Interacting electrons in disordered wires: Anderson localization and low-temperature transport

We derive a general expression for the conductivity of a disordered conductor with electron-electron interactions (treated within the standard model) and evaluate the weak localization correction delta sigma_{wl} employing no approximations beyond the accuracy of the definition of delta sigma_{wl}. Our analysis applies to all orders in the interaction and extends our previous calculation by explicitly taking into account quantum fluctuations around the classical paths for int...

We study deterministic power-law quantum hopping model with an amplitude $J(r) \propto - r^{-\beta}$ and local Gaussian disorder in low dimensions $d=1,2$ under the condition $d < \beta < 3d/2$. We demonstrate unusual combination of exponentially decreasing density of the "tail states" and localization-delocalization transition (as function of disorder strength $w$) pertinent to a small (vanishing in thermodynamic limit) fraction of eigenstates. At sub-critical disorder $w < ...

Influence of disorder on the temperature of superconducting transition (T_c) is studied within the sigma-model renormalization group framework. Electron-electron interaction in particle-hole and Cooper channels is taken into account and assumed to be short-range. Two-dimensional systems in the weak localization and antilocalization regime, as well as systems near mobility edge are considered. It is shown that in all these regimes the Anderson localization leads to strong enha...

We investigate the effect of coupling Anderson localized particles in one dimension to a system of marginally localized phonons having a symmetry protected delocalized mode at zero frequency. This situation is naturally realized for electrons coupled to phonons in a disordered nano-wire as well as for ultra-cold fermions coupled to phonons of a superfluid in a one dimensional disordered trap. To determine if the coupled system can be many-body localized we analyze the phonon-...

We numerically investigate the transport properties of interacting spinless electrons in disordered systems. We use an efficient method which is based on the diagonalization of the Hamiltonian in the subspace of the many-particle Hilbert space which is spanned by the low-energy Slater states. Low-energy properties can be calculated with an accuracy comparable to that of exact diagonalization but for larger system sizes. The method works well in the entire parameter space, and...

We consider a two-dimensional model of a Fermionic wire in contact with reservoirs along its two opposite edges. With the reservoirs biased around a Fermi level, $E$, we study the scaling of the conductance of the wire with its length, $L$ as the width of the wire $W\rightarrow\infty$. The wire is disordered along the direction of the transport so the conductance is expected to exponentially decay with the length of the wire. However, we show that our model shows a super-diff...

We show that a one dimensional disordered conductor with correlated disorder has an extended state and a Landauer resistance that is non-zero in the limit of infinite system size in contrast to the predictions of the scaling theory of Anderson localization. The delocalization transition is not related to any underlying symmetry of the model such as particle-hole symmetry. For a wire of finite length the effect manifests as a sharp transmission resonance that narrows as the le...

We consider the one-dimensional lattice model of interacting fermions with disorder studied previously by Oganesyan and Huse [Phys. Rev. B 75, 155111 (2007)]. To characterize a possible many-body localization transition as a function of the disorder strength $W$, we use an exact renormalization procedure in configuration space that generalizes the Aoki real-space RG procedure for Anderson localization one-particle models [H. Aoki, J. Phys. C13, 3369 (1980)]. We focus on the s...

We investigate the dynamics of electrons in the vicinity of the Anderson transition in $d=3$ dimensions. Using the exact eigenstates from a numerical diagonalization, a number of quantities related to the critical behavior of the diffusion function are obtained. The relation $\eta = d-D_{2}$ between the correlation dimension $D_{2}$ of the multifractal eigenstates and the exponent $\eta$ which enters into correlation functions is verified. Numerically, we have $\eta\approx 1....

In this paper we present a thorough study of transport, spectral and wave-function properties at the Anderson localization critical point in spatial dimensions $d = 3$, $4$, $5$, $6$. Our aim is to analyze the dimensional dependence and to asses the role of the $d\rightarrow \infty$ limit provided by Bethe lattices and tree-like structures. Our results strongly suggest that the upper critical dimension of Anderson localization is infinite. Furthermore, we find that the $d_U=\...