Quantum Hall Regime Research Articles

Topologically Nontrivial Valley States in Bilayer Graphene Quantum Point Contacts.

We present measurements of quantized conductance in electrostatically induced quantum point contacts in bilayer graphene. The application of a perpendicular magnetic field leads to an intricate pattern of lifted and restored degeneracies with increasing field: at zero magnetic field the degeneracy of quantized one-dimensional subbands is four, because of a twofold spin and a twofold valley degeneracy. By switching on the magnetic field, the valley degeneracy is lifted. Because of the Berry curvature, states from different valleys split linearly in magnetic field. In the quantum Hall regime fourfold degenerate conductance plateaus reemerge. During the adiabatic transition to the quantum Hall regime, levels from one valley shift by two in quantum number with respect to the other valley, forming an interweaving pattern that can be reproduced by numerical calculations.

Spin-orbit coupling effects in the quantum Hall regime probed by electron spin resonance

The spin resonance of two-dimensional (2D) electrons confined in a high-quality 4.5-nm AlAs quantum well was studied in the regime of the integer quantum Hall effect. The electron $g$-factor extracted from the magnetic field position of the spin resonance at a fixed microwave frequency demonstrated a strong nonlinear dependence on the magnetic field with discontinuities around even filling factors. The value of the $g$-factor tended to increase with a decrease of the magnetic field around each odd filling. Furthermore, the $g$-factor at the exactly odd filling factor $\ensuremath{\nu}$ turned out to be dependent on $\ensuremath{\nu}$, suggesting the entanglement between the spin degree of freedom and the orbital motion of the electrons in the regime of the integer quantum Hall effect. This suggestion is further supported, as all the experimental data are well described, when a Dresselhaus-type spin-orbit interaction is introduced into the Hamiltonian of a single electron in the quantizing magnetic field. Surprisingly, such excellent agreement was observed even in the case of tilted magnetic fields. The fitting procedure allowed us to determine the strength of the Dresselhaus spin-orbit term in a 2D electron system and to extract the fundamentally important Dresselhaus constant for bulk AlAs. Unexpectedly, not only was single spin resonance observed around even fillings, it tended to split into two well-resolved lines. Yet this finding remains a mystery and highlights the need for further experimental and theoretical efforts.

The effects of the electrochemical capacitance on the ac admittance phase of a quantum point contact

We investigate the ac admittance of a quantum point contact (QPC) in quantum hall regime. Experiment data shows that the phase of the QPC admittance is not transmission independent. With the increasing of the QPC transmission, the phase increases in large magnetic field, but stays constant in small field. The theoretical works indicated that the Coulomb interaction between the counter-propagate channels is the main reason for the non-constant phase in large field. Besides this, we also studied the other types of Coulomb interactions. Especially, the Coulomb interaction between the channels across the QPC could make the sample behave like a capacitance and thus a change from the capacitive behavior to inductive behavior is expected when the QPC is opening. Our investigation demonstrates that the Coulomb interaction can serve as a sensitive detection method for the internal properties of quantum devices, in particular, at gigahertz frequencies.

Spin transport in a graphene normal-superconductor junction in the quantum Hall regime

In graphene-superconductor heterostructures, superconductivity and the quantum Hall effect may coexist for an experimentally accessible range of magnetic fields. When the graphene edge states are coupled to a superconductor in the presence of a Zeeman field, the charge carriers with one spin projection get transmitted while the ones with the opposite spin projection get reflected within a certain energy region. This spin-filtering effect is a consequence of the interplay between specular Andreev reflections and Andreev retro-reflections. While the edge termination of graphene and the geometrical details do matter for the charge conductance, they have little effect on the spin polarization of the charge carriers.

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.

Gateless and reversible Carrier density tunability in epitaxial graphene devices functionalized with chromium tricarbonyl

Monolayer epitaxial graphene (EG) has been shown to have clearly superior properties for the development of quantized Hall resistance (QHR) standards. One major difficulty with QHR devices based on EG is that their electrical properties drift slowly over time if the device is stored in air due to adsorption of atmospheric molecular dopants. The crucial parameter for device stability is the charge carrier density, which helps determine the magnetic flux density required for precise QHR measurements. This work presents one solution to this problem of instability in air by functionalizing the surface of EG devices with chromium tricarbonyl - Cr(CO)3. Observations of carrier density stability in air over the course of one year are reported, as well as the ability to tune the carrier density by annealing the devices. For low temperature annealing, the presence of Cr(CO)3 stabilizes the electrical properties and allows for the reversible tuning of the carrier density in millimeter-scale graphene devices close to the Dirac point. Precision measurements in the quantum Hall regime show no detrimental effect on the carrier mobility.

Phase diagram of quantum Hall breakdown and nonlinear phenomena for InGaAs/InP quantum wells

We investigate non-linear magneto-transport in a Hall bar device made from a strained InGaAs/InP quantum well: a material system with attractive spintronic properties. From extensive maps of the longitudinal differential resistance (r_xx) as a function of current and magnetic (B-) field phase diagrams are generated for quantum Hall breakdown in the strong quantum Hall regime reaching filling factor $\nu$=1. By careful illumination the electron sheet density (n) is incremented in small steps and this provides insight into how the transport characteristics evolve with n. We explore in depth the energetics of integer quantum Hall breakdown and provide a simple picture for the principal features in the r_xx maps. A simple tunneling model that captures a number of the characteristic features is introduced. Parameters such as critical Hall electric fields and the exchange-enhanced g-factors for odd-filling factors including nu=1 are extracted. A detailed examination is made of the B-field dependence of the critical current as determined by two different methods and compiled for different values of n. A simple rescaling procedure that allows the critical current data points obtained from r_xx maxima for even-filling to collapse on to a single curve is demonstrated. Exchange-enhanced g-factors for odd-filling are extracted from the compiled data and are compared to those determined by conventional thermal activation measurements. The exchange-enhanced g-factor is found to increase with decreasing n.

Andreev Reflection at the Interface with an Oxide in the Quantum Hall Regime

Quantum Hall/superconductor junctions have been an attractive topic as the two macroscopically quantum states join at the interface. Despite longstanding efforts, however, experimental understanding of this system has not been settled yet. One of the reasons is that most semiconductors hosting high-mobility two-dimensional electron systems (2DES) usually form Schottky barriers at the metal contacts, preventing efficient proximity between the quantum Hall edge states and Cooper pairs. Only recently have relatively transparent 2DES/superconductor junctions been investigated in graphene. In this study, we propose another material system for investigating 2DES/superconductor junctions, that is ZnO-based heterostrcuture. Due to the ionic nature of ZnO, a Schottky barrier is not effectively formed at the contact with a superconductor MoGe, as evidenced by the appearance of Andreev reflection at low temperatures. With applying magnetic field, while clear quantum Hall effect is observed for ZnO 2DES, conductance across the junction oscillates with the filling factor of the quantum Hall states. We find that Andreev reflection is suppressed in the well developed quantum Hall regimes, which we interpret as a result of equal probabilities of normal and Andreev reflections as a result of multiple Andreev reflection at the 2DES/superconductor interface.

Edge currents driven by terahertz radiation in graphene in quantum Hall regime

We observe that the illumination of unbiased graphene in the quantum Hall regime with polarized terahertz laser radiation results in a direct edge current. This photocurrent is caused by an imbalance of persistent edge currents, which are driven out of thermal equilibrium by indirect transitions within the chiral edge channel. The direction of the edge photocurrent is determined by the polarity of the external magnetic field, while its magnitude depends on the radiation polarization. The microscopic theory developed in this paper describes well the experimental data.

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.

Crystallization in the Fractional Quantum Hall Regime Induced by Landau-Level Mixing.

The interplay between strongly correlated liquid and crystal phases for two-dimensional electrons exposed to a high transverse magnetic field is of fundamental interest. Through the nonperturbative fixed-phase diffusion MonteCarlo method, we determine the phase diagram of the Wigner crystal in the ν-κ plane, where ν is the filling factor and κ is the strength of Landau-level (LL) mixing. The phase boundary is seen to exhibit a striking ν dependence, with the states away from the magic filling factors ν=n/(2pn+1) being much more susceptible to crystallization due to Landau-level mixing than those at ν=n/(2pn+1). Our results explain the qualitative difference between the experimental behaviors observed in n- and p-doped gallium arsenide quantum wells and, in particular, the existence of an insulating state for ν<1/3 and also for 1/3<ν<2/5 in low-density p-doped systems. We predict that, in the vicinity of ν=1/5 and ν=2/9, increasing LL mixing causes a transition not into an ordinary electron Wigner crystal, but rather into a strongly correlated crystal of composite fermions carrying two vortices.

Incoherent transport on the ν=2/3 quantum Hall edge

The nature of edge state transport in quantum Hall systems has been studied intensely ever since Halperin [1] noted its importance for the quantization of the Hall conductance. Since then, there have been many developments in the study of edge states in the quantum Hall effect, including the prediction of multiple counter-propagating modes in the fractional quantum Hall regime, the prediction of edge mode renormalization due to disorder, and studies of how the sample confining potential affects the edge state structure (edge reconstruction), among others. In this paper, we study edge transport for the $\nu_{\text{bulk}}=2/3$ edge in the disordered, fully incoherent transport regime. To do so, we use a hydrodynamic approximation for the calculation of voltage and temperature profiles along the edge of the sample. Within this formalism, we study two different bare mode structures with tunneling: the original edge structure predicted by Wen [2] and MacDonald [3], and the more complicated edge structure proposed by Meir [4], whose renormalization and transport characteristics were discussed by Wang, Meir and Gefen (WMG) [5]. We find that in the fully incoherent regime, the topological characteristics of transport (quantized electrical and heat conductance) are intact, with finite size corrections which are determined by the extent of equilibration. In particular, our calculation of conductance for the WMG model in a double QPC geometry reproduce conductance results of a recent experiment by R. Sabo, et al. [17], which are inconsistent with the model of MacDonald. Our results can be explained in the charge/neutral mode picture, with incoherent analogues of the renormalization fixed points of Ref. [5]. Additionally, we find diffusive $(\sim1/L)$ conductivity corrections to the heat conductance in the fully incoherent regime for both models of the edge.

Many-body wave functions for correlated systems in magnetic fields: Monte Carlo simulations in the lowest Landau level

We put forward possible wave functions for quantum Hall states in the lowest Landau level. These were deduced from the topological approach based on the relation between braid groups and the quantum statistics, as well as the commensurability condition unavoidable for collective states in magnetic fields. In this paper we demonstrate that the -field imposes restrictions on braid trajectories (i.e. elements of the full braid group). This results in the appearance of cyclotron subgroups, instead of the full braid group, for certain filling factors. The fermion representation of cyclotron subgroups defines transformations of wave functions in the quantum Hall regime. Hence, it sets quantum statistics (transformations of under exchanges of arguments), which is unavoidable for collective states (in compliance with the framework of Feynman’s path integrals). Finally, the topological approach allows to define the hierarchy of fillings in the lowest Landau level, which agree with the hierarchy observed in quantum Hall devices (i.e. in transport measurements).The symmetry of a many-body wave function (i.e. quantum statistics) is always determined by a 1D unitary representation of the system’s braid group. Using this topologically-originated property, we demonstrate that many-body wave functions for selected fillings of the lowest Landau level may not be purely antisymmetric. Only systems composed of fermions are investigated.Additionally, we present Monte Carlo calculations in a disc geometry, which remain in a nice agreement with predictions of exact diagonalizations (expected values of potential energy and pair distribution functions are presented). No boundary potential is assumed.

Crystallization of levitons in the fractional quantum Hall regime

Using a periodic train of Lorentzian voltage pulses, which generates soliton-like electronic excitations called Levitons, we investigate the charge density backscattered off a quantum point contact in the fractional quantum Hall regime. We find a regular pattern of peaks and valleys, reminiscent of analogous self-organization recently observed for optical solitons in non-linear environments. This crystallization phenomenon is confirmed by additional side dips in the Hong-Ou-Mandel noise, a feature that can be observed in nowadays electron quantum optics experiments.

Transport measurements in twisted bilayer graphene: Electron-phonon coupling and Landau level crossing

We investigate electronic transport in twisted bilayer graphene (tBLG) under variable temperatures ($T$), carrier densities ($n$), and transverse magnetic fields, focusing on samples with small-twist-angles ($\theta$). These samples show prominent signatures associated with the van Hove singularities (VHSs) and superlattice-induced mini-gaps (SMGs). Temperature-dependent field effect measurement shows that the difference between temperature-dependent resistivity and residual resistivity, $\rho_{xx}(n,T) - \rho_{0}(n)$, follows $~T^\beta$ for $n$ between the main Dirac point (DP) and SMG. The evolution of the temperature exponent $\beta$ with $n$ exhibits a W-shaped dependence, with minima of $\beta$ ~0.9 near the VHSs and maxima of $\beta$ ~1.7 toward the SMGs. This W-shaped behavior can be qualitatively understood with a theoretical picture that considers both the Fermi surface smearing near the VHSs and flexural-acoustic phonon scattering. In the quantum Hall regime, we observe only Landau level crossings in the massless Dirac spectrum originating from the main DP but not in the parabolic band near the SMG. Such crossings enable the measurement of an enhanced interlayer dielectric constant, attributed to a reduced Fermi velocity. Moreover, we measure the Fermi velocity, interlayer coupling strength, VHS energy relative to the DP, and gap size of SMG, four important parameters used to describe the peculiar band structure of the small-$\theta$ tBLG.

Large nonlocality in macroscopic Hall bars made of epitaxial graphene

We report on nonlocal transport in large-scale epitaxial graphene on silicon carbide under an applied external magnetic field. The nonlocality is related to the emergence of the quantum Hall regime and persists up to the millimeter scale. The nonlocal resistance reaches values comparable to the local (Hall and longitudinal) resistances. At moderate magnetic fields, it is almost independent on the in-plane component of the magnetic field, which suggests that spin currents are not at play. The nonlocality cannot be explained by thermoelectric effects without assuming extraordinary large Nernst and Ettingshausen coefficients. A model based on counterpropagating edge states backscattered by the bulk reproduces quite well the experimental data.

Long-distance spin transport through a graphene quantum Hall antiferromagnet

Antiferromagnetic insulators (AFMI) are robust against stray fields, and their intrinsic dynamics could enable ultrafast magneto-optics and ultrascaled magnetic information processing. Low dissipation, long distance spin transport and electrical manipulation of antiferromagnetic order are much sought-after goals of spintronics research. Here, we report the first experimental evidence of robust long-distance spin transport through an AFMI, in our case the gate-controlled, canted antiferromagnetic (CAF) state that appears at the charge neutrality point of graphene in the presence of an external magnetic field. Utilizing gate-controlled quantum Hall (QH) edge states as spin-dependent injectors and detectors, we observe large, non-local electrical signals across a 5 micron-long, insulating channel only when it is biased into the nu=0 CAF state. Among possible transport mechanisms, spin superfluidity in an antiferromagnetic state gives the most consistent interpretation of the non-local signal's dependence on magnetic field, temperature and filling factors. This work also demonstrates that graphene in the QH regime is a powerful model system for fundamental studies of antiferromagnetic, and in the case of a large in-plane field, ferromagnetic spintronics.

The critical role of substrate disorder in valley splitting in Si quantum wells

Atomic-scale disorder at the top interface of a Si quantum well is known to suppress valley splitting. Such disorder may be inherited from the underlying substrate and relaxed buffer growth, but can also arise at the top quantum well interface due to the random SiGe alloy. Here, we perform activation energy (transport) measurements in the quantum Hall regime to determine the source of the disorder affecting the valley splitting. We consider three Si/SiGe heterostructures with nominally identical substrates but different barriers at the top of the quantum well, including two samples with pure-Ge interfaces. For all three samples, we observe a surprisingly strong and universal dependence of the valley splitting on the electron density (Ev ∼ n2.7) over the entire experimental range (Ev = 30–200 μeV). We interpret these results via tight binding theory, arguing that the underlying valley physics is determined mainly by disorder arising from the substrate and relaxed buffer growth.

Formation of helical domain walls in the fractional quantum Hall regime as a step toward realization of high-order non-Abelian excitations

We propose an experimentally-feasible system based on spin transitions in the fractional quantum Hall effect regime where parafermions, high-order non-abelian excitations, can be potentially realized. We provide a proof-of-concept experiments showing that in specially designed heterostructures spin transitions at a filling factor 2/3 can be induced electrostatically, allowing local control of polarization and on-demand formation of helical domain walls with fractionalized charge excitations, a pre-requisite ingredient for parafermions formation. We also present exact diagonalization numerical studies of domain walls formed between domains with different spin polarization in the fractional quantum Hall effect regime and show that they indeed possess electronic and magnetic structure needed for parafermion formation when coupled to an s-wave superconductor.

Impurity-generated non-Abelions

Two classes of topological superconductors and Majorana modes in condensed matter systems are known to date: one, in which impurity disorder strongly suppresses topological superconducting gap and is detrimental to Majorana modes, and the other, where Majorana fermions are protected by disorder-robust superconductor gap. In this work we predict a third class of topological superconductivity and Majorana modes, in which they appear exclusively in the presence of impurity disorder. Observation and control of Majorana fermions and other non-Abelions often requires a symmetry leading to a gap in a single-particle spectra. Disorder introduces states into the gap and enables conductance and proximity-induced superconductivity via the in-gap states. We show that disorder-enabled topological superconductivity can be realized in a quantum Hall ferromagnet, when helical domain walls are coupled to an s-wave superconductor. Solving a general quantum mechanical problem of impurity bound states in a system of spin-orbit coupled Landau levels, we show that disorder-induced Majorana modes emerge in a setting of the quantum Hall ferromagnetic transition in a CdMnTe quantum wells at a filling factor $\nu=2$. Recent experiments on transport through electrostatically controlled single domain wall in this system indicated the vital role of disorder in conductance, but left an unresolved question whether this could intrinsically preclude generation of Majorana fermions. The proposed resolution of the problem, demonstrating emergence of Majorana fermions exclusively due to impurity disorder, opens a path forward. We show that electrostatic control of domain walls in an integer quantum Hall ferromagnet allows manipulation of Majorana modes. Similar physics can emerge for ferromagnetic transitions in the fractional quantum Hall regime leading to the formation and control of higher order non-Abelian excitations.