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arXiv:cond-mat/9706008 · Physical review. B, Condensed matter

Interplay of Coulomb blockade and Aharonov-Bohm resonances in a Luttinger liquid

Jari M. Kinaret, M. Jonson, Robert I Shekhter, Sebastian Eggert

Published Feb 15, 1998• 19 citations
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Abstract

We consider a ring of strongly interacting electrons connected to two external leads by tunnel junctions. By studying the positions of conductance resonances as a function of gate voltage and magnetic flux, the interaction parameter $g$ can be determined experimentally. For a finite ring the minimum conductance is strongly influenced by device geometry and electron-electron interactions. In particular, if the tunnel junctions are close to one another, the interaction-related orthogonality catastrophe is suppressed and the valley current is unexpectedly large.

DOI
10.1103/physrevb.57.3777

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We consider a ring of strongly interacting electrons connected to two external leads by tunnel junctions. By studying the positions of conductance resonances as a function of gate voltage and magnetic flux, the interaction parameter ggg can be determined experimentally. For a finite ring the minimum conductance is strongly influenced by device geometry and electron-electron interactions. In particular, if the tunnel junctions are close to one another, the interaction-related orthogonality catastrophe is suppressed and the valley current is unexpectedly large.
We study the Josephson effect through a one-dimensional system of interacting electrons, connected to two superconductors by tunnel junctions. The interactions are treated in the framework of the Luttinger model. At zero temperature, the Josephson critical current decays algebraically with increasing distance between the junctions. In a Luttinger liquid of finite size, the Josephson current depends on the total number of electrons modulo 4. These parity effects are studied for a ring, coupled capacitively to a gate voltage and threaded by a magnetic flux. Interactions introduce qualitatively new features compared to the noninteracting case.
The nonlinear charge transfer through a tunnel junction between two Luttinger systems is studied for repulsive, finite-range interaction between electrons on the same side, V11{\mathrm{V}}_{11}V11​, and on different sides, V12{\mathrm{V}}_{12}V12​, of a junction. Features of the Coulomb blockade effect are observed if V12{\mathrm{V}}_{12}V12​=0. We predict an interaction-induced enhancement of the current if V12{\mathrm{V}}_{12}V12​>0. When V12{\mathrm{V}}_{12}V12​=V11{\mathrm{V}}_{11}V11​, the current is suppressed at small bias, but the ``charging energy,'' obtained from the asymptotic behavior at high-bias voltage, vanishes.
We show that in a ring-shaped Luttinger Liquid (LL) in contact with an electron reservoir --- the chemical potential in the ring being controlled by a gate voltage VgV_gVg​ --- both the average ring charge and the persistent current in the ring are step-like functions of VgV_gVg​ at low temperatures. The step positions are determined by the LL parameter α=vF/sα=v_F/sα=vF​/s, which therefore can be directly measured. We study electrons both with and without spin, taking into account long-range interactions in the ring.
We propose a method to detect a Luttinger liquid (LL)-like behavior of a quasione-dimensional ring of electrons that does not depend on a transport measurement.Rather, a Coulomb blockade-induced quantization of the persistent current and excess charge in a ring of interacting electrons are shown to depend on the interaction strength.Both the average ring charge and the persistent current are step-like functions of an applied gate voltage at low temperatures.The step positions are determined by the LL parameter α, which therefore can be directly measured.
We study the effect of electron-electron interaction on transport through a tunnel-coupled single-channel ring. We find that the conductance as a function of magnetic flux shows a series of interaction-induced resonances that survive thermal averaging. The period of the series is given by the interaction strength α. The physics behind this behavior is the blocking of the tunneling current by the circular current. The main mechanism of dephasing is due to circular-current fluctuations. The dephasing rate is proportional to the tunneling rate and does not depend on α.
Theoretical studies suggest that an interacting one-dimensional electron system does not behave as a Fermi liquid. Instead, it is predicted to form a Luttinger liquid characterized e.g. by the absence of fermionic quasiparticles and interaction-dependent power-laws for transport quantities. So far, however, only a limited number of experiments have provided evidence for Luttinger liquid behavior. In this thesis we consider alternative methods to detect electronic correlations in one-dimensional electron systems based on our calculations of persistent currents and quantization of charge in ballistic single channel rings. The persistent current in an isolated impurity-free Luttinger liquid ring is found to be the same as for a system of non-interacting electrons. In contrast, a Luttinger liquid behavior is revealed if the ring is weakly connected to an electron reservoir and capacitively coupled to a gate electrode. The persistent current and the average charge in the ring are shown to change in a stepwise manner with the gate voltage at low temperatures. Both the step positions and the crossover temperatures are determined by the Luttinger liquid correlation parameter .alpha.(.alpha.c) which therefore can be measured. When a potential barrier is incorporated into the ring, the presence of strong interactions between electrons leads to a suppression of the persistent current and a change in its temperature dependence. A sharp maximum of the current is predicted to occur as a function of temperature. When two barriers are introduced into the ring, the possibility of resonant tunneling for the persistent current opens up. Two kinds of resonant behavior are discovered in the closed geometry: a current independent of the barrier transparency and a current analogous to the one with a single potential barrier. The persistent current in a ring containing a gas of fractionally charged excitations obeying fractional exclusion statistics is also studied. At finite temperatures, anomalous oscillations of the current are predicted as a manifestation of the statistics of the quasiparticles.