Electron-Hole Asymmetric Chiral Breakdown of Reentrant Quantum Hall States

Reentrant integer quantum Hall (RIQH) states are believed to be correlated electron solid phases, although their microscopic description remains unclear. As bias current increases, longitudinal and Hall resistivities measured for these states exhibit multiple sharp breakdown transitions, a signature unique to RIQH states. A comparison of RIQH breakdown characteristics at multiple voltage probes indicates that these signatures can be ascribed to a phase boundary between broken-down and unbroken regions, spreading chirally from source and drain contacts as a function of bias current and passing voltage probes one by one. The chiral sense of the spreading is not set by the chirality of the edge state itself, instead depending on electron- or holelike character of the RIQH state.

Figure 1

(a) Measurement schematic combining ac (wiggly arrow) and dc (solid arrow) current bias through contacts 1 and 5. $R_{xx}=d{V}_{86}/dI$, $R_D^{+}=d{V}_{26}/dI$, and $R_D^{-}=d{V}_{84}/dI$. Curved arrows indicate edge state chirality. (b) Evolution of $R_{xx}$ with dc bias for the $R2c$ reentrant and $\nu =5/2$ FQH state, showing breakdown regions $A$, $B$, and $C$. (c) $R_{xx}$ and $R_{xy}$ ($d{V}_{37}/dI$) for filling factors $\nu =2–3$, showing the breakdown at high dc bias. (d),(e) Simultaneous measurements of (d) $R_D^{+}$ and (e) $R_D^{-}$, taken together with data in (b). Dashed lines are guides to the eye, denoting identical $\{B,I_{\mathrm{dc}}\}$ parameters in (b), (d), and (e).

Figure 2

(a) Simultaneous measurements showing the evolution of $R_D^{+}$, $R_{xy}$, and $R_D^{-}$, with dc bias, in the middle of the $R2c$ reentrant state ($I_{\mathrm{ac}}=5\mathrm{nA}$); note that this measurement uses a contact configuration rotated by 90° from Fig. 1. Evolution of (b) $R_D^{-}$, (c) $R_{xy}$, and (d) $R_D^{+}$ for the $R7a$ reentrant state with dc bias.

Figure 3

Classical simulation of dissipation (color scale and 3D projection in a.u.) due to current flow in a sample with regions of different $R_{xy}$. Hatched semicircles are melted states near each contact with $R_{xy}=h/(2.5e^2)$; the bulk (dark blue) is the (frozen) reentrant state with $R_{xy}=h/(3e^2)$. The simulation captures hot-spot locations but does not accurately capture relative magnitudes of dissipation in different hot spots.

Figure 4

Comparison of measurement geometries (a) $\mathrm{ac}\parallel \mathrm{dc}$ and (b) $\mathrm{ac}\perp \mathrm{dc}$; arrows label source and drain contacts for dc (solid arrows) and ac (wiggly arrows) bias, and edge state chirality (curved arrows). The vertical axis $E$ denotes local ac edge state potential (yellow line). Hatched areas are hypothetical melted regions for an electronlike reentrant state at intermediate dc bias $I_{\mathrm{dc}}\sim 50\mathrm{nA}$ in (c) and (d). Hot spots at the melted-frozen boundary indicated by $\star$. (c),(d) $R3a$ $R_{xx}$ maps in the $(I_{\mathrm{dc}},B)$ plane for (c) $\mathrm{ac}\parallel \mathrm{dc}$ and (d) $\mathrm{ac}\perp \mathrm{dc}$ measurement.