphite local gate screens the impurity potential in the 2DEG. More importantly, it electrostatically defines the edge of the 2DEG, which facilitates the formation of well-defined edge channels in the quantum Hall regime. The improvements enable us to observe precisely quantized Hall plateaus in electron-doped black phosphorus FET. Magneto-transport measurements under high magnetic fields further revealed a large effective mass and an enhanced Landé g-factor, which points to strong electron-electron interaction in black phosphorus 2DEG. Such strong interaction may lead to exotic many-body quantum states in the fractional quantum Hall regime.

Quantum Transport and Band Structure Evolution under High Magnetic Field in Few-Layer Tellurene

Quantum Hall effect (QHE) is a macroscopic manifestation of quantized states that only occurs in confined two-dimensional electron gas (2DEG) systems. Experimentally, QHE is hosted in high-mobility 2DEG with large external magnetic field at low temperature. Two-dimensional van der Waals materials, such as graphene and black phosphorus, are considered interesting material systems to study quantum transport because they could unveil unique host material properties due to the easy accessibility of monolayer or few-layer thin films at the 2D quantum limit. For the first time, we report direct observation of QHE in a novel low-dimensional material system, tellurene. High-quality 2D tellurene thin films were acquired from recently reported hydrothermal method with high hole mobility of nearly 3000 cm²/(V s) at low temperatures, which allows the observation of well-developed Shubnikov-de Haas (SdH) oscillations and QHE. A four-fold degeneracy of Landau levels in SdH oscillations and QHE was revealed. Quantum oscillations were investigated under different gate biases, tilted magnetic fields, and various temperatures, and the results manifest the inherent information on the electronic structure of Te. Anomalies in both temperature-dependent oscillation amplitudes and transport characteristics were observed that are ascribed to the interplay between the Zeeman effect and spin-orbit coupling, as depicted by the density functional theory calculations.

Examining epitaxial graphene surface conductivity and quantum Hall device stability with Parylene passivation

Homogeneous, single-crystal, monolayer epitaxial graphene (EG) is the one of most promising candidates for the advancement of quantized Hall resistance (QHR) standards. A remaining challenge for the electrical characterization of EG-based quantum Hall devices as a useful tool for metrology is that they are electrically unstable when exposed to air due to the adsorption of and interaction with atmospheric molecular dopants. The resulting changes in the charge carrier density become apparent by variations in the surface conductivity, the charge carrier mobility, and may result in a transition from n-type to p-type conductivity. This work evaluates the use of Parylene C and Parylene N as passivation layers for EG. Electronic transport of EG quantum Hall devices and non-contact microwave perturbation measurements of millimeter-sized areas of EG are both performed on bare and Parylene coated samples to test the efficacy of the passivation layers. The reported results, showing a significant improvement in passivation due to Parylene deposition, suggest a method for the mass production of millimeter-scale graphene devices with stable electrical properties.

Solution to the Hole-Doping Problem and Tunable Quantum Hall Effect in Bi2Se3 Thin Films

Bi₂Se₃, one of the most widely studied topological insulators (TIs), is naturally electron-doped due to n-type native defects. However, many years of efforts to achieve p-type Bi₂Se₃ thin films have failed so far. Here, we provide a solution to this long-standing problem, showing that the main culprit has been the high density of interfacial defects. By suppressing these defects through an interfacial engineering scheme, we have successfully implemented p-type Bi₂Se₃ thin films down to the thinnest topological regime. On this platform, we present the first tunable quantum Hall effect (QHE) study in Bi₂Se₃ thin films and reveal not only significantly asymmetric QHE signatures across the Dirac point but also the presence of competing anomalous states near the zeroth Landau level. The availability of doping tunable Bi₂Se₃ thin films will now make it possible to implement various topological quantum devices, previously inaccessible.

Epitaxial graphene for quantum resistance metrology

Graphene-based quantised Hall resistance standards promise high precision for the unit ohm under less exclusive measurement conditions, enabling the use of compact measurement systems. To meet the requirements of metrological applications, national metrology institutes developed large-area monolayer graphene growth methods for uniform material properties and optimized device fabrication techniques. Precision measurements of the quantized Hall resistance showing the advantage of graphene over GaAs-based resistance standards demonstrate the remarkable achievements realized by the research community. This work provides an overview over the state-of-the-art technologies in this field.

Giant Valley-Isospin Conductance Oscillations in Ballistic Graphene

At high magnetic fields the conductance of graphene is governed by the half-integer quantum Hall effect. By local electrostatic gating a p-n junction perpendicular to the graphene edges can be formed, along which quantum Hall channels copropagate. It has been predicted by Tworzidło and co-workers that if only the lowest Landau level is filled on both sides of the junction, the conductance is determined by the valley (isospin) polarization at the edges and by the width of the flake. This effect remained hidden so far due to scattering between the channels copropagating along the p-n interface (equilibration). Here we investigate p-n junctions in encapsulated graphene with a movable p-n interface with which we are able to probe the edge-configuration of graphene flakes. We observe large quantum conductance oscillations on the order of e²/h which solely depend on the p-n junction position providing the first signature of isospin-defined conductance. Our experiments are underlined by quantum transport calculations.

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.

Electron-hole asymmetry of the topological surface states in strained HgTe

Topological insulators are a new class of materials with an insulating bulk and topologically protected metallic surface states. Although it is widely assumed that these surface states display a Dirac-type dispersion that is symmetric above and below the Dirac point, this exact equivalence across the Fermi level has yet to be established experimentally. Here, we present a detailed transport study of the 3D topological insulator-strained HgTe that strongly challenges this prevailing viewpoint. First, we establish the existence of exclusively surface-dominated transport via the observation of an ambipolar surface quantum Hall effect and quantum oscillations in the Seebeck and Nernst effect. Second, we show that, whereas the thermopower is diffusion driven for surface electrons, both diffusion and phonon drag contributions are essential for the hole surface carriers. This distinct behavior in the thermoelectric response is explained by a strong deviation from the linear dispersion relation for the surface states, with a much flatter dispersion for holes compared with electrons. These findings show that the metallic surface states in topological insulators can exhibit both strong electron-hole asymmetry and a strong deviation from a linear dispersion but remain topologically protected.

Achieving Ultrahigh Carrier Mobility in Two-Dimensional Hole Gas of Black Phosphorus

We demonstrate that a field-effect transistor (FET) made of few-layer black phosphorus (BP) encapsulated in hexagonal boron nitride (h-BN) in vacuum exhibits a room-temperature hole mobility of 5200 cm²/(Vs), being limited just by the phonon scattering. At cryogenic temperatures, the FET mobility increases up to 45 000 cm²/(Vs), which is five times higher compared to the mobility obtained in earlier reports. The unprecedentedly clean h-BN-BP-h-BN heterostructure exhibits Shubnikov-de Haas oscillations and a quantum Hall effect with Landau level (LL) filling factors down to v = 2 in conventional laboratory magnetic fields. Moreover, carrier density independent effective mass of m^* = 0.26 m₀ is measured, and a Landé g-factor of g = 2.47 is reported. Furthermore, an indication for a distinct hole transport behavior with up- and down-spin orientations is found.

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.