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arXiv:2305.13357 · Physical review. B./Physical review. B

Enhancement of superconductivity in a dirty marginal Fermi liquid

Tsz Chun Wu, Patrick A. Lee, Matthew S. Foster

Published Dec 5, 2023• 4 citations
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Abstract

We study superconductivity in a two-dimensional, disordered marginal Fermi liquid. At the semiclassical level, the transition temperature ${T}_{c}$ is strongly suppressed because marginal Fermi liquid effects destroy well-defined quasiparticles. However, we show that interference between quantum-critical collective modes must be included and these enhance ${T}_{c}$, violating Anderson's theorem. Our results suggest that phase coherence in a disordered, quantum-critical system can survive and manifest in the form of collective excitations, despite the absence of coherent quasiparticles.

DOI
10.1103/physrevb.108.214506

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We study superconductivity in a two-dimensional, disordered marginal Fermi liquid. At the semiclassical level, the transition temperature Tc{T}_{c}Tc​ is strongly suppressed because marginal Fermi liquid effects destroy well-defined quasiparticles. However, we show that interference between quantum-critical collective modes must be included and these enhance Tc{T}_{c}Tc​, violating Anderson's theorem. Our results suggest that phase coherence in a disordered, quantum-critical system can survive and manifest in the form of collective excitations, despite the absence of coherent quasiparticles.
We study the electrical transport of a two-dimensional non-Fermi-liquid with disorder, and we determine the first quantum correction to the semiclassical dc conductivity due to quantum interference. We consider a system with NNN flavors of fermions coupled to SU(NNN) critical matrix bosons. Motivated by the SYK model, we employ the bilocal field formalism and derive a set of finite-temperature saddle-point equations governing the fermionic and bosonic self-energies in the large-NNN limit. Interestingly, disorder smearing induces a marginal Fermi-liquid (MFL) self-energy for the fermions. We next consider fluctuations around the saddle points and derive a MFL-Finkel'stein nonlinear sigma model. We find that the Altshuler-Aronov quantum conductance correction gives linear-TTT resistivity that can dominate over the Drude result at low temperatures. The strong temperature dependence of the quantum correction arises due to rapid relaxation of the mediating quantum-critical bosons. We verify that our calculations explicitly satisfy the Ward identity at the semiclassical and quantum levels. Our results establish that quantum interference persists in two-particle hydrodynamic modes, even when quasiparticles are subject to strong (Planckian) dissipation.
We study the superconducting instability of a two-dimensional disordered Fermi liquid weakly coupled to the soft fluctuations associated with proximity to an Ising-ferromagnetic quantum critical point. We derive interaction-induced corrections to the Usadel equation governing the superconducting gap function, and show that diffusion and localization effects drastically modify the interplay between fermionic incoherence and strong pairing interactions. In particular, we obtain the phase diagram, and demonstrate that (i) there is an intermediate range of disorder strength where superconductivity is enhanced, eventually followed by a tendency towards the superconductor-insulator transition at stronger disorder; and (ii) diffusive particle-particle modes (so-called ``Cooperons'') acquire anomalous dynamical scaling z=4z=4z=4, indicating strong non-Fermi liquid behavior.
In this paper we study a model of an sss-wave marginal Fermi liquid superconductor in two dimensions. Besides the usual Bardeen-Cooper-Schrieffer (BCS) point attractive interaction, the fermions in our system also interact via a long-range repulsive interaction v(q)=gD/q2v(q){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}g}_{D}/{q}^{2}v(q)=gD​/q2. We find that although superconductivity is not destroyed by the long-ranged repulsive interaction (demonstrated by the response to electromagnetic magnetic fields), the BCS pairing function ${\ensuremath{\Delta}}_{\mathrm{BCS}}$ is strongly suppressed, resulting in a power-law correlation $〈{\ensuremath{\Delta}}_{\mathrm{BCS}}(\stackrel{\ensuremath{\rightarrow}}{x}){\ensuremath{\Delta}}_{\mathrm{BCS}}(0)〉\ensuremath{\sim}|\stackrel{\ensuremath{\rightarrow}}{x}{|}^{\ensuremath{-}2\ensuremath{\gamma}}$. This observation is explained within a general picture of the marginal Fermi liquid.
We use a diagrammatic approach to study low-energy physics of a two-dimensional electron system where the Fermi level is near van Hove singularities in the energy spectrum. We find that in most regions of the ${\ensuremath{\epsilon}}_{F}\ensuremath{-}T$ phase diagram the system behaves as a normal Fermi liquid rather than a marginal Fermi liquid. Particularly, the imaginary part of the self-energy is much smaller than the excitation energy, which implies well-defined quasiparticle excitations, and single-particle properties are only weakly affected by the presence of the van Hove singularities. The relevance to high-temperature superconductivity is also discussed.
Quantum criticality, a manifestation of emergent scale invariance in electron wavefunctions arises from intricate many-body quantum entanglement. One of the natural venues for the criticality is clean undoped Dirac semimetals, known as a marginally-renormalized critical phase. The ground state is only slightly modified from the Slater-type product wavefunction because the scatterings from weak disorder and Coulomb interactions are suppressed. Here, using the renormalization group (RG) analysis, we show that a novel class of quantum criticality appears in Dirac semimetals when the disorder strength becomes sufficiently strong in the presence of Coulomb interactions so that a quantum phase transition from the marginally-renormalized critical phase to a disorder-dominated phase arises. The ground state at the critical point is a quantum critical non-Fermi liquid (NFL), characterized by the properties of strongly entangled low-energy states such as the absence of quasi-particles. Near the critical point, unusually wide temperature regions with NFL behaviors emerge.
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