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Register a new userDimensional Crossover of the Dephasing Time in Disordered Mesoscopic Rings
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We study dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ring weakly coupled to leads. We use an influence functional for quantum Nyquist noise to describe the crossover for the dephasing time $Tph (T)$ from diffusive or ergodic 1D ($ Tph^{-1} propto T^{2/3}, T^{1}$) to 0D behavior ($Tph^{-1} propto T^{2}$) as $T$ drops below the Thouless energy. The crossover to 0D, predicted earlier for 2D and 3D systems, has so far eluded experimental observation. The ring geometry holds promise of meeting this longstanding challenge, since the crossover manifests itself not only in the smooth part of the magnetoconductivity but also in the amplitude of Altshuler-Aronov-Spivak oscillations. This allows signatures of dephasing in the ring to be cleanly extracted by filtering out those of the leads.
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We analyze dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ring weakly coupled to leads, where we recently predicted a crossover for the dephasing time $tPh(T)$ from diffusive or ergodic 1D ($tPh^{-1} propto T^{2/3}, T^{1}$) to $0D$ behavior ($tPh^{-1} propto T^{2}$) as $T$ drops below the Thouless energy $ETh$. We provide a detailed derivation of our results, based on an influence functional for quantum Nyquist noise, and calculate all leading and subleading terms of the dephasing time in the three regimes. Explicitly taking into account the Pauli blocking of the Fermi sea in the metal allows us to describe the $0D$ regime on equal footing as the others. The crossover to $0D$, predicted by Sivan, Imry and Aronov for 3D systems, has so far eluded experimental observation. We will show that for $T ll ETh$, $0D$ dephasing governs not only the $T$-dependence for the smooth part of the magnetoconductivity but also for the amplitude of the Altshuler-Aronov-Spivak oscillations, which result only from electron paths winding around the ring. This observation can be exploited to filter out and eliminate contributions to dephasing from trajectories which do not wind around the ring, which may tend to mask the $T^{2}$ behavior. Thus, the ring geometry holds promise of finally observing the crossover to $0D$ experimentally.
Superconducting wires with broken time-reversal and spin-rotational symmetries can exhibit two distinct topological gapped phases and host bound Majorana states at the phase boundaries. When the wire is tuned to the transition between these two phases and the gap is closed, Majorana states become delocalized leading to a peculiar critical state of the system. We study transport properties of this critical state as a function of the length $L$ of a disordered multichannel wire. Applying a non-linear supersymmetric sigma model of symmetry class D with two replicas, we identify the average conductance, its variance and the third cumulant in the whole range of $L$ from the Ohmic limit of short wires to the regime of a broad conductance distribution when $L$ exceeds the correlation length of the system. In addition, we calculate the average shot noise power and variance of the topological index for arbitrary $L$. The general approach developed in the paper can also be applied to study combined effects of disorder and topology in wires of other symmetries.
We study the non-linear conductance $mathcal{G}simpartial^2I/partial V^2|_{V=0}$ in coherent quasi-1D weakly disordered metallic wires. The analysis is based on the calculation of two fundamental correlators (correlations of conductances functional derivatives and correlations of injectivities), which are obtained explicitly by using diagrammatic techniques. In a coherent wire of length $L$, we obtain $mathcal{G}sim0.006,E_mathrm{Th}^{-1}$ (and $langlemathcal{G}rangle=0$), where $E_mathrm{Th}=D/L^2$ is the Thouless energy and $D$ the diffusion constant; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal: the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, $mathcal{G}_asim0.001,(gE_mathrm{Th})^{-1}$, where $ggg1$ is the dimensionless (linear) conductance of the wire. Weakly coherent regimes are also studied: for $L_varphill L$, where $L_varphi$ is the phase coherence length, we get $mathcal{G}sim(L_varphi/L)^{7/2}E_mathrm{Th}^{-1}$, and $mathcal{G}_asim(L_varphi/L)^{11/2}(gE_mathrm{Th})^{-1}llmathcal{G}$ (at high magnetic field). When thermal fluctuations are important, $L_Tll L_varphill L$ where $L_T=sqrt{D/T}$, we obtain $mathcal{G}sim(L_T/L)(L_varphi/L)^{7/2}E_mathrm{Th}^{-1}$ (the result is dominated by the effect of screening) and $mathcal{G}_asim(L_T/L)^2(L_varphi/L)^{7/2}(gE_mathrm{Th})^{-1}$. All the precise dimensionless prefactors are obtained. Crossovers towards the zero magnetic field regime are also analysed.
The wavefunctions of a disordered two-dimensional electron gas at the quantum-critical Anderson transition are predicted to exhibit multifractal scaling in their real space amplitude. We experimentally investigate the appearance of these characteristics in the spatially resolved local density of states of a two-dimensional mixed surface alloy Bi_xPb_{1-x}/Ag(111), by combining high-resolution scanning tunneling microscopy with spin and angle-resolved inverse-photoemission experiments. Our detailed knowledge of the surface alloy electronic band structure, the exact lattice structure and the atomically resolved local density of states enables us to construct a realistic Anderson tight binding model of the mixed surface alloy, and to directly compare the measured local density of states characteristics with those from our model calculations. The statistical analyses of these two-dimensional local density of states maps reveal their log-normal distributions and multifractal scaling characteristics of the underlying wavefunctions with a finite anomalous scaling exponent. Finally, our experimental results confirm theoretical predictions of an exact scaling symmetry for Anderson quantum phase transitions in the Wigner-Dyson classes.
We report on magnetoconductance measurements of metallic networks of various sizes ranging from 10 to $10^{6}$ plaquettes, with anisotropic aspect ratio. Both Altshuler-Aronov-Spivak (AAS) $h/2e$ periodic oscillations and Aharonov-Bohm (AB) $h/e$ periodic oscillations are observed for all networks. For large samples, the amplitude of both oscillations results from the incoherent superposition of contributions of phase coherent regions. When the transverse size becomes smaller than the phase coherent length $L_phi$, one enters a new regime which is phase coherent (mesoscopic) along one direction and macroscopic along the other, leading to a new size dependence of the quantum oscillations.
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