Asymmetric-gate Mach--Zehnder interferometry in graphene: Multi-path conductance oscillations and visibility characteristics

TL;DR

The paper investigates how gate-defined asymmetry in graphene quantum Hall Mach-Zehnder interferometers affects coherence and visibility, particularly when multiple interface channels enable multi-path interference. It develops a phenomenological framework combining Dirac- and tight-binding transport descriptions with Landauer–Büttiker calculations, and employs a machine-learning assisted Fourier transform to resolve closely spaced interference frequencies from conductance oscillations. Key findings show that asymmetric gating tunes the effective MZ loop areas, leads to nested interference loops at higher filling factors, and that symmetric gating maximizes visibility, with the ML-FT analysis yielding sharp spectral peaks even for short data segments. These results establish design rules for graphene-based quantum sensors and provide a diagnostic tool for detecting subnanometer-scale shifts in interface channels.

Abstract

Graphene provides an excellent platform for investigating electron quantum interference due to its outstanding coherent properties. In the quantum Hall regime, Mach--Zehnder (MZ) electronic interferometers are realized using p--n junctions in graphene, where electron interference is highly protected against decoherence. In this work, we present a phenomenological framework for graphene-based MZ interferometry with asymmetric p--n junction configurations. We show that the enclosed interferometer area can be tuned by asymmetric gate potentials, and additional MZ pathways emerge in higher-filling-factor scenarios, e.g. $\left(ν_{n},ν_{p}\right)=\left(-3,+3\right)$. The resulting complicated beat oscillations in asymmetric-gate MZ interference are efficiently analyzed using a machine-learning--based Fourier transform, which yields improved peak-to-background ratios compared to conventional signal-processing techniques. Furthermore, we examine the impact of the asymmetric gate on the interference visibility, finding that interference visibility is enhanced under symmetric gate conditions.

Figures (4)

• Figure 1: (a) Schematic of the graphene Hall bar with an electrostatically defined p--n junction; edge-channel conductance is measured via two opposite leads attached to the same region. (b) Potential profile for the p--n junction. N and p regions are subjected to electric potential $U_{1}$ and $U_{2}$, respectively. Solid line represents an asymmetric junction potential $U_{1}=-E_{0}/2$ and $U_{2}=E_{0}\left(1+\sqrt{2}\right)/2$ for filling-factor configuration $\left(\nu_{p},\nu_{n}\right)=\left(-1,3\right)$, while dashed line represents represents a symmetric junction potential $U_{1}=-U_{2}=-E_{0}\left(1+\sqrt{2}\right)/2$ for filling-factor configuration $\left(\nu_{p},\nu_{n}\right)=\left(-3,3\right)$.
• Figure 2: Conductance oscillations, machine‐learning–based Fourier analysis results, and corresponding interface‐channel dispersions and interferometer loops for two gate‐asymmetry settings. (a) Quantum Hall conductance $G_{H}$ versus junction length $L$ for the asymmetric p--n junction $\left(dU=0\right)$ at a filling-factor configuration $\left(\nu_{p},\nu_{n}\right)=\left(-1,3\right)$; the visibility of the oscillations is indicated. (b) Machine-learning Fourier transform of the conductance oscillation in (a), showing the valley-split MZ frequencies. (c) Energy spectrum of the interface channels for $\left(\nu_{p},\nu_{n}\right)=\left(-1,3\right)$; solid dots mark the two modes $k_{0}$ and $k_{+1}$ crossing the Fermi energy $E=0$. (d) Schematic of the corresponding Mach-Zehnder interfereometer loop: the shaded area $A_{\rm MZ}$ enclosed by the two counter-propagating edge channels in the p– and n–regions encloses magnetic flux $\Phi=B\cdot A_{\rm MZ}$. (e) Conductance oscillations for the symmetric junction potential $dU=E_{0}/\sqrt{2}$ at $(\nu_{p},\nu_{n})=(-3,3)$; the visibility is noted. (f) Machine‐learning Fourier transform of the oscillations in (e), with the valley-split MZ frequencies. (g) Dispersion of the interface channels for $(\nu_{p},\nu_{n})=(-3,3)$; three Fermi‐level crossings indicate three interface modes $k_{-1}$, $k_{0}$ and $k_{+1}$, respectively. (h) Schematic of the nested Mach–Zehnder loops $A^{p}_{\rm MZ}$ and $A^{n}_{\rm MZ}$ formed by the two pairs of interface channels in the higher–filling–factor case.
• Figure 3: Evolution of graphene Mach-Zehnder interference with varying p--n junction asymmetry. (a) Stacked plots of the quantum Hall conductance $G_{H}$ versus junction length for a series of potential-difference values $dU$. The arrow at right indicates the direction of increasing $dU$. The dashed horizontal line marks the singular filling-factor case that one region of p--n junction is nearly metallic (Fermi energy touches the first Landu level). (b) ML-FT spectra computed from each trace in (a), illustrating the evolution of the dominant beat frequencies and the emergence of additional frequency components as $dU$ grows.
• Figure 4: Dependence of MZ interference visibility on p--n junction asymmetry $dU$. Visibility is extracted from conductance oscillations (Fig. \ref{['fig:MLFourier']}(a)) for filing-factor configurations $\left(\nu_{p},\mu_{n}\right)=\left(-1,3\right)$ at small $dU$ and $\left(\nu_{p},\mu_{n}\right)=\left(-3,3\right)$ once $dU$ exceeds the threshold (vertical dashed line at $dU=E_{0}/2$. Each marker denotes the calculated visibility for a given $dU$. The sharp increase in visibility beyond $dU=E_{0}/2$ reflects the transition from single-loop to nested multi-path MZ interference.