Spectroscopic study of quantized breakdown voltage states of the quantum Hall effect

Abstract

Quantized breakdown voltage states are observed in a second, wide, highquality GaAs/AlGaAs sample made from another wafer, demonstrating that quantization of the longitudinal voltage drop along the sample is a general feature of the quantum Hall effect in the breakdown regime. The voltage states are interpreted in a simple energy conservation model as occurring when electrons are excited to higher Landau levels and then return to the original level. A spectroscopic study of these dissipative voltage states reveals how well they are quantized. The statistical variations of the quantized voltages increase linearly with quantum number.

<title>Breakdown of the interger quantum Hall effect: a microscopic model with a hydronamical analogy</title>

“…However, above a critical current value, the dissipative voltage, V, measured along the direction of current flow increases rapidly, leading to quantum Hall breakdown. In certain experiments, including those on the US resistance standard samples at the National Institute of Standards and Technology (NIST) [1], breakdown occurs as a series of up to twenty regular steps in V. This is fundamentally different from the conventional type of breakdown where one observes a single sharp increase of the longitudinal magnetoresistance.…”

Model for the Voltage Steps in the Breakdown of the Integer Quantum Hall Effect

“…In this work we develop a theoretical model to account for the dissipative steps observed by the NIST group [11,12] and others [13,14]. We show that in the presence of charged impurity-induced disorder the quantum Hall fluid (QHF) is unstable when the local fluid velocity exceeds a critical value.…”

“…Because of the absence of empty states into which the excited electron can relax, and neglecting weak, second order Auger processes, we can assume Step like breakdown in the integer quantum Hall effect, from Ref. [11]. Each step contributes a multiple of ' 5 mV to the dissipative longitudinal voltage.…”

“…The NIST experiments on the U.S. resistance standard samples [11] were carried out at 2 and B 12:3 T. The experiments show a series of dissipative steps in V x of regular height V x ' 5 mV, see Fig. 1.…”

“…(9) as a function of E y . The parameters used refer to the experimental conditions of[11,15]: (a) m ? 0:07m e , N s 3 10 15 m ÿ2 and B 12:3 T; (b) m ?…”