Synergetic Ferroelectricity and Superconductivity in Zero-Density Dirac Semimetals near Quantum Criticality

Vladyslav Kozii, Avraham Klein, Rafael M. Fernandes, and Jonathan Ruhman

Phys. Rev. Lett. 129, 237001 – Published 29 November 2022

Abstract

We study superconductivity in a three-dimensional zero-density Dirac semimetal in proximity to a ferroelectric quantum critical point. We find that the interplay of criticality, inversion-symmetry breaking, and Dirac dispersion gives rise to a robust superconducting state at the charge-neutrality point, where no Fermi surface is present. Using Eliashberg theory, we show that the ferroelectric quantum critical point is unstable against the formation of a ferroelectric density wave (FDW), whose fluctuations, in turn, lead to a first-order superconducting transition. Surprisingly, long-range superconducting and FDW orders are found to cooperate with each other, in contrast to the more usual scenario of phase competition. Therefore, we suggest that driving charge neutral Dirac materials, e.g., ${Pb}_{x} {Sn}_{1 - x} Te$ , through a ferroelectric quantum critical point may lead to superconductivity intertwined with FDW order.

Received 19 October 2021
Revised 5 February 2022
Accepted 31 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.237001

Physics Subject Headings (PhySH)

Critical phenomena Ferroelectricity Pairing mechanisms Quantum phase transitions Spin-orbit coupling Superconductivity

Dirac semimetal

Eliashberg theory Green's function methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Vladyslav Kozii ^1,2,3, Avraham Klein ^4,5, Rafael M. Fernandes⁵, and Jonathan Ruhman ^6,7

¹Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
²Department of Physics, University of California, Berkeley, California 94720, USA
³Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁴Physics Department, Ariel University, Ariel 40700, Israel
⁵School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
⁶Department of Physics, Bar-Ilan University, 52900 Ramat Gan, Israel
⁷Center for Quantum Entanglement Science and Technology, Bar-Ilan University, 52900 Ramat Gan, Israel