Landauer conductance in the diffusive regime
- Computational Physics and Engineering Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6114 (United States)
- Metals and Ceramics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6114 (United States)
We present a derivation of the dc Landauer conductance formula in three dimensions starting from a mean-field approximation of the Kubo formula using a Green function for electron propagation that contains a self-energy that may be complex. Unlike some previous derivations of the Landauer formula from the Kubo formula, we find a nonzero contribution to the current from the volume integral over the leads, even without the mean-field approximation. Because we use a complex self-energy to describe the sample, the sum of the reflection and the transmission probabilities is in general less than one. In the four-probe case the conductance of a sample with length L, electron mean free path l, transmission amplitude t({bold k}{sub {parallel}}), and reflection amplitude r({bold k}{sub {parallel}}) is given by (e{sup 2}/h)2N{summation}{sub {bold k}{sub {parallel}}}[1{minus}{vert_bar}r{vert_bar}{sup 2}{minus}(1{minus}{vert_bar}r{vert_bar}{sup 2}{minus}{vert_bar}t{vert_bar}{sup 2} )C]/{summation}{sub {bold k}{sub {parallel}}}(1+{vert_bar}r{vert_bar}{sup 2}{minus}{vert_bar}t{vert_bar}{sup 2}) for each spin, where N is the number of channels and C=1/(1{minus}e{sup {minus}L/lcos{theta}}){minus}lcos{theta}/L with cos{theta}={vert_bar}{bold k}{sub {parallel}}{vert_bar}/k{sub F}. In the diffusive limit L{gt}l we obtain the three-dimensional Boltzmann solution. In the ballistic limit L{lt}l we obtain one-dimensional Boltzmann solutions for N independent channels. If one applies the multiprobe one-dimensional B{umlt u}ttiker formula to a system where R+T{le}1, one reproduces our result for a single channel. {copyright} {ital 1997} {ital The American Physical Society}
- OSTI ID:
- 491646
- Journal Information:
- Physical Review, B: Condensed Matter, Vol. 55, Issue 16; Other Information: PBD: Apr 1997
- Country of Publication:
- United States
- Language:
- English
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