Superconductivity near a nematic quantum critical point -- the interplay between hot and lukewarm regions

Abstract

We present a strong coupling dynamical theory of the superconducting transition in a metal near a QCP towards $Q=0$ nematic order. We use a fermion-boson model, in which we treat the ratio of effective boson-fermion coupling and the Fermi energy as a small parameter $\lambda$. We solve, both analytically and numerically, the linearized Eliashberg equation. Our solution takes into account both strong fluctuations at small momentum transfers $\sim \lambda k_F$ and weaker fluctuations at large momentum transfers. The strong fluctuations determine $T_c$, which is of order ${\lambda }^2{E}_F$ for both s- and d- wave pairing. The weaker fluctuations determine the angular structure of the superconducting order parameter $F({\theta }_k)$ along the Fermi surface, separating between hot and lukewarm regions. In the hot regions $F({\theta }_k)$ is largest and approximately constant. Beyond the hot region, whose width is ${\theta }_h\sim {\lambda }^{1/3}$, $F({\theta }_k)$ drops by a factor ${\lambda }^{4/3}$. The s- and d- wave states are not degenerate but the relative difference $(T_c^s-T_c^d)/T_c^s\sim {\lambda }^2$ is small.

arXiv commentRevised title and figures

References in corpus (36)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• A Common Thread: the pairing interaction for the unconventional superconductors
• Nematic order in iron superconductors - who is in the driver's seat?
• Nematic Fermi Fluids in Condensed Matter Physics
• Quantum Theory of a Nematic Fermi Fluid
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
• Quantum critical point lying beneath the superconducting dome in iron-pnictides
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• On the low energy properies of fermions with singular interactions
• Scattering and Pairing in Cuprate Superconductors
• Enhancement of superconductivity near a nematic quantum critical point
• Are non-Fermi-liquids stable to Cooper pairing?
• Non-Fermi Liquid Fixed Point in 2+1 Dimensions
• Nematicity and quantum paramagnetism in FeSe
• Charge-density-wave order with momentum $(2Q,0)$ and $(0,2Q)$ within the spin-fermion model: continuous and discrete symmetry breaking, preemptive composite order, and relation to pseudogap in hole-doped cuprates
• Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point
• The key ingredients of the electronic structure of FeSe
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Recent Developments in Non-Fermi Liquid Theory
• Renormalization Group Approach to Low Temperature Properties of a Non-Fermi Liquid Metal
• Ising nematic quantum critical point in a metal: a Monte Carlo study
• Pseudogap temperature $T^{\star }$ of cuprate superconductors from the Nernst effect
• Coherent vs incoherent pairing in 2D systems near magnetic instability
• Gauge Fields and Pairing in Double-Layer Composite Fermion Metals
• Electronic in-plane symmetry breaking at field-tuned quantum criticality in CeRhIn5
• Instabilities near the onset of spin density wave order in metals
• Metallic quantum critical points with finite BCS couplings
• Superconductivity near a quantum-critical point: The special role of the first Matsubara frequency
• Fermi liquid near Pomeranchuk quantum criticality
• Gap anisotropy and universal pairing scale in a spin fluctuation model for cuprates
• Quantum-critical pairing with varying exponents
• Quantum critical metals in $d=3+1$
• Antiferromagnetism in metals: from the cuprate superconductors to the heavy fermion materials
• Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter
• Dynamical susceptibility of a near-critical non-conserved order parameter and B2g Raman response in Fe-based superconductors

Cited by in corpus (26)

• Ironing out the details of unconventional superconductivity
• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. I: The $\gamma$-model and its phase diagram at $T=0$. The case $0<\gamma <1$
• The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal
• Superconductivity of incoherent electrons in Yukawa-SYK model
• Superconductivity Mediated by Nematic Fluctuations in Tetragonal $\text{Fe}{\text{Se}}_{1-x}{\text{S}}_x$
• Collective modes near a Pomeranchuk instability
• Implicit renormalization approach to the problem of Cooper instability
• A theory of criticality for quantum ferroelectric metals
• Valley-polarized nematic order in twisted moiré systems: In-plane orbital magnetism and non-Fermi liquid to Fermi liquid crossover
• Superconductivity due to fluctuating loop currents
• Intra-unit-cell singlet pairing mediated by altermagnetic fluctuations
• Tests of nematic-mediated superconductivity applied to Ba${}_{1-x}$Sr${}_x$Ni${}_2$As${}_2$
• Strain-tuned quantum criticality in electronic Potts-nematic systems
• Classification of electronic nematicity in three-dimensional crystals and quasicrystals
• Potential Lifshitz transition at optimal substitution in nematic pnictide Ba${}_{1-x}$Sr${}_x$Ni${}_2$As${}_2$
• A critical nematic phase with pseudogap-like behavior in twisted bilayers
• Instabilities of quantum critical metals in the limit $N_f\to 0$
• One-dimensional scattering of two-dimensional fermions near quantum criticality
• Nematic order driven by superconducting correlations
• Elastic Quantum Criticality in Nematics and Altermagnets via the Elasto-Caloric Effect
• Microscopic origin of the nemato-elastic coupling and dynamics of hybridized collective nematic-phonon excitations
• Quasiparticle scattering in a superconductor near a nematic critical point: resonance mode and multiple attractive channels
• Superconductivity near a nematoelastic quantum critical point
• Unconventional superconductivity from electronic dipole fluctuations
• Compatible Instability: Gauge Constraints of Elasticity Inherited by Electronic Nematic Criticality
• Superconductivity near an Ising nematic quantum critical point in two dimensions