Semicircle: An exact relation in the Integer and Fractional Quantum Hall Effect

TL;DR

This paper reports experimental verification of a semi-circle relation between conductivities in quantum Hall insulators, demonstrating precise quantization of Hall resistance in two-dimensional systems at high magnetic fields.

Contribution

It provides the first experimental confirmation of an exact semi-circle relation in both integer and fractional quantum Hall regimes, linking theoretical predictions with observed data.

Findings

Quantized Hall resistance observed in 2D systems

Semi-circle relation between conductivities confirmed

Results consistent across different material systems

Abstract

We present experimental results on the quantized Hall insulator in two dimensions. This insulator, with vanishing conductivities, is characterized by the quantization (within experimental accuracy) of the Hall resistance in units of the quantum unit of resistance, h/e^2. The measurements were performed in a two dimensional hole system, confined in a Ge/SiGe quantum well, when the magnetic field is increased above the nu=1 quantum Hall state. This quantization leads to a nearly perfect semi-circle relation for the diagonal and Hall conductivities. Similar results are obtained with a higher mobility n-type modulation doped GaAs/AlGaAs sample, when the magnetic field is increased above the nu=1/3 fractional quantum Hall state.