Impact of disorder on the superconducting transition temperature near a Lifshitz transition

Abstract

Multi-band superconductivity is realized in a plethora of systems, from high-temperature superconductors to very diluted superconductors. While several properties of multi-band superconductors can be understood as straightforward generalizations of their single-band counterparts, recent works have unveiled rather unusual behaviors unique to the former case. In this regard, a regime that has received significant attention is that near a Lifshitz transition, in which one of the bands crosses the Fermi level. In this work, we investigate how impurity scattering ${\tau }^{-1}$ affects the superconducting transition temperature $T_c$ across a Lifshitz transition, in the regime where intra-band pairing is dominant and inter-band pairing is subleading. This is accomplished by deriving analytic asymptotic expressions for $T_c$ and $\partial T_c/\partial {\tau }^{-1}$ in a two-dimensional two-band system. When the inter-band pairing interaction is repulsive, we find that, despite the incipient nature of the band crossing the Fermi level, inter-band impurity scattering is extremely effective in breaking Cooper pairs, making $\partial T_c/\partial {\tau }^{-1}$ quickly approach the limiting Abrikosov-Gor'kov value of the high-density regime. In contrast, when the inter-band pairing interaction is attractive, pair-breaking is much less efficient, affecting $T_c$ only mildly at the vicinity of the Lifshitz transition. The consequence of this general result is that the behavior of $T_c$ across a Lifshitz transition can be qualitatively changed in the presence of strong enough disorder: instead of displaying a sharp increase across the Lifshitz transition, as in the clean case, $T_c$ can actually display a maximum and be suppressed at the Lifshitz transition. These results shed new light on the non-trivial role of impurity scattering in multi-band superconductors.

arXiv comment17 pages, 12 figures

References in corpus (35)

• Beyond Eliashberg superconductivity in MgB2: anharmonicity, two-phonon scattering, and multiple gaps
• Observation of Fermi-surface-dependent nodeless superconducting gaps in Ba0.6K0.4Fe2As2
• A Universal Critical Density Underlying the Physics of Electrons at the LaAlO3/SrTiO3 Interface
• Quantum criticality in ferroelectrics
• Effect of magnetic and non-magnetic impurities on highly anisotropic superconductivity
• Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent systems
• Quantum critical origin of the superconducting dome in SrTiO${}_3$
• Critical doping for the onset of a two-band superconducting ground state in SrTiO${}_{3-\delta }$
• s+is State with Broken Time Reversal Symmetry in Fe-Based Superconductors
• Disorder induced transition between s_+- and s_++ states in two-band superconductors
• Resonant and crossover phenomena in a multiband superconductor tuning the chemical potential near a band edge
• Importance of Fermi surface topology for high temperature superconductivity in electron-doped iron arsenic superconductors
• Microscopic theory of type-1.5 superconductivity in multiband systems
• Superconductivity at very low density: the case of strontium titanate
• Topological superconductivity and unconventional pairing in oxide interfaces
• On the Possibility of New High Tc Superconductors by Producing metal Heterostructures as in the Cuprate Perovskites
• Electron pairing in the presence of incipient bands in iron-based superconductors
• Two-band superconductors: Hidden criticality deep in the superconducting state
• Superconductivity vs bound state formation in a two-band superconductor with small Fermi energy -- applications to Fe-pnictides/chalcogenides and doped SrTiO3
• Spectroscopic Evidence for Multiple Order Parameter Components in the Heavy Fermion Superconductor CeCoIn_5
• Using controlled disorder to distinguish $s_{\pm }$ and $s_{++}$ gap structure in Fe-based superconductors
• Two-band superconductivity in doped SrTiO${}_3$ films and interfaces
• Unconventional multi-band superconductivity in bulk SrTiO${}_3$ and LaAlO${}_3$/SrTiO${}_3$ interfaces
• Band hybridization induced odd-frequency pairing in multiband superconductors
• Shadow gap in the over-doped (Ba${}_{1-x}$K${}_x$)Fe${}_2$As${}_2$ compound
• High-temperature superconductivity stabilized by electron-hole interband coupling in collapsed tetragonal phase of KFe2As2 under high pressure
• Interface energy of two band superconductors
• Shape Resonances in superconducting gaps in a 2DEG at oxide-oxide interface
• BCS superconductivity near the band edge: Exact results for one and several bands
• Pair breaking in multi-orbital superconductors: an application to oxide interfaces
• Upper critical field as a probe for multiband superconductivity in bulk and interfacial STO
• Effect of nonmagnetic impurities on $s_{\pm }$ superconductivity in the presence of incipient bands
• Robustness of quantum critical pairing against disorder
• A second superconducting energy gap of Nb_3Sn observed by breakjunction point-contact spectroscopy
• Strong Landau-quantization effects in high-magnetic-field superconductivity of a two-dimensional multiple-band metal near the Lifshitz transition

Cited by in corpus (8)

• Superconductivity in dilute SrTiO${}_3$: a review
• Metallicity and superconductivity in doped strontium titanate
• Unconventional multi-band superconductivity in bulk SrTiO${}_3$ and LaAlO${}_3$/SrTiO${}_3$ interfaces
• Eliashberg equations for an electron-phonon version of the Sachdev-Ye-Kitaev model: Pair Breaking in non-Fermi liquid superconductors
• Anisotropic superconductivity mediated by ferroelectric fluctuations in cubic systems with spin-orbit coupling
• Multiple-gap response of type-I noncentrosymmetric BeAu superconductor
• The effect of interorbital scattering on superconductivity in doped Dirac materials
• Modulation of superconductivity by quantum confinement in doped strontium titanate