arXiv:1202.4632 · Physical Review Letters

Nonlinear Conductance of Long Quantum Wires at a Conductance Plateau Transition: Where Does the Voltage Drop?

Tobias Micklitz, Alex Levchenko, Achim Rosch

Published Jul 19, 2012• 10 citations

Abstract

We calculate the linear and nonlinear conductance of spinless fermions in clean, long quantum wires, where short-ranged interactions lead locally to equilibration. Close to the quantum phase transition, where the conductance jumps from zero to one conductance quantum, the conductance obtains a universal form governed by the ratios of temperature, bias voltage, and gate voltage. Asymptotic analytic results are compared to solutions of a Boltzmann equation which includes the effects of three-particle scattering. Surprisingly, we find that for long wires the voltage predominantly drops close to one end of the quantum wire due to a thermoelectric effect.

DOI: 10.1103/physrevlett.109.036405

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arXiv:1202.4632 · Physical Review Letters

Nonlinear Conductance of Long Quantum Wires at a Conductance Plateau Transition: Where Does the Voltage Drop?

Tobias Micklitz, Alex Levchenko, Achim Rosch

Published Jul 19, 2012• 10 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.109.036405

Related papers

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T

. Specifically, unlike in the two-terminal setup, the nonlinear conductances cannot be generically obtained from the linear ones by simply replacing

T

with the ``corresponding'' bias voltage or the largest one. Remarkably, a finite tunneling bias voltage prevents the interaction-induced breakup of the main wire into two disconnected pieces in the limit of zero

T

and a zero source-drain voltage.

V

, if

V

is the largest energy scale compared to temperature

T

and inverse wire length ${L}^{\ensuremath{-}1}$, and interpolates between these quantities in the crossover regimes.

1∕2

model with a repulsive on-site interaction or the spinless model with an attractive nearest neighbor interaction, we find that the conductance increases with increasing wire length or decreasing temperature. This can be explained using the Born approximation in scattering theory. For a strong impurity, the conductance is significantly different for a repulsive and an attractive impurity; this is due to the existence of a bound state in the latter case. In general, the large density deviations close to the impurity have an appreciable effect on the conductance at short distances which is not captured by the renormalization group equations.

J

. Inhomogeneity of the electron density due to the coupling of the wire to the leads results in violation of spin-charge separation in the device. As a result the spins affect the conductance of the wire. At zero temperature the low-energy spin excitations propagate freely through the wire, and its conductance remains

2{e}^{2}∕h

. Since the energy of the elementary excitations in the spin chain (spinons) cannot exceed $\ensuremath{\pi}J∕2$, the conductance of the wire acquires an exponentially small negative correction $\ensuremath{\delta}\phantom{\rule{0.2em}{0ex}}G\ensuremath{\propto}\ensuremath{-}\mathrm{exp}(\ensuremath{-}\ensuremath{\pi}J∕2T)$ at low temperatures

T⪡J

. At higher temperatures,

T⪢J

, most of the spin excitations in the leads are reflected by the wire, and the conductance levels off at a new universal value

{e}^{2}∕h

We investigate transport of spinless fermions through a single site dot junction of

M

one-dimensional quantum wires. The semi-infinite wires are described by a tight-binding model. Each wire consists of two parts, the noninteracting leads and a region of finite extent in which the fermions interact via a nearest-neighbor interaction. The functional renormalization group method is used to determine the flow of the linear conductance as a function of a low-energy cutoff for a wide range of parameters. Several fixed points are identified and their stability is analyzed. We determine the scaling exponents governing the low-energy physics close to the fixed points. Some of our results can already be derived using the non-self-consistent Hartree-Fock approximation.