Weak localization and coulomb interaction in disordered systems

Amit Dutta, Lars Fritz, Diptiman Sen

We study a one-dimensional system of spinless electrons in the presence of a long-range Coulomb interaction (LRCI) and a random chemical potential at each site. We present a Tomonaga-Luttinger liquid description of the system. We use the bosonization technique followed by the replica trick to average over the quenched randomness. An expression for the localization length of the system is obtained using the renormalization-group method and also a physical argument. We then find the density of states for different values of the energy; we get different expressions depending on whether the scale of energy is larger than or smaller than the inverse of the localization length. We work in the limit of weak disorder where the localization length is very large, at that length scale, the LRCI has the effect of reducing the interaction parameter K to a value much smaller than the noninteracting value of unity.

A. MacKinnon

Rahul Nandkishore, S. A. Parameswaran

We investigate the interplay of Coulomb interactions and short-range-correlated disorder in three-dimensional systems where absent disorder the noninteracting band structure hosts a quadratic band crossing. Though the clean Coulomb problem is believed to host a non-Fermi liquid phase, disorder and Coulomb interactions have the same scaling dimension in a renormalization group (RG) sense, and thus should be treated on an equal footing. We therefore implement a controlled $\ensuremath{\varepsilon}$ expansion and apply it at leading order to derive RG flow equations valid when disorder and interactions are both weak. We find that the non-Fermi liquid fixed point is unstable to disorder, and demonstrate that the problem inevitably flows to strong coupling, outside the regime of applicability of the perturbative RG. An examination of the flow to strong coupling suggests that disorder is asymptotically more important than interactions, so that the low-energy behavior of the system can be described by a noninteracting sigma model in the appropriate symmetry class (which depends on whether exact particle-hole symmetry is imposed on the problem). We close with a discussion of general principles unveiled by our analysis that dictate the interplay of disorder and Coulomb interactions in gapless semiconductors, and of connections to many-body localized systems with long-range interactions.

Poorya Rabi-‌‌beigi, Rostam Moradian, Chinedu E. Ekuma

Rheinischen Friedrich-Wilhelms-Universität

V. E. Kravtsov

We have shown that in systems where the Coulomb interaction is strongly suppressed, the superconducting transition temperature may be enhanced by disorder close to the Anderson localization transition. This phenomenon is based on the enhancement by disorder of the matrix element of attraction in the Cooper channel. For enhancement to take place one needs (i) strong disorder which makes the single-particle wave functions strongly inhomogeneous in space and (ii) strong correlation of the patterns of inhomogeneity for different wavefunctions. One case where such correlation is well known is the system close to the Anderson transition. We review the notion of multifractality of wavefunctions in this region and show how the enhancement of T c arises out of the multifractal correlations.