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arXiv:1306.4618 · Physical Review B

Enhancement of critical temperatures in disordered bipartite lattices

Luca Dell’Anna

Published Nov 20, 2013• 22 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.88.195139

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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 \ensuremathσ\ensuremath{\sigma}\ensuremathσ-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 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 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=3d=3d=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 ϵϵϵ expansion in d=2+ϵd=2+ϵd=2+ϵ dimensions. We find that in d=2d=2d=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>2d>2d>2 dimensions (ϵ>0)(ϵ>0)(ϵ>0) occurs for disorder strengths of order ϵϵϵ, and is therefore perturbatively accessible for ϵ⪡1ϵ⪡1ϵ⪡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.
An instability of a diffusive Fermi liquid, indicative of a metal-insulator transition (expected to be of first order), arising solely from the competition between quenched disorder and short-ranged interparticle interactions is identified in Hubbard-like models for spinless fermions, subject to (complex) random hopping at half filling on bipartite lattices. The instability, found within a Finkel'stein nonlinear $\ensuremath{\sigma}$ model treatment in d=(2+ϵ)>2d=(2+ϵ)>2d=(2+ϵ)>2 dimensions, originates from an underlying particle-hole-like (so-called chiral) symmetry, shared by both disorder and interactions. In the clean, interacting Fermi liquid this symmetry is responsible for the (completely different) nesting instability.
The Holstein Hamiltonian describes fermions hopping on a lattice and interacting locally with dispersionless phonon degrees of freedom. In the low-density limit, dressed quasiparticles, polarons and bipolarons, propagate with an effective mass. At higher densities, pairs can condense into a low-temperature superconducting phase and, at or near commensurate filling on a bipartite lattice, to charge density wave (CDW) order. CDW formation breaks a discrete symmetry and hence occurs via a second-order (Ising) transition and therefore at a finite Tcdw{T}_{\mathrm{cdw}}Tcdw​ in two dimensions. Quantum Monte Carlo calculations have determined Tcdw{T}_{\mathrm{cdw}}Tcdw​ for a variety of geometries, including square, honeycomb, and Lieb lattices. The superconducting transition, on the other hand, in d=2d=2d=2 is in the Kosterlitz-Thouless universality class and is much less well characterized. In this paper we determine Tsc{T}_{\mathrm{sc}}Tsc​ for the square lattice for several values of the density $\ensuremath{\rho}$ and phonon frequency ${\ensuremath{\omega}}_{0}$. We find that quasilong-range order sets in at ${T}_{\mathrm{sc}}\ensuremath{\lesssim}t/20$, where ttt is the near-neighbor hopping amplitude, consistent with previous rough estimates from simulations which extrapolated to only the temperatures we reach from considerably higher TTT. We also show evidence of a discontinuous evolution of the density as the CDW transition is approached at half filling.
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.
Motivated by the recently experimental reported signatures of the tunable Mott insulating state and superconductivity in an ABC graphene trilayer superlattice, we investigate the charge compressibility, the spin correlation, and the superconducting instability within the Hubbard model on a three-layer honeycomb lattice. It is found that an antiferromagnetically ordered Mott insulator emerges beyond a critical Uc{U}_{c}Uc​ at half-filling, and the electronic correlation drives a d+idd+idd+id superconducting pairing to be dominant over other pairing patterns in a wide doped region. The effective pairing interaction with d+idd+idd+id pairing symmetry is strongly enhanced with the increasing of on-site interaction and suppressed as the interlayer coupling strength increases. Our intensive numerical results demonstrate that the insulating state and superconductivity in an ABC graphene trilayer are driven by strong electric correlation, and it may offer an attractive systems to explore rich correlated behaviors.