Semiclassical theory of the tunneling anomaly in partially spin-polarized compressible quantum Hall states

TL;DR

This paper develops a semiclassical hydrodynamic theory to explain the tunneling anomaly in partially spin-polarized quantum Hall states, revealing a new regime dominated by finite compressibility rather than Coulomb energy.

Contribution

It introduces a novel semiclassical hydrodynamic framework for the tunneling anomaly in spin-polarized quantum Hall states, contrasting with previous instanton-based approaches.

Findings

The tunneling anomaly cannot be explained by mean-field Coulomb energy alone.

A new regime is identified where finite compressibility dominates the tunneling behavior.

Experimental observations are consistent with the compressibility-driven regime.

Abstract

Electron tunneling into a system with strong interactions is known to exhibit an anomaly, in which the tunneling conductance vanishes continuously at low energy due to many-body interactions. Recent measurements have probed this anomaly in a quantum Hall bilayer of the half-filled Landau level, and shown that the anomaly apparently gets stronger as the half-filled Landau level is increasingly spin polarized. Motivated by this result, we construct a semiclassical hydrodynamic theory of the tunneling anomaly in terms of the charge-spreading action associated with tunneling between two copies of the Halperin-Lee-Read state with partial spin polarization. This theory is complementary to our recent work (arXiv:1709.06091) where the electron spectral function was computed directly using an instanton-based approach. Our results show that the experimental observation cannot be understood within conventional theories of the tunneling anomaly, in which the spreading of the injected charge is driven by the mean-field Coulomb energy. However, we identify a qualitatively new regime, in which the mean-field Coulomb energy is effectively quenched and the tunneling anomaly is dominated by the finite compressibility of the composite Fermion liquid.