Topological phase transitions in multi-component superconductors

Abstract

We study the phase transition between a trivial and a time-reversal-invariant topological superconductor in a single-band system. By analyzing the interplay of symmetry, topology and energetics, we show that for a generic normal state band structure, the phase transition occurs via extended intermediate phases in which even- and odd-parity pairing components coexist. For inversion-symmetric systems, the coexistence phase spontaneously breaks time-reversal symmetry. For noncentrosymmetric superconductors, the low-temperature intermediate phase is time-reversal breaking, while the high-temperature phase preserves time-reversal symmetry and has topologically protected line nodes. Furthermore, with approximate rotational invariance, the system has an emergent $U(1)\times U(1)$ symmetry, and novel topological defects, such as half vortex lines binding Majorana fermions, can exist. We analytically solve for the dispersion of the Majorana fermion and show that it exhibit small and large velocities at low and high energies. Relevance of our theory to superconducting pyrochlore oxide Cd${}_2$Re${}_2$O${}_7$ and half-Heusler materials is discussed.

14 pages, 7 figures; to appear on Phys. Rev. Lett

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• Nonreciprocal optical response in parity-breaking superconductors
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• Superconductivity vs quantum criticality: effects of thermal fluctuations
• Direct Evidence for Time-Reversal Symmetry Breaking in Topological Superconductor Sr0.1Bi2Se3
• Spin triplet nematic pairing symmetry and superconducting double transition in U${}_{1-x}$Th${}_x$Be${}_{13}$
• Emergent vortex Majorana zero mode in iron-based superconductors
• Nonunitary Superconductivity in Complex Quantum Materials
• Nonreciprocal Meissner response in parity-mixed superconductors
• Detection of topological phase transitions through entropy measurements: the case of germanene
• Piezoelectric effect and diode effect in anapole and monopole superconductors
• Kelvin knots in superconducting state
• Split Fermi Surfaces of the Spin-Orbit-Coupled Metal Cd2Re2O7 Probed by de Haas-van Alphen Effect
• Superconducting Diode Effect in Multiphase Superconductors
• Linear optical response from the odd parity Bardasis-Schrieffer mode in locally non-centrosymmetric superconductors
• Effects of spin orbit coupling in superconducting proximity devices -- application to $\mathrm{CoS}{\mathrm{i}}_2/TiS{\mathrm{i}}_2$ heterostructures
• Nonreciprocal superconductivity
• High-order Time-Reversal Symmetry Breaking Normal State
• Vortices and composite order in $\mathrm{SU}(N)$ theories coupled to Abelian gauge field
• Single branch of chiral Majorana modes from doubly degenerate Fermi surfaces
• Spontaneous magnetization in unitary superconductors with time reversal symmetry breaking
• Magnetic parity violation and parity-time-reversal-symmetric magnets
• Degeneracy between even- and odd-parity superconductivity in the quasi-1D Hubbard model and implications for Sr2RuO4
• Spin-orbit-coupled superconductivity with spin-singlet non-unitary pairing
• Model studies of topological phase transitions in materials with two types of magnetic atoms
• Domain Control by Adjusting Anisotropic Stress in Pyrochlore Oxide Cd2Re2O7
• Possible two-component pairings in electron-doped Bi${}_2$Se${}_3$ based on a tight-binding model
• Many-body wave function and edge magnetization of an open $p+is$ superconducting chain
• Axionic $p+is$ superconductivity from two pairing channels