Transition to an insulating phase induced by attractive interactions in the disordered three-dimensional Hubbard model

Abstract

We study numerically the interplay of disorder and attractive interactions for spin-1/2 fermions in the three-dimensional Hubbard model. The results obtained by projector quantum Monte Carlo simulations show that at moderate disorder, increasing the attractive interaction leads to a transition from delocalized superconducting states to the insulating phase of localized pairs. This transition takes place well within the metallic phase of the single-particle Anderson model. PACS numbers: 71.30.+h, 74.20.-z, 71.10.-w Two limiting cases of the non-trivial problem of quantum transport in three dimensions (3D) in the presence of disorder and attractive interactions between particles were worked out by Anderson in the late 1950s [1,2]. In the limit of weak interactions, the increase of disorder leads to the Anderson transition from metallic transport to the localized insulating phase [1]. Whereas, in the absence of disorder, attractive interactions between spin-1/2 fermions lead to the appearance of BCS superconductivity which is not affected by the introduction of weak disorder [2]. These limiting cases have been extensively investigated and detailed information is now available for the one-particle Anderson transition (see e.g. [3][4][5]) and the weakly disordered BCS superconductor (see e.g. [6][7][8]). However, a theoretical treatment of the intermediate regime, where both disorder and interactions are important, is difficult due to the absence of relevant small parameters. New results on the physical properties of transport in this regime are therefore of fundamental interest. Furthermore, an understanding of this realistic regime would contribute to the interpretation of recent experiments on 3D superconductors, where both disorder and interactions are naturally present in the physical systems studied [9][10][11][12]. Indeed, the experimental results of Ref. [9] indicate an intriguing correlation between the Anderson transition in a strong magnetic field and optimal doping for the superconducting transition temperature. Also, an explanation of the unusual resistivity dependence on magnetic field observed in Ref.[11] requires a better understanding of the interplay between disorder and attractive interactions. In addition, recent breakthroughs in cold-atom experimental techniques have provided new possibilities for investigations of interacting atoms on 3D optical lattices, leading to the observation of a superfluid to Mott insulator quantum phase transition for ultra-cold atoms [13]. These extremely clean experiments open unprecedented possibilities for precise studies of lattice models with experimentally tunable interactions and provide new challenges for theoretical investigations.Numerical simulations provide a valuable tool for the study of the non-trivial regime where both interactions and disorder play a relevant role. Among various numerical approaches, quantum Monte Carlo methods constitute the most promising possibility for the simulation of 3D systems with a large number of particles [14][15][16][17...

Fractal superconductivity near localization threshold

“…One expects that the mobility of the formed pairs is less than the mobility of the original electrons; this enhances the effect of the disorder. This expectation is conformed by the data [38]. We show that in the physically relevant regime of weak attraction, the situation is opposite: the superconductivity survives deep in the regime of localized states.…”

“…(38,45). We encounter an unexpectedly strong increase of T c in the small λ limit with respect to the usual result, T c ∝ exp(−1/λ) for a conventional BCS superconductor (with the same λ).…”

“…The importance of the analytical treatment of the weak coupling regime T c ≪ E F is demonstrated in particular, by the numerical work [38] which has studied the 3D disordered Hubbard model with strong local attraction (4 times larger than bandwidth). In this regime the electrons are strongly bound to each other even in translationally invariant systems.…”

Superconductor-insulator quantum phase transition

“…A similar problem on a three-dimensional lattice with L 3 sites was solved in Ref. [64], where the same Hamiltonian (51) was investigated, but the problem was formulated somewhat differently. At U = 0, the Hamiltonian ( 51) is reduced to the single-particle Anderson model with a metal-insulator transition at W/t = W c /t ≈ 16.5.…”

Quantum Monte Carlo study of disordered fermions

“…Other studies of disorder effects also involved only very small systems. 19,20 Motivated by the physics of the SI transition, in this article we study the effects of disorder in a strongly correlated fermionic model. Our model is unconventional and has been built so that it can be studied using the recently discovered meron cluster algorithms.…”