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• W2904249976 abstract "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 superconductivity. In a class of large $N$ models, 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, where non-Fermi liquid part of the self-energy $Sigma (omega_m)$ is large for a generic Matsubara frequency $omega_m = pi T(2m+1)$, but vanishes at $omega_m = pm pi T$, while the pairing interaction between fermions with these two frequencies remains strong. This peculiarity gives rise to a non-zero $T_c$ even at large $N$[Y. Wang et al PRL 117, 157001 (2016)]. We consider the system behavior below $T_c$ and contrast the two cases when $omega_m = pm pi T$ are either special or not. We obtain the solution of the non-linear gap equations in real frequency axis and obtain the spectral function $A(omega)$ and the density of states $N(omega)$. In a conventional BCS-type superconductor $A(omega)$ and $N(omega)$ are peaked at the gap value $Delta (T)$, and the peak position shifts to a smaller $omega$ as temperature increases, i.e. the gap closes in. However when superconductivity is induced by fermions with $omega_m = pm pi T$, the peak in $N(omega)$ remains at a finite frequency even at $T =T_c-0$, the gap just fills in. The spectral function $A(omega)$ either shows almost the same gap filling behavior, or its peak position shifts to zero frequency already at a finite $Delta$ (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." @default.
• W2904249976 created "2018-12-22" @default.
• W2904249976 creator A5021460990 @default.
• W2904249976 creator A5066432492 @default.
• W2904249976 creator A5078429551 @default.
• W2904249976 creator A5083939692 @default.
• W2904249976 date "2019-04-15" @default.
• W2904249976 modified "2023-10-13" @default.
• W2904249976 title "Special role of the first Matsubara frequency for superconductivity near a quantum critical point: Nonlinear gap equation below <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> and spectral properties in real frequencies" @default.
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