Enhancement of critical temperatures in disordered bipartite lattices

Luca Dell’Anna

We study the strong enhancement, induced by random hopping, of the critical temperatures characterizing the transitions to superconductivity, charge-density wave, and antiferromagnetism, which can occur in bipartite lattice models at half filling, like graphene, by means of an extended Finkel'stein nonlinear $\ensuremath{\sigma}$-model renormalization group approach. We show that if Cooper channel interaction dominates, superconducting critical temperature can be enhanced at will, since superconductivity cannot be broken by entering any Anderson insulating phase. If instead, staggered interactions are relevant, antiferromagnetic order is generated by disorder at a temperature well above that expected for a clean system.

K. Herrmanns

Luca Dell’Anna

We study the enhancement of critical temperatures related to superconductivity, charge density wave and antiferromagnetism driven by disorder, by means of an extended Finkel'stein non-linear {\sigma}-model renormalization group approach. We show that the critical temperature for Cooper pairs can be enhanced both in the presence of Anderson localization and in its absence, close to the Gade-Wegner criticality. In the latter case, which may be relevant for electrons randomly hopping on a bipartite lattice at half-filling, like graphene or half-filled square lattice, superconductivity and magnetic order can compete depending on the strength of disorder and residual repulsive interaction.

Giancarlo Jug, B. N. Shalaev

Luca Dell’Anna, S. Fantoni, Pasquale Sodano +1 more

We study the effect of random on-site energies on the critical temperature of a non-interacting Bose gas on a lattice. In our derivation the on-site energies are distributed according a Gaussian probability distribution function having vanishing average and variance ν 0 2 . By using the replicated action obtained by averaging on the disorder, we perform a perturbative expansion for the Green functions of the disordered system. We evaluate the shift of the chemical potential induced by the disorder and we compute, for ν 0 2 ≪ 1, the critical temperature for condensation. We find that, for large filling, disorder slightly enhances the critical temperature for condensation.

Uwe Krey