Gap anisotropy and universal pairing scale in a spin-fluctuation model of cuprate superconductors

We study the interplay between superconductivity and non-Fermi liquid behavior of a Fermi surface coupled to a massless SU (N ) matrix boson near the quantum critical point. The presence of thermal infrared singularities in both the fermionic self-energy and the gap equation invalidates the Eliashberg approximation, and makes the quantum-critical pairing problem qualitatively different from that at zero temperature. Taking the large N limit, we solve the gap equation beyond the Eliashberg approximation, and obtain the superconducting temperature Tc as a function of N . Our results show an anomalous scaling between the zero-temperature gap and Tc. For N greater than a critical value, we find that Tc vanishes with a Berezinskii-Kosterlitz-Thouless scaling behavior, and the system retains non-Fermi liquid behavior down to zero temperature. This confirms and extends previous renormalization-group analyses done at T = 0, and provides a controlled example of a naked quantum critical point. We discuss the crucial role of thermal fluctuations in relating our results with earlier work where superconductivity always develops due to the special role of the first Matsubara frequency.

Section: Introductionmentioning

confidence: 99%

Superconductivity versus quantum criticality: Effects of thermal fluctuations

Wang

Torroba

2018

“…A system does not need to possess coherent quasiparticles to develop a pairing instability, 48,49 but fermionic coherence emerges below the actual T c much in the same way as it emerges in the SDW ordered state. The spectral function in the antinodal region then displays a coherent superconducting peak and a hump centered at, roughly, the energy of the antinodal SDW gap at T = 0.…”

Section: Introductionmentioning

confidence: 99%

Pseudogap in underdoped cuprates and spin-density-wave fluctuations

Sedrakyan

Chubukov

2010

We analyze fermionic spectral function in the spin-density-wave (SDW) phase of quasi-2D cuprates at small but finite T. We use a non-perturbative approach and sum up infinite series of thermal self-energy terms, keeping at each order nearly-divergent (T/J) |log epsilon| terms, where epsilon is a deviation from a pure two-dimensionality, and neglecting regular T/J corrections. We show that, as SDW order decreases, the spectral function in the antinodal region acquires peak/hump structure: the coherent peak position scales with SDW order parameter, while the incoherent hump remains roughly at the same scale as at T=0 when SDW order is the strongest. We identify the hump with the pseudogap observed in ARPES and argue that the presence of coherent excitations at low energies gives rise to magneto-oscillations in an applied field. We show that the same peak/hump structure appears in the density of states and in optical conductivity.Comment: 14 pages, 12 figures, to be published in PR

“…interaction gives rise to a singular fermionic self-energy, and a coherent Fermi-liquid behavior get destroyed below a certain temperature T coh , either on the full Fermi surface 13,15,34,35 or in the hot regions [6][7][8]13,19,36,37 . The same interaction, however, also mediates fermion-fermion interaction in the particle-particle channel.…”

mentioning

confidence: 99%

Special role of the first Matsubara frequency for superconductivity near a quantum critical point: Nonlinear gap equation below Tc and spectral properties in real frequencies

Wu¹,

Abanov

Wang

et al. 2019

Near a quantum-critical point in a metal a strong fermion-fermion interaction, mediated by a soft boson, destroys fermionic coherence and also gives rise to an attraction in one or more pairing channels. The two tendencies compete with each other, and in a class of large N models, where the tendency to incoherence is parametrically stronger, one would naively expect an incoherent (non-Fermi liquid) normal state behavior to persist down to T = 0. However, this is not the case for quantum-critical systems described by Eliashberg theory. In such systems, non-Fermi liquid part of the self-energy Σ(ω m ) is large for a generic Matsubara frequency ω m = πT (2m + 1), but vanishes for fermions with ω m = ±πT , while the pairing interaction between fermions with these two frequencies remains strong. It has been shown [Y. Wang et al PRL 117, 157001 (2016)] that this peculiarity gives rise to a non-zero T c , even at large N , when superconductivity is not expected from scaling analysis. We consider the system behavior below T c and contrast the conventional case, when ω m = ±πT are not special, and the case when the pairing is induced by fermions with ω m = ±πT . We obtain the solution of the non-linear gap equations in Matsubara frequencies and then convert to real frequency axis and obtain the spectral function A(ω) and the density of states N (ω). In a conventional BCS-type superconductor A(ω) and N (ω) are peaked at the gap value ∆(T ), and the peak position shifts to a smaller ω as temperature increases towards T c , i.e. the gap "closes in". We show that in a situation when superconductivity is induced by fermions with ω m = ±πT , the peak N (ω) remains at a finite frequency even at T = T c − 0, the gap just "fills in". The spectral function A(ω) either shows almost the same "gap filling" behavior as the density of states, or its peak position shifts to zero frequency already at a finite ∆ ("emergent Fermi arc" behavior), depending on the strength of the thermal contribution. We compare our results with the data for the cuprates and argue that "gap filling" behavior holds in the antinodal region, while the "emergent Fermi arc" behavior holds in the nodal region. I. INTRODUCTION.The pairing near a quantum-critical point (QCP) in a metal is a fascinating subject due to highly non-trivial interplay between superconductivity and non-Fermi liquid (NFL) behavior 1? ? -33 . In most cases, the dominant interaction between low-energy fermions near a QCP is mediated by critical fluctuations of the order parameter. In dimensions D ≤ 3, this