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Superconductivity near a Ferroelectric Quantum Critical Point in Ultralow-Density Dirac Materials

Author(s)
Kozii, Vladyslav; Bi, Zhen
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Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/
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Abstract
The experimental observation of superconductivity in doped semimetals and semiconductors, where the Fermi energy is comparable to or smaller than the characteristic phonon frequencies, is not captured by the conventional theory. In this paper, we propose a mechanism for superconductivity in ultralow-density three-dimensional Dirac materials based on the proximity to a ferroelectric quantum critical point. We derive a low-energy theory that takes into account both the strong Coulomb interaction and the direct coupling between the electrons and the soft phonon modes. We show that the Coulomb repulsion is strongly screened by the lattice polarization near the critical point even in the case of a vanishing carrier density. Using a renormalization group analysis, we demonstrate that the effective electron-electron interaction is dominantly mediated by the transverse phonon mode. We find that the system generically flows towards strong electron-phonon coupling. Hence, we propose a new mechanism to simultaneously produce an attractive interaction and suppress strong Coulomb repulsion, which does not require retardation. For comparison, we perform the same analysis for covalent crystals, where lattice polarization is negligible. We obtain qualitatively similar results, though the screening of the Coulomb repulsion is much weaker. We then apply our results to study superconductivity in the low-density limit. We find a strong enhancement of the transition temperature upon approaching the quantum critical point. Finally, we also discuss scenarios to realize a topological p-wave superconducting state in covalent crystals close to the critical point.
Date issued
2019-09
URI
https://hdl.handle.net/1721.1/126172
Department
Massachusetts Institute of Technology. Department of Physics
Journal
Physical review. X
Publisher
American Physical Society (APS)
Citation
Kozii, Vladyslav, Zhen Bi and Jonathan Ruhman. “Superconductivity near a Ferroelectric Quantum Critical Point in Ultralow-Density Dirac Materials.” Physical review. X, vol. 9, 2019, 031046 © 2019 The Author(s)
Version: Final published version
ISSN
2160-3308

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