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arXiv:cond-mat/0305335 · Physical review. B, Condensed matter

Microscopic mechanisms of dephasing due to electron-electron interactions

Rok Žitko, J. Bonča

Published Aug 13, 2003• 10 citations
arXivHTMLPDF

Abstract

We develop a nonperturbative numerical method to study tunneling of a single electron through an Aharonov-Bohm ring where several strongly interacting electrons are bound. Inelastic processes and spin-flip scattering are taken into account. The method is applied to study microscopic mechanisms of dephasing in a nontrivial model. We show that the electron-electron interactions described by the Hubbard Hamiltonian lead to strong dephasing: the transmission probability at flux $\ensuremath{\Phi}=\ensuremath{\pi}$ is high even at small interaction strength. In addition to inelastic scattering, we identify two energy-conserving mechanisms of dephasing: symmetry-changing and spin-flip scattering. The many-electron state on the ring determines which of these mechanisms will be at play: transmitted current can occur either in elastic or inelastic channels, with or without changing the spin of the scattering electron.

DOI
10.1103/physrevb.68.085313

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•Jan 1, 2011•0 citations
We develop a nonperturbative numerical method to study tunneling of a single electron through an Aharonov-Bohm ring where several strongly interacting electrons are bound. Inelastic processes and spin-flip scattering are taken into account. The method is applied to study microscopic mechanisms of dephasing in a nontrivial model. We show that the electron-electron interactions described by the Hubbard Hamiltonian lead to strong dephasing: the transmission probability at flux \ensuremathΦ=\ensuremathπ\ensuremath{\Phi}=\ensuremath{\pi}\ensuremathΦ=\ensuremathπ is high even at small interaction strength. In addition to inelastic scattering, we identify two energy-conserving mechanisms of dephasing: symmetry-changing and spin-flip scattering. The many-electron state on the ring determines which of these mechanisms will be at play: transmitted current can occur either in elastic or inelastic channels, with or without changing the spin of the scattering electron.
We present a detailed analysis of the Aharonov-Bohm interference oscillations manifested through transmission of an electron in a mesoscopic ring with a magnetic impurity atom inserted in one of its arms. The electron interacts with the impurity through the exchange interaction leading to exchange spin-flip scattering. Transmission in the spin-flipped and spin-unflipped channels are explicitly calculated. We show that the spin-flipper acts as a dephasor in spite of absence of any inelastic scattering. The spin-conductance (related to spin-polarized transmission coefficient) is asymmetric in the flux reversal as opposed to the two probe conductance which is symmetric under flux reversal.
We study a simple model of dephasing of Aharonov-Bohm oscillations in the transmission of an electron across a mesoscopic ring. A magnetic impurity in one of the arms of the ring couples to the electron spin via an exchange interaction. This interaction leads to spin flip scattering and induces dephasing via entanglement. This is akin to the models evoked earlier to explain destruction of interference due to which-path information in double-slit experiments. Total transmission is found to be symmetric under flux reversal but not the spin polarization.
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.
We study manifestations of spin-charge separation (SCS) in transport through a tunnel-coupled interacting single-channel quantum ring. We focus on the high-temperature case (temperature TTT larger than the level spacing $\mathrm{\ensuremath{\Delta}}$) and discuss both the classical (flux-independent) and interference contributions to the tunneling conductance of the ring in the presence of magnetic flux. We demonstrate that the SCS effects, which arise solely from the electron-electron interaction, lead to the appearance of a peculiar fine structure of the electron spectrum in the ring. Specifically, each level splits into a series of sublevels, with their spacing governed by the interaction strength. In the high-TTT limit, the envelope of the series contains of the order of $T/\mathrm{\ensuremath{\Delta}}$ sublevels. At the same time, SCS suppresses the tunneling width of the sublevels by a factor of $\mathrm{\ensuremath{\Delta}}/T$. As a consequence, the classical transmission through the ring remains unchanged compared to the noninteracting case: the suppression of tunneling is compensated by the increase of the number of tunneling channels. On the other hand, the flux-dependent contribution to the conductance depends on the interaction-induced dephasing rate which is known to be parametrically increased by SCS in an infinite system. We show, however, that SCS is not effective for dephasing in the limit of weak tunneling. Moreover, generically, in the almost closed ring, the dephasing rate does not depend on the interaction strength and is determined by the tunneling coupling to the leads. In certain special symmetric cases, dephasing is further suppressed. Similarly to the spinless case, the high-TTT conductance shows, as a function of magnetic flux, a sequence of interaction-induced sharp negative peaks on top of the classical contribution.
We study transport in interacting one-dimensional systems with a scattering object. In particular we are interested in inelastic scattering processes. Very recent theoretical [3] and experimental [54] research points toward a strong influence of incoherent scattering on the low-temperature transport features of one-dimensional systems with extended scatterers. Furthermore, if inelastic processes are strong a straightforward application of the renormalization group (RG) approach is not possible. In the field of transport in one-dimensional weakly interacting electron systems, this procedure is the state-of-the art method to extend results for weak interaction to the low temperature regime [18,27,43, 47, 52,57, 62, 67,74]. The underlying assumption, namely that the first-order correction in interaction incorporates all effects of the interaction and reproduces itself in higher orders, is widely accepted as a valid “educated guess” disregarding the fact that inelastic processes, if present, arise in subleading orders. Indeed, for the simple case of a single impurity in an infinite wire it is common believe that the approach is valid [6,74]. Having this in mind, systems with a great variety of additional degrees of freedom were treated in the same fashion: Junctions of wires [43] and more complex geometries [18], anti-resonant [47] and resonant [57, 62] scatterers, just to name a few. A careful examination of the interplay between the renormalization and possible inelastic processes or dephasing in these cases is missing. Our strategy is to calculate the second order in interaction for the single impurity situation, thereby establishing a framework with a real-space diagrammatic technique, and to apply this tool to more complex situations, i.e., a finite interacting region and an additional impurity. The diagrammatic technique enables us to identify specific diagrams where the particle number at a given energy is not conserved or the interaction can lead to dephasing in the system. In particular, by modelling the compound scatterer by an energy dependent S-matrix of the Breit-Wigner type, we are able to find a fingerprint of weak dephasing which carries some features of its counterpart in disordered Luttinger liquids [32].