Book

High Precision Measurements of the Quantum Hall Effect

by Klaus von Klitzing

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Summary

This book presents experimental results and theoretical analysis of the Quantum Hall Effect (QHE), a phenomenon observed in two-dimensional electron systems subjected to strong magnetic fields and low temperatures. The central thesis is that the Hall resistance in the QHE exhibits a remarkable quantization into integer multiples of the von Klitzing constant, $R_K = h/e^2$, with extraordinary precision. This quantization is fundamentally linked to the topology of the electron system and offers a metrological standard for electrical resistance.

The book details the experimental setup, measurement techniques, and the observed plateaus in Hall resistance. Key ideas include the role of impurities and disorder in defining the quantized states, the concept of topological invariants characterizing the quantum states, and the robustness of the quantization against variations in sample parameters. Readers gain an understanding of a fundamental quantum mechanical effect with profound implications for condensed matter physics and metrology, providing a basis for precise resistance measurements.

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Key concepts

  • Quantum Hall Effect (QHE) — A phenomenon where the Hall conductivity of a 2D electron gas is quantized in integer or fractional multiples of fundamental constants under strong magnetic fields and low temperatures.
  • Quantized Hall Resistance — The observation that the Hall resistance of a 2D electron system in the QHE occurs in discrete, precisely defined plateaus, given by $R_H = (h/e^2)/n$, where $n$ is an integer.
  • von Klitzing Constant ($R_K$) — The fundamental constant $h/e^2$, approximately 25812.8 ohms, derived from Planck's constant ($h$) and the elementary charge ($e$), which defines the precise value of the quantized Hall resistance plateaus.
  • Two-Dimensional Electron Gas (2DEG) — An electron system confined to move in only two dimensions, typically formed at the interface of semiconductor heterostructures.
  • Topological Invariants — Mathematical quantities that characterize the fundamental properties of quantum states, explaining the robustness and precise quantization of the QHE.