Publication

On Variable Range Hopping near the Fermi Energy: One-Dimensional Systems

Klaus Maschke
2022

Abstract

Model calculations on variable range hopping conduction in quasi-one-dimensional systems are presented. It is shown that the temperature behaviour of the conductivity depends strongly on the geometry of the sample consisting of ID strands. Comparison with an analytical theory is made. Careful numerical evaluation of an integral in the latter approach is necessary to obtain reasonable agreement with the results of the model calculation.

Official source

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Klaus Maschke
2022

Abstract

Official source

Related concepts (32)

Fermi gas

A Fermi gas is an idealized model, an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer spin. These statistics determine the energy distribution of fermions in a Fermi gas in thermal equilibrium, and is characterized by their number density, temperature, and the set of available energy states. The model is named after the Italian physicist Enrico Fermi.

Electrical resistivity and conductivity

Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SI unit of electrical resistivity is the ohm-metre (Ω⋅m).

Fermi energy

The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band. The term "Fermi energy" is often used to refer to a different yet closely related concept, the Fermi level (also called electrochemical potential).

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