Selective equilibration of spin-polarized quantum Hall edge states in graphene

Uncovering the spin ordering in magic-angle graphene via edge state equilibration

The flat bands in magic-angle twisted bilayer graphene (MATBG) provide an especially rich arena to investigate interaction-driven ground states. While progress has been made in identifying the correlated insulators and their excitations at commensurate moiré filling factors, the spin-valley polarizations of the topological states that emerge at high magnetic field remain unknown. Here we introduce a technique based on twist-decoupled van der Waals layers that enables measurement of their electronic band structure and-by studying the backscattering between counter-propagating edge states-the determination of the relative spin polarization of their edge modes. We find that the symmetry-broken quantum Hall states that extend from the charge neutrality point in MATBG are spin unpolarized at even integer filling factors. The measurements also indicate that the correlated Chern insulator emerging from half filling of the flat valence band is spin unpolarized and suggest that its conduction band counterpart may be spin polarized.

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.

Anomalous quantized plateaus in two-dimensional electron gas with gate confinement

Quantum information can be coded by the topologically protected edges of fractional quantum Hall (FQH) states. Investigation on FQH edges in the hope of searching and utilizing non-Abelian statistics has been a focused challenge for years. Manipulating the edges, e.g. to bring edges close to each other or to separate edges spatially, is a common and essential step for such studies. The FQH edge structures in a confined region are typically presupposed to be the same as that in the open region in analysis of experimental results, but whether they remain unchanged with extra confinement is obscure. In this work, we present a series of unexpected plateaus in a confined single-layer two-dimensional electron gas (2DEG), which are quantized at anomalous fractions such as 9/4, 17/11, 16/13 and the reported 3/2. We explain all the plateaus by assuming surprisingly larger filling factors in the confined region. Our findings enrich the understanding of edge states in the confined region and in the applications of gate manipulation, which is crucial for the experiments with quantum point contact and interferometer.

Heat Equilibration of Integer and Fractional Quantum Hall Edge Modes in Graphene

Hole-conjugate states of the fractional quantum Hall effect host counterpropagating edge channels which are thought to exchange charge and energy. These exchanges have been the subject of extensive theoretical and experimental works; in particular, it is yet unclear if the presence of integer quantum Hall edge channels stemming from fully filled Landau levels affects heat equilibration along the edge. In this Letter, we present heat transport measurements in quantum Hall states of graphene demonstrating that the integer channels can strongly equilibrate with the fractional ones, leading to markedly different regimes of quantized heat transport that depend on edge electrostatics. Our results allow for a better comprehension of the complex edge physics in the fractional quantum Hall regime.

Spin-Selective Equilibration among Integer Quantum Hall Edge Channels

The equilibration between quantum Hall edge modes is known to depend on the disorder potential and the steepness of the edge. Modern samples with higher mobilities and setups with lower electron temperatures call for a further exploration of the topic. We develop a framework to systematically measure and analyze the equilibration of many (up to 8) integer edge modes. Our results show that spin-selective coupling dominates even for non-neighboring channels with parallel spin. Changes in magnetic field and bulk density let us control the equilibration until it is almost completely suppressed and dominated only by individual microscopic scatterers. This method could serve as a guideline to investigate and design improved devices, and to study fractional and other exotic states.

Compact SQUID Realized in a Double-Layer Graphene Heterostructure

2D systems that host 1D helical states are advantageous from the perspective of scalable topological quantum computation when coupled to a superconductor. Graphene is particularly promising for its high electronic quality, its versatility in van der Waals heterostructures, and its electron- and hole-like degenerate 0th Landau level. Here we study a compact double-layer graphene SQUID (superconducting quantum interference device), where the superconducting loop is reduced to the superconducting contacts connecting two parallel graphene Josephson junctions. Despite the small size of the SQUID, it is fully tunable by the independent gate control of the chemical potentials in both layers. Furthermore, both Josephson junctions show a skewed current-phase relationship, indicating the presence of superconducting modes with high transparency. In the quantum Hall regime, we measure a well-defined conductance plateau of 2e²/h indicative of counter-propagating edge channels in the two layers.

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.

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.

Topological insulator n-p-n junctions in a magnetic field

Electrical transport in three dimensional topological insulators (TIs) occurs through spin-momentum locked topological surface states that enclose an insulating bulk. In the presence of a magnetic field, surface states get quantized into Landau levels giving rise to chiral edge states that are naturally spin-polarized due to spin momentum locking. It has been proposed that p-n junctions of TIs exposed to external magnetic fields can manifest unique spin dependent effects, apart from forming basic building blocks for highly functional spintronic devices. Here, for the first time we study electrostatically defined n-p-n junctions of dual-gated devices of the three dimensional topological insulator BiSbTe1.25Se1.75 in the presence of a strong magnetic field, revealing striking signatures of suppressed or enhanced electrical transport depending upon the chirality of quantum Hall edge states created at the n-p and p-n junction interfaces. Theoretical modeling combining the electrostatics of the dual gated TI n-p-n junction with the Landauer Buttiker formalism for transport through a network of chiral edge states explains our experimental data. Our work not only opens up a route towards exotic spintronic devices but also provides a test bed for investigating the unique signatures of quantum Hall effects in topological insulators.

Electrical generation and detection of spin waves in a quantum Hall ferromagnet

Spin waves are collective excitations of magnetic systems. An attractive setting for studying long-lived spin-wave physics is the quantum Hall (QH) ferromagnet, which forms spontaneously in clean two-dimensional electron systems at low temperature and in a perpendicular magnetic field. We used out-of-equilibrium occupation of QH edge channels in graphene to excite and detect spin waves in magnetically ordered QH states. Our experiments provide direct evidence for long-distance spin-wave propagation through different ferromagnetic phases in the N = 0 Landau level, as well as across the insulating canted antiferromagnetic phase. Our results will enable experimental investigation of the fundamental magnetic properties of these exotic two-dimensional electron systems.

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.

Quantum transport in graphene p-n junctions with moiré superlattice modulation

We present simulations of quantum transport in graphene p-n junctions (pnJs) in which moiré superlattice potentials are incorporated to demonstrate the interplay between pnJs and moiré superlattice potentials. It is shown that the longitudinal and Hall resistivity maps can be strongly modulated by the pnJ profile, junction height, and moiré potentials. Device resistance measurements are subsequently performed on graphene/hexagonal- boron-nitride heterostructure samples with accurate alignment of crystallographic orientations to complement and support the simulation results.

Interplay of Chiral and Helical States in a Quantum Spin Hall Insulator Lateral Junction

We study the electronic transport across an electrostatically gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without an applied magnetic field. We control the carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the bulk gap, the magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus that reflect the equilibration between 1D chiral modes across the junction. As the carrier density approaches zero in the central region and at moderate fields, we observe oscillations in the resistance that we attribute to Fabry-Perot interference in the helical states, enabled by the broken time reversal symmetry. At higher fields, those oscillations disappear, in agreement with the expected absence of helical states when band inversion is lifted.

Mach-Zehnder interferometry using spin- and valley-polarized quantum Hall edge states in graphene

Confined to a two-dimensional plane, electrons in a strong magnetic field travel along the edge in one-dimensional quantum Hall channels that are protected against backscattering. These channels can be used as solid-state analogs of monochromatic beams of light, providing a unique platform for studying electron interference. Electron interferometry is regarded as one of the most promising routes for studying fractional and non-Abelian statistics and quantum entanglement via two-particle interference. However, creating an edge-channel interferometer in which electron-electron interactions play an important role requires a clean system and long phase coherence lengths. We realize electronic Mach-Zehnder interferometers with record visibilities of up to 98% using spin- and valley-polarized edge channels that copropagate along a pn junction in graphene. We find that interchannel scattering between same-spin edge channels along the physical graphene edge can be used to form beamsplitters, whereas the absence of interchannel scattering along gate-defined interfaces can be used to form isolated interferometer arms. Surprisingly, our interferometer is robust to dephasing effects at energies an order of magnitude larger than those observed in pioneering experiments on GaAs/AlGaAs quantum wells. Our results shed light on the nature of edge-channel equilibration and open up new possibilities for studying exotic electron statistics and quantum phenomena.

Lateral p-n Junction in an Inverted InAs/GaSb Double Quantum Well

We present transport measurements on a lateral p-n junction in an inverted InAs/GaSb double quantum well at zero and nonzero perpendicular magnetic fields. At a zero magnetic field, the junction exhibits diodelike behavior in accordance with the presence of a hybridization gap. With an increasing magnetic field, we explore the quantum Hall regime where spin-polarized edge states with the same chirality are either reflected or transmitted at the junction, whereas those of opposite chirality undergo a mixing process, leading to full equilibration along the width of the junction independent of spin. These results lay the foundations for using p-n junctions in InAs/GaSb double quantum wells to probe the transition between the topological quantum spin Hall and quantum Hall states.

Oscillating Magnetoresistance in Graphene p-n Junctions at Intermediate Magnetic Fields

We report on the observation of magnetoresistance oscillations in graphene p-n junctions. The oscillations have been observed for six samples, consisting of single-layer and bilayer graphene, and persist up to temperatures of 30 K, where standard Shubnikov-de Haas oscillations are no longer discernible. The oscillatory magnetoresistance can be reproduced by tight-binding simulations. We attribute this phenomenon to the modulated densities of states in the n- and p-regions.

Tunable transmission of quantum Hall edge channels with full degeneracy lifting in split-gated graphene devices

Charge carriers in the quantum Hall regime propagate via one-dimensional conducting channels that form along the edges of a two-dimensional electron gas. Controlling their transmission through a gate-tunable constriction, also called quantum point contact, is fundamental for many coherent transport experiments. However, in graphene, tailoring a constriction with electrostatic gates remains challenging due to the formation of p–n junctions below gate electrodes along which electron and hole edge channels co-propagate and mix, short circuiting the constriction. Here we show that this electron–hole mixing is drastically reduced in high-mobility graphene van der Waals heterostructures thanks to the full degeneracy lifting of the Landau levels, enabling quantum point contact operation with full channel pinch-off. We demonstrate gate-tunable selective transmission of integer and fractional quantum Hall edge channels through the quantum point contact. This gate control of edge channels opens the door to quantum Hall interferometry and electron quantum optics experiments in the integer and fractional quantum Hall regimes of graphene.

Quantum point contacts are gate-tunable constrictions allowing for control of charge carrier transmission in 2D electron gases. Here, the authors fabricate a hBN/graphene/hBN van der Waals heterojunction to enable quantum point contact devices in the integer and fractional quantum Hall regimes.

Helical edge states and fractional quantum Hall effect in a graphene electron-hole bilayer

Helical 1D electronic systems are a promising route towards realizing circuits of topological quantum states that exhibit non-Abelian statistics. Here, we demonstrate a versatile platform to realize 1D systems made by combining quantum Hall (QH) edge states of opposite chiralities in a graphene electron-hole bilayer at moderate magnetic fields. Using this approach, we engineer helical 1D edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong non-local transport signals and suppressed backscattering due to the opposite spin polarizations of the counterpropagating modes. Unlike other approaches used for realizing helical states, the graphene electron-hole bilayer can be used to build new 1D systems incorporating fractional edge states. Indeed, we are able to tune the bilayer devices into a regime hosting fractional and integer edge states of opposite chiralities, paving the way towards 1D helical conductors with fractional quantum statistics.

Gate-controlled conductance enhancement from quantum Hall channels along graphene p-n junctions

The formation of quantum Hall channels inside the bulk of graphene is studied using various contact and gate geometries. p-n junctions are created along the longitudinal direction of samples, and enhanced conductance is observed in the case of bipolar doping due to the new conducting channels formed in the bulk, whose position, propagating direction and, in one geometry, coupling to electrodes are determined by the gate-controlled filling factor across the device. This effect could be exploited to probe the behavior and interaction of quantum Hall channels protected against uncontrolled scattering at the edges.

Spin Superfluidity in the ν=0 Quantum Hall State of Graphene

Strong electron interactions can lead to a variety of broken-symmetry phases in monolayer graphene. In the quantum Hall regime, the interaction effect are enhanced by the formation of highly degenerate Landau levels, catalyzing the emergence of such phases. Recent magnetotransport studies show evidence that the ν=0 quantum Hall state of graphene is in an insulating canted antiferromagnetic phase with the Néel vector lying within the graphene plane. Here, we show that this Néel order can be detected via two-terminal spin transport. We find that a dynamic and inhomogeneous texture of the Néel vector can mediate nearly dissipationless (superfluid) transport of spin angular momentum polarized along the z axis, which could serve as a strong support for the antiferromagnetic scenario. The injection and detection of spin current in the ν=0 region can be achieved using the two spin-polarized edge channels of the |ν|=2 quantum Hall state. Measurements of the dependence of the spin current on the length of the ν=0 region would provide direct evidence for spin superfluidity.

Manipulating interface states in monolayer-bilayer graphene planar junctions

We report on transport properties of monolayer-bilayer graphene planar junctions in a magnetic field. Due to its unique geometry, the edge and interface states can be independently manipulated by either interlayer potential or Zeeman field, and the conductance exhibits interesting quantized behaviors. In the hybrid graphene junction, the quantum Hall (QH) conductance is no longer antisymmetric with respect to the charge neutrality point. When the Zeeman field is considered, a quantum spin Hall (QSH) phase is found in the monolayer region while the weak-QSH phase stays in the bilayer region. In the presence of both interlayer potential and Zeeman field, the bilayer region hosts a QSH phase, whereas the monolayer region is still in a QH phase, leading to a spin-polarized current in the interface. In particular, the QSH phase remains robust against the disorder.

Edge mixing dynamics in graphene p-n junctions in the quantum Hall regime

Massless Dirac electron systems such as graphene exhibit a distinct half-integer quantum Hall effect, and in the bipolar transport regime co-propagating edge states along the p–n junction are realized. Additionally, these edge states are uniformly mixed at the junction, which makes it a unique structure to partition electrons in these edge states. Although many experimental works have addressed this issue, the microscopic dynamics of electron partition in this peculiar structure remains unclear. Here we performed shot-noise measurements on the junction in the quantum Hall regime as well as at zero magnetic field. We found that, in sharp contrast with the zero-field case, the shot noise in the quantum Hall regime is finite in the bipolar regime, but is strongly suppressed in the unipolar regime. Our observation is consistent with the theoretical prediction and gives microscopic evidence that the edge states are uniquely mixed along the p–n junction.

A graphene p–n junction can be created by connecting electrical gates that generate electron-doped and hole-doped areas in a flake. Here, the authors use shot-noise measurements to provide microscopic evidence that edge states are uniquely mixed along the junction in the quantum Hall regime.

Quantum Hall conductance of graphene combined with charge-trap memory operation

The combination of quantum Hall conductance and charge-trap memory operation was qualitatively examined using a graphene field-effect transistor. The characteristics of two terminal quantum Hall conductance appeared clearly on the background of a huge conductance hysteresis during a gate-voltage sweep for a device using monolayer graphene as a channel,hexagonal boron-nitride flakes as a tunneling dielectric and defective silicon oxide as the charge storage node. Even though there was a giant shift of the charge neutrality point, the deviation of quantized resistance value at the state of filling factor 2 was less than 1.6% from half of the von Klitzing constant. At high Landau level indices, the behaviors of quantum conductance oscillation between the increasing and the decreasing electron densities were identical in spite ofa huge memory window exceeding 100 V. Our results indicate that the two physical phenomena, two-terminal quantum Hall conductance and charge-trap memory operation, can be integrated into one device without affecting each other.

Conductance oscillations induced by ballistic snake states in a graphene heterojunction

The realization of p-n junctions in graphene, combined with the gapless and chiral nature of its massless Dirac fermions has led to the observation of many intriguing phenomena such as the quantum Hall effect in the bipolar regime, Klein tunnelling and Fabry-Pérot interferences, all of which involve electronic transport across p-n junctions. Ballistic snake states propagating along the p-n junctions have been predicted to induce conductance oscillations, manifesting their twisting nature. However, transport studies along p-n junctions have so far only been performed in low mobility devices. Here, we report the observation of conductance oscillations due to ballistic snake states along a p-n interface in high-quality graphene encapsulated by hexagonal boron nitride. These snake states are exceptionally robust as they can propagate over 12 μm, limited only by the size of our sample, and survive up to at least 120 K. The ability to guide carriers over a long distance provide a crucial building block for graphene-based electron optics.

Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene

The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary charge. Three decades later, the field of FQHE is still active with new discoveries and new technical developments. A significant portion of attention in FQHE has been dedicated to filling factor 5/2 state, for its unusual even denominator and possible application in topological quantum computation. Traditionally, FQHE has been observed in high-mobility GaAs heterostructure, but new materials such as graphene also open up a new area for FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in graphene.

Anomalous sequence of quantum Hall liquids revealing a tunable Lifshitz transition in bilayer graphene

Bilayer graphene is a unique system where both the Fermi energy and the low-energy electron dispersion can be tuned. This is brought about by an interplay between trigonal warping and the band gap opened by a transverse electric field. Here, we drive the Lifshitz transition in bilayer graphene to experimentally controllable carrier densities by applying a large transverse electric field to a h-BN-encapsulated bilayer graphene structure. We perform magnetotransport measurements and investigate the different degeneracies in the Landau level spectrum. At low magnetic fields, the observation of filling factors -3 and -6 quantum Hall states reflects the existence of three maxima at the top of the valence-band dispersion. At high magnetic fields, all integer quantum Hall states are observed, indicating that deeper in the valence band the constant energy contours are singly connected. The fact that we observe ferromagnetic quantum Hall states at odd-integer filling factors testifies to the high quality of our sample. This enables us to identify several phase transitions between correlated quantum Hall states at intermediate magnetic fields, in agreement with the calculated evolution of the Landau level spectrum. The observed evolution of the degeneracies, therefore, reveals the presence of a Lifshitz transition in our system.