Abstract
We study the interplay between superconductivity and non-Fermi liquid behavior of a Fermi surface coupled to a massless 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 limit, we solve the gap equation beyond the Eliashberg approximation, and obtain the superconducting temperature as a function of . Our results show an anomalous scaling between the zero-temperature gap and . For greater than a critical value, we find that 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 , 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.
- Received 29 August 2017
- Revised 21 December 2017
DOI:https://doi.org/10.1103/PhysRevB.97.054502
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