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arXiv:cond-mat/0304158 · Europhysics Letters (EPL)

Resonant tunneling in a Luttinger liquid for arbitrary barrier transmission

S Hügle, Reinhold Egger

Published May 1, 2004• 18 citations
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Abstract

A numerically exact dynamical quantum Monte Carlo approach has been developed and applied to transport through a double barrier in a Luttinger liquid with arbitrary transmission. For strong transmission, we find broad Fabry-Pérot Coulomb-blockade peaks, with a lineshape parametrized by a single parameter, but at sufficiently low temperatures, non-Lorentzian universal lineshapes characteristic of coherent resonant tunneling emerge, even for strong interactions. For weak transmission, our data supports the recently proposed correlated sequential tunneling picture and is consistent with experimental results on intrinsic nanotube dots.

DOI
10.1209/epl/i2003-10229-5

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A numerically exact dynamical quantum Monte Carlo approach has been developed and applied to transport through a double barrier in a Luttinger liquid with arbitrary transmission. For strong transmission, we find broad Fabry-Pérot Coulomb-blockade peaks, with a lineshape parametrized by a single parameter, but at sufficiently low temperatures, non-Lorentzian universal lineshapes characteristic of coherent resonant tunneling emerge, even for strong interactions. For weak transmission, our data supports the recently proposed correlated sequential tunneling picture and is consistent with experimental results on intrinsic nanotube dots.
The resonant tunneling through a double-barrier structure in a one-dimensional system of interacting spinless fermions is studied. The conductance is calculated as a function of gate voltage and temperature. It is shown that even in Luttinger liquids the line shape of resonances is almost the same as that of the noninteracting Fermi liquid provided that the temperature is not too low. The temperature dependence, on the other hand, is drastically changed by the interaction, and the height of the conductance peak is a nonmonotonic function of temperature for weak repulsive interaction.
We study resonant tunneling in a Luttinger liquid with a double barrier enclosing a dot region. Within a microscopic model calculation the conductance GGG as a function of temperature TTT is determined over several decades. We identify parameter regimes in which the peak value Gp(T){G}_{p}(T)Gp​(T) shows distinctive power-law behavior. For intermediate dot parameters, Gp{G}_{p}Gp​ behaves in a nonuniversal way.
We generalize the fermionic renormalization group method to analytically describe transport through a double barrier structure in a one-dimensional system. Focusing on the case of weakly interacting electrons, we investigate thoroughly the dependence of the conductance on the strength and the shape of the double barrier for arbitrary temperature T. Our approach allows us to systematically analyze the contributions to renormalized scattering amplitudes from different characteristic scales absent in the case of a single impurity, without restricting the consideration to the model of a single resonant level. Both a sequential resonant tunneling for high T and a resonant transmission for T smaller than the resonance width are studied within the unified treatment of transport through strong barriers. For weak barriers, we show that two different regimes are possible. Moderately weak impurities may get strong due to a renormalization by interacting electrons, so that transport is described in terms of theory for initially strong barriers. The renormalization of very weak impurities does not yield any peak in the transmission probability; however, remarkably, the interaction gives rise to a sharp peak in the conductance, provided the asymmetry is not too high.
We generalize the fermionic renormalization group method to describe analytically transport through a double barrier structure in a one-dimensional system. Focusing on the case of weakly interacting electrons, we investigate thoroughly the dependence of the conductance on the strength and the shape of the double barrier for arbitrary temperature T. Our approach allows us to systematically analyze the contributions to renormalized scattering amplitudes from different characteristic scales absent in the case of a single impurity, without restricting the consideration to the model of a single resonant level. Both a sequential resonant tunneling for high T and a resonant transmission for T smaller than the resonance width are studied within the unified treatment of transport through strong barriers. For weak barriers, we show that two different regimes are possible. Moderately weak impurities may get strong due to a renormalization by interacting electrons, so that transport is described in terms of theory for initially strong barriers. The renormalization of very weak impurities does not yield any peak in the transmission probability; however, remarkably, the interaction gives rise to a sharp peak in the conductance, provided asymmetry is not too high.
We study transport through two Luttinger liquids (one-dimensional electrons interacting through a Coulomb repulsion in a metal) coupled together at two points. External voltage biases are incorporated through boundary conditions. We include density-density couplings as well as single-particle hops at the contacts. For weak repulsive interactions, transport through the wires remains undisturbed by the interwire couplings, which renormalize to zero. For strong repulsive interactions, the interwire couplings become strong. For symmetric barriers and no external voltage bias, a single gate voltage is sufficient to tune for resonance transmission in both wires. However, for asymmetric couplings or for finite external biases, the system is insulating.