Cascade of vestigial orders in two-component superconductors: Nematic, ferromagnetic, s-wave charge-4e, and d-wave charge-4e states

Hecker, Matthias; Willa, Roland; Schmalian, Jörg; Fernandes, Rafael M.

doi:10.1103/physrevb.107.224503

Cascade of vestigial orders in two-component superconductors: Nematic, ferromagnetic, s -wave charge- 4e , and d -wave charge- 4e states

Journal Article · Mon Jun 05 04:00:00 EDT 2023 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.107.224503· OSTI ID:2421409

^[1]; ^[2]; Schmalian, Jörg ^[3]; Fernandes, Rafael M. ^[4]

Univ. of Minnesota, Minneapolis, MN (United States); OSTI
Karlsruhe Inst. of Technology (KIT) (Germany); Institute of Systems Engineering, Sion (Switzerland)
Karlsruhe Inst. of Technology (KIT) (Germany)
Univ. of Minnesota, Minneapolis, MN (United States)

Electronically ordered states that break multiple symmetries can melt in multiple stages, similarly to liquid crystals. In a partially melted phase, known as vestigial phase, a bilinear made out of combinations of the multiple components of the primary order parameter condenses. Multicomponent superconductors are thus natural candidates for vestigial order since they break both the U⁡(1)-gauge and also time-reversal or lattice symmetries. Here, we use group theory to classify all possible real-valued and complex-valued bilinears of a generic two-component superconductor on a tetragonal or hexagonal lattice. While the more widely investigated real-valued bilinears correspond to vestigial nematic or ferromagnetic order, the little explored complex-valued bilinears correspond to a vestigial charge-4e condensate, which itself can have an underlying s-wave, d_x²–y²-wave, or d_xy-wave symmetry. To properly describe the fluctuating regime of the superconducting Ginzburg-Landau action and thus access these competing vestigial phases, we employ both a large-N and a variational method. We show that while vestigial order can be understood as a weak-coupling effect in the large-N approach, it is akin to a moderate-coupling effect in the variational method. Despite these distinctions, both methods yield similar results in wide regions of the parameter space spanned by the quartic Landau coefficients. Specifically, we find that the nematic and ferromagnetic phases are the leading vestigial instabilities, whereas the various types of charge-4⁢e order are attractive albeit subleading vestigial channels. The only exception is for the hexagonal case, in which the nematic and s-wave charge-4e vestigial states are degenerate. Finally, we discuss the limitations of our approach, as well as the implications of our results for the realization of exotic charge-4⁢e states in material candidates.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Minnesota, Minneapolis, MN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE)

Grant/Contract Number:: SC0020045

OSTI ID:: 2421409

Alternate ID(s):: OSTI ID: 2478705

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 22 Vol. 107; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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