Thermal ionization of impurity-bound quasiholes in the fractional quantum Hall effect

Abstract

We study the interplay between a Coulomb impurity and quasiholes in a fractional quantum Hall (FQH) state at finite temperatures. While a repulsive impurity can pin a quasihole and stabilize the FQH state, an attractive impurity cannot bind quasiholes. We demonstrate that at finite temperatures, a quasihole can be thermally ionized from a repulsive impurity, resulting in an ionization phase transition. We propose an experimental setup using exciton sensing to detect such a thermal ionization of quasiholes.

Figures (3)

• Figure 1: Calculation in the $N_\phi=21$ system with $N=7$ particles. (a) Energy spectrum as a function of the impurity charge $Z$. $E_g$ is the ground state energy. For $-0.3<Z<0.4$, the ground state is almost three-fold degenerate. (b) Particle entanglement spectrum by retaining $N_a=3$ particles at finite temperatures for $Z=0.2$. There are 637 states below the entanglement gap, consistent with the generalized Pauli principle for the system of 21 orbitals. (c) Phase diagram of the FQH entanglement gap for a system of 21 orbitals. The two green vertical lines indicate where the energy gap vanishes at zero temperature. The color bar is normalized by the gap of the PES at zero temperature.
• Figure 2: Calculation in the $N_\phi=22$ system with $N=7$ particles. (a) Energy spectrum as a function of the impurity charge $Z$. $E_g$ is the ground state energy. There are 22 states below the energy gap $\Delta_2$ (blue), corresponding to the number of free quasihole excitations, and three states below the energy gap $\Delta_1$ (green), corresponding to the FQH state with one pinned quasihole. (b) Particle entanglement spectrum at finite temperatures for $Z=0.0816$. There are 637 states below the entanglement gap $\Delta_1$, consistent with the generalized Pauli principle for a system of 21 orbitals, and 770 states below the entanglement gap $\Delta_2$, consistent with the generalized Pauli principle for a system of 22 orbitals. (c) Phase diagram of entanglement gap $\Delta_1$. The green vertical lines indicate where the energy gap $\Delta_1$ vanishes at zero temperature. (d) Phase diagram of entanglement gap $\Delta_2$. The blue vertical lines indicate where the energy gap $\Delta_2$ vanishes at zero temperature. Here, the particle entanglement spectrum is obtained by retaining $N_a=3$ particles.
• Figure 3: Schematics of the experimental proposal using an interlayer exciton.