Spontaneous localization at a potential saddle point from edge state reconstruction in a quantum Hall point contact

TL;DR

Spontaneous localization arises when soft gate-defined confinement at a quantum Hall point contact forms a classical saddle point, prompting Coulomb-driven reconstruction of edge states in monolayer graphene. By combining low-temperature transport measurements with self-consistent Thomas-Fermi simulations, the study demonstrates that fractional edge strips, notably at $\nu=\tfrac{1}{3}$, can reorganize into localized islands that yield Coulomb-blockaded resonances and fractional conductance plateaus. The reconstruction is controlled by the confinement softness parameter $E_V/E_C$ and gate geometry, with an unreconstructed, monotonic transmission limit recovered for sharp edges (large $E_V/E_C$). These results provide direct evidence for Coulomb-driven edge reconstruction at QPC boundaries and offer a framework for engineering and detecting fractional edge modes in graphene-based quantum Hall devices, with implications for tunable edge-state spectroscopy and interferometry.

Abstract

Quantum point contacts (QPCs) are an essential component in mesoscopic devices. Here, we study the transmission of quantum Hall edge modes through a gate-defined QPC in monolayer graphene. We observe resonant tunneling peaks and a nonlinear conductance pattern characteristic of Coulomb-blockaded localized states. The in-plane electric polarizability reveals the states are localized at a classically-unstable electrostatic saddle point. We explain this unexpected finding within a self-consistent Thomas-Fermi model, finding that localization of a zero-dimensional state at the saddle point is favored whenever the applied confinement potential is sufficiently soft compared to the Coulomb energy. Our results provide a direct demonstration of Coulomb-driven reconstruction at the boundary of a quantum Hall system.

Figures (7)

• Figure 1: Optical Micrograph of Measured Device Transport contacts to the monolayer are labeled C1-8, while the gates are labeled by their corresponding control voltages $V_i$.
• Figure 2: Coulomb blockaded resonances on the electron side. All data in this figure was taken at B = 9T and T = 20mK. (a) Two terminal conductance across the device plotted against $V_{NS}$ and $V_{EW}$. (b) Differential conductance versus source-drain bias plotted along the white dashed line in (a) as well as the corresponding zero-bias line cut. Along the white dashed line $\nu_{EW} = 3$ and $\nu_{NS} = 0$. (c-d) Two terminal conductance plotted against $V_{N(W)}$ and $V_{S(E)}$ for the Coulomb blockaded resonances marked by the white dashed line in (a). The primary resonance shown in (d) is demarcated by the white dot in (a). (e-f) Diagonal conductance across the device plotted against $V_{N(W)}$ and $V_{S(E)}$ for the transmission step between $G_D = 1$, and $G_D = 2$.
• Figure 3: Effective model considered within the Thomas-Fermi framework.(a) Top-view of the gate setup, which involves four square gates labeled N,S,E, and W respectively, each of which is held at a potential denoted by $V_{N,S,E,W}$. The back-gate (gray) is held at constant $V_B$. We allow for the gate displacement from the center to be different for E/W and N/S gates. (b) Side-view of the gates reveals two distances $d_t$ and $d_b$ for the separation between the 2DEG and the top gate or bottom gate, respectively. (c) The chemical potential $\mu$ and internal energy $E_\textrm{xc}$ derived from Ref. yang_experimental_2021 which is taken as input data for the Thomas-Fermi calculation carried out here.
• Figure 4: Extended reconstructed electron density profiles in a QPC geometry in the fractional regime. (a-b) Fractional reconstruction in an integer bulk filling ($\nu=1$) with $E_C = \,46.4~meV$ in the regime where the confining potential is sharper than presented in main text Fig. 3a. (a) With $E_V / E_C = 0.50$, the $\nu=\frac{1}{3}$ island disappears and the $\nu=\frac{1}{3}$ strips become narrower. (b) With $E_V/E_C = 0.57$, the $\nu=\frac{1}{3}$ strips disappear completely.
• Figure 5: Reconstructed electron density profiles in a QPC geometry in the integer reconstruction regime. (a-c) Integer reconstruction in an integer bulk filling ($\nu=1$) with $E_C = \,11.6~meV$ as the confining potential smoothness is varied. (a) With $E_V / E_C = 0.18$, the reconstructed $\nu=1$ stripes extend along the entire edge. (b) With $E_V/E_C = 0.47$, the reconstructed $\nu=1$ stripes shrink to a single circular dot with $\nu=1$ in the center of the QPC. (c) With $E_V/E_C = 0.55$, no reconstruction is observed.