Session Q65: Quantum Hall Effect: Transport Phenomena

Downstream Noise of a Superconductor-Quantum Hall Interface

Interfaces between a Quantum Hall region and a superconductor allow for the formation of hybrid electron-hole states known as chiral Andreev edge states. These states have been previously identified by our group via measurements of the non-local DC resistance of a graphene sample with a superconducting contact. We perform measurements of the shot noise in a device which shows significant DC signatures of the chiral Andreev edge state. While we observe noise signatures comparable to those of a recent sudy, we find no correlation between the shot noise and the DC chiral Andreev edge state signal. We discuss alternative explanations of the observed signal.    

Aharonov-Bohm oscillations in bilayer graphene Fabry-Pérot interferometry

Quantum Hall edge state interferometry has been an important tool in probing the charge and statistics of elementary excitations of the quantum Hall and fractional quantum Hall (FQH) effect of a two-dimensional electron gas [1]. Two recent measurements have reported the observations of Aharonov-Bohn oscillations in monolayer graphene quantum Hall interferometers [2,3]. High-quality bilayer graphene is an appealing platform because of the existence of not only odd-denominator FQH states but also candidate non-Abelian even-denominator FQH states with large energy gaps. In this talk, we report on the fabrication and measurements of bilayer graphene Fabry-Pérot interferometer devices and the observation of Aharonov-Bohm oscillations at multiple integer quantum Hall states. We evaluate the edge state interference dephasing under dc bias and at elevated temperatures and discuss the edge mode velocities at different filling factors. We also discuss the progress and challenges towards detecting fractional and non-Abelian statistics in this platform.

[1] Nakamura et al., arXiv:2107.02136

[2] Ronen et al., Nat. Nanotech. 16, 563–569 (2021)

[3] Déprez et al., Nat. Nanotech. 16, 555-562 (2021)   

Integrated-conductance approach to scaling at the integer quantum Hall transition

We develop a method to study integer quantum Hall (IQH) criticality from finite size scaling of the energy-integrated conductance about the critical point. This method is inspired from the number of conducting states method of Bhatt and colleagues [Phys. Rev. B 99, 24205 (2019)] but (i) applies to non-Hamiltonian models including the Chalker Coddington (CC) network model and (ii) can access system sizes nearly two orders of magnitude larger than before.  Using this method, we find the localization length exponent ν ~ 2.6 for the CC network model, in agreement with the accepted literature value. We also confirm a substantially different value of ν for the two-layer analog of the CC network model, thought to be in the same universality class. This method may be useful for evaluating predictions from the conformal field theory recently proposed by M. Zirnbauer [Nucl. Phys. B 941, 458 (2019)] and for studying other Anderson transitions described by network models.   

SU(4) symmetry breaking and Andreev edge states in quantum Hall graphene-superconductor junctions

A quantum Hall (QH) edge state in proximity to a superconductor becomes a mixture of electron-like and hole-like states due to Andreev processes. Such a state is called an Andreev edge state. In graphene, valley and spin degeneracy lead to an approximate SU(4) symmetry that is reflected in the approximate 4-fold degeneracy of graphene's Landau levels (LL). Interactions and the Zeeman effect break such approximate symmetry and the corresponding degeneracy of the LLs. We present the effects of SU(4) symmetry breaking using a simple low-energy model for Andreev edge states. For the N=0 graphene LL we study how the competition between interactions and Zeeman effect that lead to the canted antiferromagnetic phase affect the transport of the Andreev edge states. For the N=1 LL we investigate how Zeeman and valley splitting may be used to modulate Andreev edge state interference patterns.   

Density dependence of the excitation gap in Si/SiGe bilayers

We report low-temperature magneto-transport measurements of an undoped Si/SiGe asymmetric double quantum well heterostructure. The density in both layers is tuned independently utilizing a top and a bottom gate, allowing the investigation of quantum wells at both imbalanced and matched densities. Integer quantum Hall states at total filling factor ν_T = 1 and ν_T = 2 are observed in both density regimes, and the evolution of their excitation gaps is reported as a function of density. The ν_T = 1 gap evolution departs from the behavior generally observed for valley splitting in the single layer regime. Furthermore, by comparing the ν_T = 2 gap to the single particle tunneling energy, Δ_SAS, obtained from Schrödinger-Poisson simulations, evidence for the onset of spontaneous inter-layer coherence (SIC) is observed for a relative filling fraction imbalance smaller than 50%.   

Breakdown of the topological protection by cavity vacuum fields in the integer quantum hall effect

We measure electronic transport at mK temperatures in high mobility GaAs/AlGaAs based heterostructures ultrastrongly coupled to planar circuit resonators. We focus our study on the integer quantum Hall regime. The integer quantum Hall effect is a prototypical topological insulator, where disordered bulk electrons act as an insulator, and the edges are conductive. This system is extremely robust to local defects because of the short range of the disorder potential. This feature allows measuring the quantized resistance in samples with very different geometries and materials. On the other hand, topological protection is not immune to non-local perturbations. Cavity vacuum fields can mediate long-range electron hopping [1], eventually leading to a breakdown of the quantized plateaus.  We experimentally demonstrate the breakdown of topological protection in the integer Hall regime [2]. We show that this effect is most visible at odd filling factors, where the levels are split by the Zeeman energy.  At the same time, the zero field transport is not changed by the cavity and the transport features associated to fractional states are still visible.

[1] C. Ciuti, Arxiv 2107.09435 (2021)

[2] F. Appugliese et al., Arxiv 2107.14145 (2021)   

Imaging inhomogenous Hall states in transport

The quantum Hall state is the archetypical example of topological matter. Its topology is characterized in terms of Chern numbers, which are defined in momentum space. Along similar lines, topology is generally said to be non-local. However, that does not mean that momentum space is a prerequisite for topological physics. In this talk, I will present recent results on inhomogenous quantum Hall systems, and discuss how to think of them in terms of a spatially variying topological character. I will close by describing how their spatially variying topological character can be mapped in transport experiments.   

Bias controlled switching of spin polarization between ν = ±1 quantum Hall edges at graphene pn junction

Differentiating between the ground states of the half-filled zeroth Landau level in graphene is the key to

understand their low-energy excitations. One promising route for this is to study the effects of different

ground states of ν = 0 filling on nearby edge states belonging to fillings |ν| > 0. In this regard, graphene

pn junction is an ideal platform, as in the symmetry broken quantum Hall (QH) regime, the co-propagating

electron and hole-like edge states at the junction are separated by a narrow ν = 0 region. Here, we report

bias controlled tunneling between ν = ±1 QH edges in a graphite gated hBN encapsulated monolayer

graphene device. At zero bias, we observe finite tunneling (t ∼ 0.5), which remains almost constant up

to ∼ 120μV at 8T. Strikingly, above ∼ 120μV the tunnelling sharply falls and exhibits repeated smaller

peaks at discrete energies before vanishing completely. Moreover, the tunneling shows unique dependence

on filling, magnetic field and temperature. The tunneling at zero bias is anomalous as it is is expected to

be zero between ν = ±1 edges due to their orthogonal spin polarization. Thus, from tunneling to fully

blockade suggests bias-controlled switching of spin polarization between ν = ±1 edges, which is further

corroborated with our detailed theoretical calculations.   

Shot Noise Fano Factor: Bulk or Edge Property

The quasiparticle charge in the Fractional Quantum Hall effect (FQHE) has long been measured via quantum shot-noise measurements. Here, we demonstrate that the standard Fano factor of shot noise (F=1 for integers), stemming from either weakly backscattered charged quasiparticle (in a QPC) at low temperature (T∼10 mK), with or without accompanying neutral modes, depends only on the bulk filling away from the QPC and not on the structure (and conductance) of the edge modes or the filling factor within the QPC constriction. We employed a novel method in which two different QHE bulks’ fillings are interfaced, thus giving birth to novel 1D chiral modes at the interface. The interface modes have an ‘effective filling’ (edge conductance), which is different from the filling of each of the interfacing bulks, and moreover, different from the filling within the QPC constriction. Our results are explained within a new theoretical paradigm for shot noise.   

A new paradigm of universal Fano factor on and off conductance plateaus in quantum Hall systems: experiment and theory

The orthodox framework to account for shot noise in quantum transport relies on electron beam partitioning. This is the case for quantum Hall (QH) platforms in the presence of a quantum point contact (QPC). Consequently one expects vanishing noise on a conductance plateau, where each chiral edge mode is either fully transmitted or entirely backscattered, hence no beam partitioning. Surprisingly, recent experiments on diverse quantum Hall phases and disparate geometries reveal on-the-plateau shot noise with the Fano factor being equal to the bulk filling fraction (rather than the quasi-particle charge).

To account for these observations we present a new theoretical paradigm of shot noise that relies on the ubiquitous presence of counter-propagating neutral edge modes (``neutralons") at the edge. These neutrals may be of either a topological (hole-like filling fractions) or edge reconstruction (particle-like or integer filling fractions) origin. We show that even on an intermediate transmission plateau within the QPC shot noise can be generated via creating and then annihilating neutralons, leading to a Fano factor which is equal to the bulk filling fraction. This Fano factor remains robust even off the conductance plateau.   

Comparing Cr-Doped (BixSb1-x)2Te3 to Graphene as a Future Platform for Quantum Hall Resistance Standards

Since 2017, epitaxial graphene has been the base material for the US national standard for resistance. Due to a relaxed magnetic field and temperature requirement, these graphene-based devices enabled more user-friendly access to the quantum Hall effect and could more easily be deployed into US and global industries compared to GaAs-based devices. A future avenue of research within electrical metrology is to remove the need for strong magnetic fields, as is currently the case for devices exhibiting the quantum Hall effect. New materials, like magnetically doped topological insulators (MTIs), offer access to the quantum anomalous Hall effect, which in its ideal form, could become a future resistance standard needing only a small permanent magnet to activate a quantized resistance value. Furthermore, these devices could operate at zero-field for measurements, making the dissemination of the ohm more economical and portable. Here we present results on precision measurements of the h/e^2 quantized plateau of Cr-Doped (Bi_xSb_1-x)₂Te₃ and give them context by comparing them to modern graphene-based resistance standards. Ultimately, MTI-based devices could be combined in a single system with magnetic-field-averse Josephson voltage standards to obtain an alternative quantum current standard.   

Non-linear transport near ν= 1 in a high mobility two-dimensional electron gas and the breakdown of integer quantum Hall Wigner solid

The integer quantum Hall Wigner solid was recently observed in high mobility GaAs two-dimensional electron gas samples near filling factor ν = 1. We performed large signal current-voltage characteristic measurements in the region of this phase. We observed well-defined breakdown behavior in the regions of both the integer quantum Hall Wigner solid and the Anderson insulator. To our surprise, we find that the critical current exhibits a monotonic dependence as the filling factor moves away from the center of the ν = 1 plateau, even in the region of the Wigner solid. Therefore, it appears that the breakdown in the current-voltage characteristics measured along the ν = 1 integer quantum Hall plateau does not differentiate the reentrant integer quantum Hall Wigner solid from the Anderson insulator.     

Side-gate controlled graphene quantum Hall point contacts and interferometer

The vanishing band gap of graphene has long presented challenges for fabricating high-quality quantum point contacts (QPCs) -- the partially transparent p-n interfaces introduced by conventional split-gates tend to short the QPCs. This complication has hindered the fabrication of high-quality graphene quantum Hall Fabry-P\'erot interferometers, until recently split-gate QPCs operating in the symmetry-breaking regime have been successfully introduced. In contrast to this top-gated geometry, here we present a simple recipe to fabricate QPCs by etching a narrow trench in the graphene sheet to separate the conducting channel from self-aligned graphene side gates. We demonstrate QPC operation in a wide range of magnetic fields and further utilize this technique to study the Aharonov-Bohm interference in a quantum Hall interferometer.   

Resonant States in Graphene QPCs in the Quantum Hall Regime

Recent work has shown that bilayer graphene Van der Waals heterostructures host even denominator and other fractional quantum Hall states with energy gaps considerably larger than those observed in high mobility GaAs 2DEGs.  However, a barrier to leveraging these intrinsic properties is the challenge of patterning local electrostatic potentials while preserving high mobility edge channels. In particular, both additive and subtractive nanofabrication processes tend to disorder the two dimensional electron layer in the regions of interest.  In this talk, I will describe the fabrication and characterization of graphene quantum point contacts using pre-cut graphite split gates.  By cutting the graphite top gate with AFM oxidation lithography, we are able to electrostatically define a highly tunable QPC that is directly integrated into a high mobility graphene based Van der Waals heterostructure.  First, we demonstrate highly tunable transmission of multiple integer edge modes.  We find that by increasing the electric field across these gates while keeping the bulk filing factor fixed, even split gate geometries with gaps as large as 180nm can pinch off all edge channels up to nu = 2.  In addition, we observe resonant transmission deep in the pinch off regime.  By studying the differential conductance of these resonant features we observe coulomb diamonds consistent with a quantum dot localized to the saddle point defined by the electrostatic gate potentials.  These results suggest that resonant states can form in graphene QPCs via an entirely intrinsic mechanism in the absence of disorder in the channel.  Understanding how these resonant states form, and how they may affect transmission in the fractional quantum Hall regime will be essential for future studies of edge state physics including Fabry-Perot interferometry, quasiparticle tunneling, and noise thermometry.