Microwave-Induced Dephasing in One-Dimensional Metal Wires

We report on the effect of monochromatic microwave (MW) radiation on the weak localization corrections to the conductivity of quasi-one-dimensional (1D) silver wires. Due to the improved electron cooling in the wires, the MW-induced dephasing was observed without a concomitant overheating of electrons over wide ranges of the MW power $P_{MW}$ and frequency $f$. The observed dependences of the conductivity and MW-induced dephasing rate on $P_{MW}$ and $f$ are in agreement with the theory by Altshuler, Aronov, and Khmelnitsky \cite{Alt81}. Our results suggest that in the low-temperature experiments with 1D wires, saturation of the temperature dependence of the dephasing time can be caused by an MW electromagnetic noise with a sub-pW power.Comment: 4 pages with 4 figures, paper revised, accepted by Phys Rev Let

Anderson localisation in tight-binding models with flat bands

We consider the effect of weak disorder on eigenstates in a special class of tight-binding models. Models in this class have short-range hopping on periodic lattices; their defining feature is that the clean systems have some energy bands that are dispersionless throughout the Brillouin zone. We show that states derived from these flat bands are generically critical in the presence of weak disorder, being neither Anderson localised nor spatially extended. Further, we establish a mapping between this localisation problem and the one of resonances in random impedance networks, which previous work has suggested are also critical. Our conclusions are illustrated using numerical results for a two-dimensional lattice, known as the square lattice with crossings or the planar pyrochlore lattice.Comment: 5 pages, 3 figures, as published (this version includes minor corrections

Quantum coherence in a ferromagnetic metal: time-dependent conductance fluctuations

Quantum coherence of electrons in ferromagnetic metals is difficult to assess experimentally. We report the first measurements of time-dependent universal conductance fluctuations in ferromagnetic metal (Ni$_{0.8}$Fe$_{0.2}$) nanostructures as a function of temperature and magnetic field strength and orientation. We find that the cooperon contribution to this quantum correction is suppressed, and that domain wall motion can be a source of coherence-enhanced conductance fluctuations. The fluctuations are more strongly temperature dependent than those in normal metals, hinting that an unusual dephasing mechanism may be at work.Comment: 5 pages, 4 figure

Weak localization effect on thermomagnetic phenomena

The quantum transport equation (QTE) is extended to study weak localization (WL) effects on galvanomagnetic and thermomagnetic phenomena. QTE has many advantages over the linear response method (LRM): (i) particle-hole asymmetry which is necessary for the Hall effect is taken into account by the nonequilibrium distribution function, while LRM requires expansion near the Fermi surface, (ii) when calculating response to the temperature gradient, the problem of WL correction to the heat current operator is avoided, (iii) magnetic field is directly introduced to QTE, while the LRM deals with the vector potential and and special attention should be paid to maintain gauge invariance, e.g. when calculating the Nernst effect the heat current operator should be modified to include the external magnetic field. We reproduce in a very compact form known results for the conductivity, the Hall and the thermoelectric effects and then we study our main problem, WL correction to the Nernst coefficient (transverse thermopower).Comment: 20 pages 2 figure

Universal conductance fluctuations in Dirac materials in the presence of long-range disorder

We study quantum transport in Dirac materials with a single fermionic Dirac cone (strong topological insulators and graphene in the absence of intervalley coupling) in the presence of non-Gaussian long-range disorder. We show, by directly calculating numerically the conductance fluctuations, that in the limit of very large system size and disorder strength, quantum transport becomes universal. However, a systematic deviation away from universality is obtained for realistic system parameters. By comparing our results to existing experimental data on 1/f noise, we suggest that many of the graphene samples studied to date are in a non-universal crossover regime of conductance fluctuations.Comment: 5 pages, 3 figures. Published versio

Level correlations in integrable systems

We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger scales. We apply our results to a rectangle with incommensurate sides and show that they are in excellent agreement with the limiting cases established in the semiclassical theory of level rigidity.Comment: 5 page

Critical level statistics and anomalously localized states at the Anderson transition

We study the level-spacing distribution function $P(s)$ at the Anderson transition by paying attention to anomalously localized states (ALS) which contribute to statistical properties at the critical point. It is found that the distribution $P(s)$ for level pairs of ALS coincides with that for pairs of typical multifractal states. This implies that ALS do not affect the shape of the critical level-spacing distribution function. We also show that the insensitivity of $P(s)$ to ALS is a consequence of multifractality in tail structures of ALS.Comment: 8 pages, 5 figure

Interaction effects and phase relaxation in disordered systems

This paper is intended to demonstrate that there is no need to revise the existing theory of the transport properties of disordered conductors in the so-called weak localization regime. In particular, we demonstrate explicitly that recent attempts to justify theoretically that the dephasing rate (extracted from the magnetoresistance) remains finite at zero temperature are based on the profoundly incorrect calculation. This demonstration is based on a straightforward evaluation of the effect of the electron-electron interaction on the weak localization correction to the conductivity of disordered metals. Using well-controlled perturbation theory with the inverse conductance $g$ as the small parameter, we show that this effect consists of two contributions. First contribution comes from the processes with energy transfer smaller than the temperature. This contribution is responsible for setting the energy scale for the magnetoresistance. The second contribution originates from the virtual processes with energy transfer larger than the temperature. It is shown that the latter processes have nothing to do with the dephasing, but rather manifest the second order (in $1/g$) correction to the conductance. This correction is calculated for the first time. The paper also contains a brief review of the existing experiments on the dephasing of electrons in disordered conductors and an extended qualitative discussion of the quantum corrections to the conductivity and to the density of electronic states in the weak localization regime.Comment: 34 pages, 13 .eps figure

Non-linear effects and dephasing in disordered electron systems

The calculation of the dephasing time in electron systems is presented. By means of the Keldysh formalism we discuss in a unifying way both weak localization and interaction effects in disordered systems. This allows us to show how dephasing arises both in the particle-particle channel (weak localization) and in the particle-hole channel (interaction effect). First we discuss dephasing by an external field. Besides reviewing previous work on how an external oscillating field suppresses the weak localization correction, we derive a new expression for the effect of a field on the interaction correction. We find that the latter may be suppressed by a static electric field, in contrast to weak localization. We then consider dephasing due to inelastic scattering. The ambiguities involved in the definition of the dephasing time are clarified by directly comparing the diagrammatic approach with the path-integral approach. We show that different dephasing times appear in the particle-particle and particle-hole channels. Finally we comment on recent experiments.Comment: 28 pages, 6 figures (14ps-files

Transport of interacting electrons in arrays of quantum dots and diffusive wires

We develop a detailed theoretical investigation of the effect of Coulomb interaction on electron transport in arrays of chaotic quantum dots and diffusive metallic wires. Employing the real time path integral technique we formulate a new Langevin-type of approach which exploits a direct relation between shot noise and interaction effects in mesoscopic conductors. With the aid of this approach we establish a general expression for the Fano factor of 1D quantum dot arrays and derive a complete formula for the interaction correction to the current which embraces all perturbative results previously obtained for various quasi-0D and quasi-1D disordered conductors and extends these results to yet unexplored regimes.Comment: 12 pages, 2 figure