Unconventional Superconductivity in Luttinger Semimetals: Theory of Complex Tensor Order and the Emergence of the Uniaxial Nematic State

Physical Review Letters
Igor Boettcher, Igor F Herbut

Abstract

We investigate unconventional superconductivity in three-dimensional electronic systems with the chemical potential close to a quadratic band touching point in the band dispersion. Short-range interactions can lead to d-wave superconductivity, described by a complex tensor order parameter. We elucidate the general structure of the corresponding Ginzburg-Landau free energy and apply these concepts to the case of an isotropic band touching point. For a vanishing chemical potential, the ground state of the system is given by the superconductor analogue of the uniaxial nematic state, which features line nodes in the excitation spectrum of quasiparticles. In contrast to the theory of real tensor order in liquid crystals, however, the ground state is selected here by the sextic terms in the free energy. At a finite chemical potential, the nematic state has an additional instability at weak coupling and low temperatures. In particular, the one-loop coefficients in the free energy indicate that at weak coupling genuinely complex orders, which break time-reversal symmetry, are energetically favored. We relate our analysis to recent measurements in the half-Heusler compound YPtBi and discuss the role of cubic crystal symmetry.

References

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Jun 1, 2010·Nature Materials·Stanislav ChadovShou Cheng Zhang
Dec 3, 2013·Physical Review Letters·Eun-Gook MoonLeon Balents
Sep 23, 2014·Physical Review Letters·Igor F Herbut, Lukas Janssen
Nov 26, 2015·Science Advances·Yasuyuki NakajimaJohnpierre Paglione
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Apr 8, 2017·Physical Review Letters·D F AgterbergC Timm

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Citations

Apr 17, 2019·Proceedings of the National Academy of Sciences of the United States of America·Takumi OhtsukiSatoru Nakatsuji
Sep 17, 2019·Physical Review Letters·Shingo KobayashiMasatoshi Sato
Dec 19, 2020·Physical Review Letters·Julia M Link, Igor F Herbut

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