One-dimensional conductance through an arbitrary potential

Details One-dimensional conductance through an arbitrary potential One-dimensional conductance through an arbitrary potential

2003-01-30

arxiv.org/abs/cond-mat/0301586v3

Phys. Rev. B 69, 113315 (2004)

Physics

Condensed Matter

Strongly Correlated Electrons

5 pages, no figure

Scientific paper

10.1103/PhysRevB.69.113315

The finite-size Tomonaga-Luttinger Hamiltonian with an arbitrary potential is mapped onto a non-interacting Fermi gas with renormalized potential. This is done by means of flow equations for Hamiltonians and is valid for small electron-electron interaction. This method also yields an alternative bosonization formula for the transformed field operator which makes no use of Klein factors. The two-terminal conductance can then be evaluated using the Landauer formula. We obtain similar results for infinite systems at finite temperature by identifying the flow parameter with the inverse squared temperature in the asymptotic regime. We recover the algebraic behavior of the conductance obtained by Kane and Fisher in the limit of low temperatures and weak electron-electron interaction, but our results remain valid for arbitrary external potential.

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