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Quantized Nonlinear Conductance in Ballistic Metals.

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We introduce a new terminal conductance for D-dimensional Fermi gases, generalizing Landauer conductance. In 2D, this conductance is quantized and measures the Fermi sea

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Area of Science:

  • Condensed Matter Physics
  • Quantum Transport

Background:

  • The Landauer conductance formula is a cornerstone of quantum transport in one dimension.
  • Generalizing quantum transport formalisms to higher dimensions presents significant theoretical challenges.

Purpose of the Study:

  • To introduce a D+1 dimensional nonlinear frequency-dependent terminal conductance for characterizing D-dimensional Fermi gases.
  • To generalize the concept of Landauer conductance to higher dimensions.
  • To explore the physical implications and experimental feasibility of this new conductance measure.

Main Methods:

  • Development of a nonlinear frequency-dependent terminal conductance theory.
  • Analysis of a D-dimensional Fermi gas model.
  • Investigation of a 2D ballistic conductor system.

Main Results:

  • A generalized D+1 terminal conductance is introduced, characterizing D-dimensional Fermi gases.
  • For a 2D ballistic conductor, the conductance is shown to be quantized.
  • The quantized conductance in 2D is demonstrated to probe the Euler characteristic of the Fermi sea.

Conclusions:

  • The proposed terminal conductance offers a novel way to characterize Fermi gases in higher dimensions.
  • The quantization of conductance in 2D systems provides a direct link to topological properties (Euler characteristic).
  • Experimental verification using 2D Dirac materials like graphene with a triple point contact geometry is proposed.