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arXiv:0906.2654 · Physical Review B

Persistent currents in nanorings and quantum decoherence by Coulomb interaction

Andrew G. Semenov, Andrei D. Zaikin

Published Oct 8, 2009• 6 citations
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Abstract

Employing instanton technique we evaluate equilibrium persistent current (PC) produced by a quantum particle moving in a periodic potential on a ring and interacting with a dissipative environment formed by diffusive electron gas. The model allows for detailed nonperturbative analysis of interaction effects and, depending on the system parameters, yields a rich structure of different regimes. We demonstrate that at low temperatures PC is exponentially suppressed at sufficiently large ring perimeters $2\ensuremath{\pi}R>{L}_{\ensuremath{\varphi}}$, where the dephasing length ${L}_{\ensuremath{\varphi}}$ is set by interactions and does not depend on temperature. This behavior represents a clear example of quantum decoherence by electron-electron interactions at $T\ensuremath{\rightarrow}0$.

DOI
10.1103/physrevb.80.155312

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Employing instanton technique we evaluate equilibrium persistent current (PC) produced by a quantum particle moving in a periodic potential on a ring and interacting with a dissipative environment formed by diffusive electron gas. The model allows for detailed nonperturbative analysis of interaction effects and, depending on the system parameters, yields a rich structure of different regimes. We demonstrate that at low temperatures PC is exponentially suppressed at sufficiently large ring perimeters 2\ensuremathπR>L\ensuremathφ2\ensuremath{\pi}R>{L}_{\ensuremath{\varphi}}2\ensuremathπR>L\ensuremathφ​, where the dephasing length L\ensuremathφ{L}_{\ensuremath{\varphi}}L\ensuremathφ​ is set by interactions and does not depend on temperature. This behavior represents a clear example of quantum decoherence by electron-electron interactions at T\ensuremath→0T\ensuremath{\rightarrow}0T\ensuremath→0.
We investigate fluctuations of persistent current (PC) in nanorings both with and without dissipation and decoherence. We demonstrate that such PC fluctuations may persist down to zero temperature provided there exists either interaction with an external environment or an external (periodic) potential produced, e.g., by quantum phase slips in superconducting nanorings. Provided quantum coherence is maintained in the system PC noise remains coherent and can be tuned by an external magnetic flux ΦxΦ_xΦx​ piercing the ring. If quantum coherence gets suppressed by interactions with a dissipative bath PC noise becomes incoherent and ΦxΦ_xΦx​-independent.
We introduce a model for the persistent current carried by spinless fermions moving in a ring with a high-dimensional cross section. The effects of both disorder and electron - electron interaction are considered. It is found that the non-interacting system behaves like previously considered low-dimensional models. The more complicated interacting/disordered case is analysed by means of a functional integral which is evaluated in the limit of infinite dimensionality by expanding in the number of transverse channels. To leading order in this expansion scheme, the Coulomb interaction does not affect the persistent current. It is found that the insensitivity to interaction effects is due to the absence of local contributions to the Coulomb vertex in our model (which in turn is a consequence of the neglect of the electron spin). It is argued that the physical mechanism suppressing the interaction in the high-dimensional spinless model applies to the analogous low-dimensional case as well.
A perturbative approach for large (in comparison with electron overlap and onsite disorder) long-range Coulomb interaction is developed for a 1D ring model. The explicit expression for low-lying energy levels has been obtained. It is shown that in the case of strong repulsive long-range interaction persistent current does not depend exclusively on the filling factor nu =p/q but is extremely sensitive to its denominator q. It also depends on the common factor M of electrons and sites number. In the absence of a common factor (M=1) there exists only one quasiparticle that experiences no strong Coulomb interaction, thus moving freely with bare electron overlap, which provides an unexpectedly large persistent current. For the case of an arbitrary M and a large enough q a system of M weakly interacting quasiparticles has been introduced, which undergoes a metal-insulator transition at unusually small overlap even for a filling factor close to one half. Suppression of the persistent current by disorder is taken into account. Comparison of analytically obtained expressions with the results of numerical calculations shows a reasonable agreement.
We investigate low-temperature dephasing in several model systems, where a quantum degree of freedom is coupled to a bath. Dephasing, defined as the decay of the coherence of inital non-equilibrium states, also influences the dynamics of equilibrium correlation and response functions, as well as static interference effects. In particular in the latter case dephasing should be distinguished from renormalization effects. For illustration, and because of its relevance for quantum state engineering in dissipative environments, we first reconsider dephasing in spin-boson models. Next we review Caldeira-Leggett models, with applications, e.g., to persistent currents in mesoscopic rings. Then, we analyze the more general problem of a particle which interacts with a quantum field V(t,r(t)), the fluctuations of which are characterized by a dielectric function epsilon(omega,k). Finally, we compare this model, both the formulation as well as the results, to the problem of interacting electrons in a diffusive conductor.
We investigate low-temperature dephasing in several model systems, where a quantum degree of freedom is coupled to a bath.Dephasing, defined as the decay of the coherence of inital non-equilibrium states, also influences the dynamics of equilibrium correlation and response functions, as well as static interference effects.In particular in the latter case dephasing should be distinguished from renormalization effects.For illustration, and because of its relevance for quantum state engineering in dissipative environments, we first reconsider dephasing in spinboson models.Next we review Caldeira-Leggett models, with applications, e.g., to persistent currents in mesoscopic rings.Then, we analyze the more general problem of a particle which interacts with a quantum field V (t, r(t)), the fluctuations of which are characterized by a dielectric function (ω, k).Finally, we compare this model, both the formulation as well as the results, to the problem of interacting electrons in a diffusive conductor.