Conductance Oscillations and Phase Coherence in Submicron Metal Films

Abstract

Neglecting band structure and correlation effects, the freely moving electrons in a disordered metal film can be described as plane waves ψ(F) oc exp $\Psi \left( {\vec r} \right)\; \propto \exp \left( {i\vec k\cdot \vec r} \right)with\left| {\vec k} \right| = 2\pi /\lambda$ with |λ| = 2 π/λ the wave vector. When we restrict ourselves to the low temperature limit, the contribution of the inelastic scattering (at other electrons or phonons) to the electrical conductivity can be neglected. The scattering at lattice defects and impurities will cause an elastic diffusion of the charge carriers. Due to the Pauli principle, only the electrons near the Fermi level contribute to the conductivity which is given by the Einstein relation

$$</m:math> {\sigma _o} = {e^2}N\left( {{E_F}} \right)D $$

((1))

N(E _F) represents the electronic density of states near the Fermi level and $D = \frac{1}{3}{v_F}{\ell _{e\ell }}$ is the diffusion constant with v _F the intrinsic electron (Fermi) velocity and 𝓁 _e the elastic mean free path. The diffusion approach will be valid only for the electronic transport in disordered metals and on a length scale L much larger than the mean free path 𝓁 _e (diffusive regime). On a length scale L ≪ 𝓁 _e, we enter the ballistic regime. The ballistic limit which can be studied in high-quality GaAs/GaAlAs heterostructures, is discussed in detail in other chapters of this volume.