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• W3023495985 abstract "We analyze a class of quantum-critical models, in which momentum integration and the selection of a particular pairing symmetry can be done explicitly, and the competition between non-Fermi liquid and pairing can be analyzed within an effective model with dynamical electron-electron interaction $V(Omega_m)sim 1/|Omega_m|^gamma$ (the $gamma$-model). In this paper, the first in the series, we consider the case $T=0$ and $0<gamma <1$. We argue that tendency to pairing is stronger, and the ground state is a superconductor. We argue, however, that superconducting state is highly non-trivial as there exists a discrete set of topologically distinct solutions for the pairing gap $Delta_n (omega_m)$ ($n = 0, 1, 2..., infty$). All solutions have the same spatial pairing symmetry, but differ in the time domain: $Delta_n (omega_m)$ changes sign $n$ times as a function of Matsubara frequency $omega_m$. The $n =0$ solution $Delta_0 (omega_m)$ is sign-preserving and tends to a finite value at $omega_m =0$, like in BCS theory. The $n = infty$ solution corresponds to an infinitesimally small $Delta (omega_m)$. As a proof, we obtain the exact solution of the linearized gap equation at $T=0$ on the entire frequency axis for all $0<gamma <1$, and an approximate solution of the non-linear gap equation.We argue that the presence of an infinite set of solutions opens up a new channel of gap fluctuations. We extend the analysis to the case where the pairing component of the interaction has additional factor $1/N$ and show that there exists a critical $N_{cr} >1$, above which superconductivity disappears, and the ground state becomes a non-Fermi liquid.We show that all solutions develop simultaneously once $N$ gets smaller than $N_{cr}$." @default.
• W3023495985 created "2020-05-13" @default.
• W3023495985 creator A5066432492 @default.
• W3023495985 creator A5078429551 @default.
• W3023495985 date "2020-07-30" @default.
• W3023495985 modified "2023-09-29" @default.
• W3023495985 title "Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal. I. The <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>γ</mml:mi></mml:math> model and its phase diagram at <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> : The case <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mn>0</mml:mn><mml:mo><</mml:mo><mml:mi>γ</mml:…" @default.
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