Electron transport through a circular constriction

Details Electron transport through a circular constriction Electron transport through a circular constriction

1998-11-20

arxiv.org/abs/cond-mat/9811296v1

Phys. Rev. B 60, 3963 (1999).

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, 3 figures

Scientific paper

10.1103/PhysRevB.60.3963

We calculate the conductance of a circular constriction of radius $a$ in an insulating diaphragm which separates two conducting half-spaces characterized by the mean free path $\ell$. Our exact result interpolates between the Maxwell conductance in diffusive ($\ell \ll a$) and the Sharvin conductance in ballistic ($\ell \gg a$) transport regime. Following the earlier approach of Wexler we find the explicit form of the Green's function for the linearized Boltzmann operator. The formula for the conductance deviates by less than 11% from the naive interpolation formula obtained by adding resistances in the diffusive and the ballistic regime.

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