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.
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.
We uncover a disorder-driven instability in the diffusive Fermi liquid phase of a class of many-fermion systems, indicative of a metal-insulator transition of first-order type, which arises solely from the competition between quenched disorder and interparticle interactions. Our result is expected to be relevant for sufficiently strong disorder in
d=3 spatial dimensions. Specifically, we study a class of half-filled, Hubbard-like models for spinless fermions with (complex) random hopping and short-ranged interactions on bipartite lattices in $d\ensuremath{\geqslant}2$. In a given realization, the hopping disorder breaks time-reversal invariance but preserves the special ``nesting'' symmetry responsible for the charge density wave instability of the ballistic Fermi liquid. This disorder may arise, e.g., from the application of a random magnetic field to the otherwise clean model. We derive a low-energy effective field theory description for this class of disordered, interacting fermion systems, which takes the form of a Finkel'stein nonlinear sigma model $(\mathrm{FNL}\ensuremath{\sigma}\mathrm{M})$ (A. M. Finkel'stein, Zh. Eksp. Teor. Fiz. 84, 168 (1983) [Sov. Phys. JETP 57, 97 (1983)]). We analyze the $\mathrm{FNL}\ensuremath{\sigma}\mathrm{M}$ using a perturbative, one-loop renormalization group analysis controlled via an
ϵ expansion in
d=2+ϵ dimensions. We find that in
d=2 dimensions, the interactions destabilize the conducting phase known to exist in the disordered, noninteracting system. The metal-insulator transition that we identify in
d>2 dimensions
(ϵ>0) occurs for disorder strengths of order
ϵ, and is therefore perturbatively accessible for
ϵ⪡1. We emphasize that the disordered system has no localized phase in the absence of interactions, so that a localized phase and the transition into it can only appear due to the presence of the interactions.
The magnetic ground state phase diagram of the disordered Hubbard model at half-filling is computed in dynamical mean-field theory supplemented with the spin resolved, typical local density of states. The competition between many-body correlations and disorder is found to stabilize paramagnetic and antiferromagnetic metallic phases at weak interactions. Strong disorder leads to Anderson localization of the electrons and suppresses the antiferromagnetic long-range order. Slater and Heisenberg antiferromagnets respond characteristically differently to disorder. The results can be tested with cold fermionic atoms loaded into optical lattices.
Anomalous metals are observed in numerous experiments on disordered two-dimensional systems proximate to superconductivity. A characteristic feature of an anomalous metal is that its low-temperature conductivity has a weakly temperature dependent value, significantly higher than that of a disordered Fermi liquid. We propose a dynamical mean-field model of an anomalous metal: interacting electrons similar in structure to that of the well-studied universal Hamiltonian of mesoscopic metallic grains, but with independent random interactions between pairs of sites, involving Cooper pair hopping and spin exchange. We find evidence for critical anomalous phases or points between a superconducting phase and a disordered Fermi liquid phase in this model. Our results are obtained by a renormalization group analysis in a weak coupling limit, and a complementary solution at large
M when the spin symmetry is generalized to
USp(M). The large
M limit describes the anomalous metal by fractionalization of the electron into spinons, holons, and doublons, with these partons forming critical non-Fermi liquids in the Sachdev-Ye-Kitaev class. We compute the low-temperature conductivity in the large
M limit and find temperature-independent values moderately enhanced from that in the disordered metal.
The interplay between electron-electron correlations and disorder has been a central theme of condensed matter physics over the past several decades, with particular interest in the possibility that interactions might cause delocalization of an Anderson insulator into a metallic state, and the disrupting effects of randomness on magnetic order and the Mott phase. Here we extend this physics to explore electron-phonon interactions and show, via exact quantum Monte Carlo simulations, that the suppression of the charge density wave correlations in the half-filled Holstein model by disorder can stabilize a superconducting phase. Our simulations thus capture qualitatively the suppression of charge ordered phases and emergent superconductivity recently seen experimentally.
We have considered the half-filled disordered attractive Hubbard model on a square lattice, in which the on-site attraction is switched off on a fraction
f of sites, while keeping a finite
U on the remaining ones. Through quantum Monte Carlo simulations for several values of
f and
U and for system sizes ranging from $8\ifmmode\times\else\texttimes\fi{}8$ to $16\ifmmode\times\else\texttimes\fi{}16$, we have calculated the configurational averages of the equal-time pair structure factor
Ps and, for a more restricted set of variables, the helicity modulus ${\ensuremath{\rho}}_{s}$, as functions of temperature. Two finite-size scaling Ans\"atze for
Ps have been used: one for zero temperature and the other for finite temperatures. We have found that the system sustains superconductivity in the ground state up to a critical impurity concentration
fc, which increases with
U, at least up to
U=4 (in units of the hopping energy). Also, the normalized zero-temperature gap as a function of
f shows a maximum near $f\ensuremath{\sim}0.07$ for $2\ensuremath{\lesssim}U\ensuremath{\lesssim}6$. Analyses of the helicity modulus and of the pair structure factor led to the determination of the critical temperature as a function of
f for
U=3, 4, and 6: they also show maxima near $f\ensuremath{\sim}0.07$, with the highest
Tc increasing with
U in this range. We argue that, overall, the observed behavior results from both the breakdown of charge-density-wave-superconductivity degeneracy and the fact that free sites tend to ``push'' electrons toward attractive sites; the latter effect being more drastic at weak couplings.