Observation of Inter-Valley Gap Anomaly of Two Dimensional electrons in Silicon

TL;DR

This study investigates the energy gaps at odd-integer quantum Hall states in high-quality silicon 2D electron systems under tilted magnetic fields, revealing unexpected behaviors near coincidence angles.

Contribution

It provides the first systematic analysis of valley gap anomalies at odd-integer quantum Hall states in silicon, highlighting strong coupling effects between nearly degenerate Landau levels.

Findings

Valley splitting is independent of in-plane magnetic fields outside the coincidence region.

Valley gap at ν=3 varies significantly on either side of the coincidence.

Energy gaps at ν=3 and 5 increase rapidly near the coincidence angles.

Abstract

We report here a systematic study of the energy gaps at the odd-integer quantum Hall states $\nu=3$ and 5 under tilted magnetic (B) fields in a high quality Si two-dimensional electron system. Out of the coincidence region, the valley splitting is independent of the in-plane B fields. However, the $\nu=3$ valley gap differs by about a factor of 3 ($\Delta_v\sim$ 0.4K vs. 1.2K) at either side of the coincidence. More surprisingly, instead of reducing to zero, the energy gaps at $\nu=3$ and 5 rise rapidly when approaching the coincidence angles. We believe that such anomaly is related to strong coupling of the nearly degenerate Landau levels.