Bulk Tunneling at Integer Quantum Hall Transitions

TL;DR

This paper investigates the bulk tunneling density of states near integer quantum Hall transitions, revealing distinct behaviors for Coulomb and short-range interactions through nonperturbative calculations.

Contribution

It provides the first nonperturbative calculation of the tunneling density of states at integer quantum Hall transitions for both Coulomb and short-range interactions.

Findings

Coulomb interactions produce a quantum Coulomb gap in TDOS.

Short-range interactions lead to a universal power-law behavior in TDOS.

The results highlight the role of interaction range in tunneling phenomena.

Abstract

The tunneling into the {\em bulk} of a 2D electron system (2DES) in strong magnetic field is studied near the integer quantum Hall transitions. We present a nonperturbative calculation of the tunneling density of states (TDOS) for both Coulomb and short-ranged electron-electron interactions. In the case of Coulomb interaction, the TDOS exhibits a 2D quantum Coulomb gap behavior, $\nu(\ve)=C_Q\ave/e^4$, with $C_Q$ a nonuniversal coefficient of quantum mechanical origin. For short-ranged interactions, we find that the TDOS at low bias follows $\nu(\ve)/\nu (0)=1+(\ave/\ve_0)^\gamma$, where $\gamma$ is a universal exponent determined by the scaling dimension of short-ranged interactions.