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Physical Review Research

Disorder stabilized breached-pair phase in an s -wave superconductor

Madhuparna Karmakar, Subhojit Roy, Shantanu Mukherjee, Rajesh Narayanan

Published Dec 5, 2022• 3 citations
Publisher

Abstract

The breached-pair state wherein superconductivity coexists with magnetic polarization is known to exist as a ground state of an imbalanced Fermi system only under very fine-tuned conditions. Here, we show that an s-wave superconductor that is well described by a spin-selectively disordered attractive Hubbard model away from half filling has the breached-pair state as a ground-state without the need for such fine-tuning. The existence of this breached-pair phase is established by laying recourse to a Monte Carlo technique called static path approximation (SPA). Further, by using the SPA, we map out the entire phase diagram of the spin-selectively disordered attractive Hubbard model and show that apart from the breached-pair phase, the many-body system hosts the putative s-wave superconducting state and a polarized Fermi-liquid state.

DOI
10.1103/physrevresearch.4.043159

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The breached-pair state wherein superconductivity coexists with magnetic polarization is known to exist as a ground state of an imbalanced Fermi system only under very fine-tuned conditions. Here, we show that an s-wave superconductor that is well described by a spin-selectively disordered attractive Hubbard model away from half filling has the breached-pair state as a ground-state without the need for such fine-tuning. The existence of this breached-pair phase is established by laying recourse to a Monte Carlo technique called static path approximation (SPA). Further, by using the SPA, we map out the entire phase diagram of the spin-selectively disordered attractive Hubbard model and show that apart from the breached-pair phase, the many-body system hosts the putative s-wave superconducting state and a polarized Fermi-liquid state.
We report a quantum phase transition in Pauli limited d-wave superconductors and give the mean field estimates of the associated quantum critical point. For a population imbalanced d-wave superconductor a stable ground state phase viz quantum breached pair phase has been identified which comprises of spatial coexistence of gapless superconductivity and nonzero magnetization. Based on the thermodynamic and quasiparticle indicators we for the first time analyze this phase, discuss the thermal behavior of Pauli limited d-wave superconductor, give accurate estimates of the thermal scales associated with such systems and map out the pseudogap regime. Our work shows that while the Pauli limited superconductors are known to exhibit exotic modulated superconducting phase at large imbalance of fermion populations; in the regime of weak imbalance an intriguing phase of competing orders is realized. We have established that rather than the superconducting pairing field, it is the average magnetization of the system that quantifies this quantum phase transition. Given that the existing Pauli limited superconductors possess unconventional pairing state symmetry of the superconducting order, our work promises to open up new avenues in the experimental research of these materials. We have also demonstrated an alternate scenario wherein the quantum breached pair phase is a natural outcome for a d-wave superconductor with unequal effective masses of the fermion species.
The half-filled attractive Hubbard model exhibits a simultaneous charge-density wave and superconducting order in its ground state. In this paper we use approximation-free quantum Monte Carlo techniques to explore the effect of disorder in the site energies on this degeneracy. We find that superconducting order survives randomness out to a critical amount of disorder, but charge ordering is immediately destroyed. This settles the issue as to whether disordered site energies, which do not break time-reversal invariance, can destroy pairing correlations. We also locate the precise ratio of disorder to bandwidth required for the disorder-driven transition from the superconducting state. We explore the validity of a strong-coupling picture which maps the system onto a Heisenberg model in a random magnetic field.
The phase diagram of the unconstrained t−Jt-Jt−J model is calculated using the random phase approximation. It is found that the extended sss and the dx2−y2d_{x^2-y^2}dx2−y2​-channels are {\em not} degenerate near half filling. Extended sss-pairing with a low TcT_cTc​ occurs only for a band containing less then 0.4 electrons or holes per unit cell, whereas in a large region around half-filling ddd-wave pairing is the only stable superconducting solution. At half filling superconductivity is suppressed due to the formation of the anti-ferromagnetic Mott-Hubbard insulating state. By extending the analysis to the unconstrained t−t′−Jt-t'-Jt−t′−J model, it is proven that, if a Fermi surface is assumed similar to the one that is known to exist in cuprous oxide superconductors, the highest superconducting TcT_cTc​ is reached for about 0.70.70.7 electron per site, whereas the anti-ferromagnetic solution still occurs for 111 electron per site. It is shown, that the maximum ddd-wave superconducting mean field transition temperature is half the maximum value that the Neèl temperature can have in the Mott-insulating state.
We study sss-wave superconductivity in the two-dimensional attractive Hubbard model in an applied magnetic field, assume the extreme Pauli limit, and examine the role of spatial fluctuations in the coupling regime corresponding to BCS-BEC crossover. We use a decomposition of the interaction in terms of an auxiliary pairing field, retain the static mode, and sample the pairing field via a Monte Carlo approach. The method requires iterative solution of the Bogoliubov--de-Gennes equations for amplitude- and phase-fluctuating configurations of the pairing field. We establish the full thermal phase diagram of this strong-coupling problem. At low field we observe the magnetized but homogeneous ``breached pair'' superfluid phase. It reveals that Tc{T}_{c}Tc​ scales an order of magnitude below the mean-field estimate, spontaneous inhomogeneity in the field-induced magnetization, and a strong nonmonotonicity in the temperature dependence of the low-energy density of states. We compare our results to the experimental phase diagram of the imbalanced Fermi gas at unitarity. At higher field we obtain the modulated Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases. The thermal transition from the FFLO phases to the normal state is strongly first order. We track the fermionic momentum distribution, the density of states, and the pairing structure factor deep into the normal state. The pairing structure factor retains weak signature of finite momentum pairing to a high temperature despite the low Tc{T}_{c}Tc​ itself, while the spin-resolved density of states changes from the ``pseudogapped'' FFLO character to gapless and pseudogapped again with increasing temperature.
We investigate the disorder-driven superconductor to insulator quantum phase transition (SIT) in an interacting fermion model using determinantal quantum Monte Carlo (QMC) methods. The disordered superconductor is modeled by an attractive Hubbard model with site disorder chosen randomly from a uniform distribution. The superconducting state which exists for small disorder is shown to evolve into an insulating phase beyond a critical disorder. The transition is tracked by the vanishing of (a) the superfluid stiffness, and (b) the charge stiffness or the delta function peak in the optical conductivity at zero frequency. We also show the behavior of the charge, spin, pair, and current correlations in the presence of disorder. Results for the temperature dependence of the dc conductivity, obtained by an approximate analytic continuation technique, are also presented both in the metallic phase above Tc{T}_{c}Tc​ and the insulating phase. We discuss some of the complications in extracting the resistance at the transition point.