Mesoscopic decoherence in Aharonov-Bohm rings

Abstract

We study electron decoherence by measuring the temperature dependence of Aharonov-Bohm (AB) oscillations in quasi-1D rings, etched in a high-mobility GaAs/GaAlAs heterostructure. The oscillation amplitude is influenced both by phase-breaking and by thermal averaging. Thermal averaging is important when the temperature approaches the energy scale, on which the AB oscillations shift their phase. For the phase-breaking, it is demonstrated that the damping of the oscillation amplitude is proportional to the length of the interfering paths. For temperatures T from 0.3 to 4 K we find the phase coherence length The understanding of decoherence in quantum mechanical systems gives valuable insight into the cross-over from quantum to classical behavior. Quantum phenomena like weak localization, universal conductance fluctuations and the Aharonov-Bohm effect, that are observed in mesoscopic electronic systems, make these systems well suited for studying decoherence. The loss of electron phase coherence is interesting in its own right because it reveals information about the fundamental physics of the electron scattering mechanisms. Moreover, from the perspective of possible phase-coherent mesoscopic electronic devices 1 , knowledge of phase-breaking length and time scales is crucial.At low temperatures, electron-electron scattering is usually the dominating source of phase-breaking. In disordered 1D and 2D conductors, the loss of phase coherence at low temperatures has been studied intensively, both theoretically and experimentally 2 . In clean electron systems, the number of investigations are fewer 3-6 . In 2D, experiments consistent with the expected 7 electronelectron scattering time τ φ ∼ (T 2 ln T ) −1 has been carried out 3,4 . In open quantum dots (a 0D system), an unexpected T −1 contribution was found 5,6 . In general, phase breaking mechanisms in ballistic, mesoscopic systems of dimensionality less than 2, are presently not well understood.Aharonov-Bohm (AB) rings are obvious systems for probing phase coherence. Here, the interference of two electron paths leads to conductance oscillations of period h/e [or frequency e/h] in the magnetic flux enclosed by the paths. The oscillation amplitude is a direct measure of the interference strength, and it has been used to study decoherence in disordered systems 8 . For AB rings with a 2DEG elastic mean free path longer than the circumference of the device (e.g. 9-15 and references therein), systematic studies of phase-breaking have been scarce.In this paper, we report measurements of the phase coherence length L φ via the temperature dependence of AB conductance oscillations in quasi-1D rings, made by shallow etching in GaAs/GaAlAs heterostructures. Two mechanisms are important for the temperature dependence of the oscillation amplitude: phase-breaking, and thermal averaging. At finite temperature, the measured conductance is a weighted average over an energy interval of finite width, proportional to the temperature. We discuss, how thermal averaging influences the AB os...

Electron lifetime in Luttinger liquids

“…We like to stress that a dephasing time varying as T −1 has been reported in Refs. [11,12] that seems to reinforce the thesis that electron-electron interactions should not be ignored in quantum wires. The work presented here can be extended in many directions: in particular, muti-channels and systems with backscattering may be considered.…”

“…Here, we like to underline that interference experiments of Ref. [11,12] performed in the ballistic limit report a dephasing time that varies as 1/T . It is relevant to remember that those results might be explained from the electron-electron interaction (that can be intrinsic or induced by side-gates).…”

“…In two dimensions, experiments consistent with the energy relaxation time τ φ ∝ (T 2 ln T ) −1 have been carried out in clean samples [10]. Recent Aharonov-Bohm (AB) oscillations measured on very clean (ballistic) quasi 1D rings with only a few propagating channels support a dephasing time which varies as τ φ ∝ T −1 and the dephasing of the electronic wavefunctions has been distinguished from thermal averaging effects [11]. The same results have been reproduced in a four-terminal geometry [12].…”

“…Of interest to us is thus to elucidate the notion of electron decoherence in a 1D very clean ballistic system with only one propagating channel by generically taking the electron-electron interaction into account, producing a Luttinger liquid (T is much smaller than the electron bandwidth). We shall explain why the dephasing time of ballistic 1D conductors in Aharonov-Bohm experiments follows τ φ ∝ T −1 , considering the one channel case, that seems to be of experimental interest [11,12]. One very peculiar aspect of the LL is the breakdown of the Landau's quasiparticle picture and the electron fractionalization mechanism implying that genuine charged excitations carry fractional quantum numbers (for spinful but also for spin-polarized electrons); consult Ref.…”

“…We stress that the electron lifetime can be detected through the dephasing of Aharonov-Bohm oscillations as observed in Refs. [11,12] or via momentum-resolved tunneling [26,27]. Keep in mind that the phase-breaking time of clean LLs, that controls the exponential suppression of electronic interferences as a function of the length of the interfering paths, is determined by the single-particle Green's function [21,25,28].…”