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  • Open Access

Strain modulation effects on the topological properties of a chiral p−wave superconductor

Yuto Shibata1,2,* and Manfred Sigrist2

  • 1Condensed Matter Theory Group, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland
  • 2Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland

  • *yshibata@phys.ethz.ch

Phys. Rev. Research 4, 043044 – Published 18 October, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.043044

Abstract

We present a study of strain modulation effects on electronic structures of a two-dimensional single-band chiral p−wave superconductor within the BCS mean-field scheme. We employ a lattice model and solve the Bogolyubov-de Gennes equations numerically. Implementing strain modulations through spatially varying hopping matrix elements, we observe the appearance of spontaneous supercurrents from the resulting spatial modulation of order parameter amplitudes. Moreover, sufficiently strong strain modulation induces the formation of topologically distinct domains within the system and causes the appearance of chiral edge modes, which is captured by spectral functions and local Chern markers.

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References (25)

  1. A. Steppke, L. Zhao, M. E. Barber, T. Scaffidi, F. Jerzembeck, H. Rosner, A. S. Gibbs, Y. Maeno, S. H. Simon, A. P. Mackenzie, and C. W. Hicks, Strong peak in Tc of Sr2RuO4 under uniaxial pressure, Science 355, eaaf9398 (2017).
  2. Y. S. Li, N. Kikugawa, D. A. Sokolov, F. Jerzembeck, A. S. Gibbs, Y. Maeno, C. W. Hicks, J. Schmalian, M. Nicklas, and A. P. Mackenzie, High-sensitivity heat-capacity measurements on Sr2RuO4 under uniaxial pressure, Proc. Natl. Acad. Sci. USA 118, e2020492118 (2021).
  3. V. Grinenko, S. Ghosh, R. Sarkar, J. C. Orain, A. Nikitin, M. Elender, D. Das, Z. Guguchia, F. Brückner, M. E. Barber et al., Split superconducting and time-reversal symmetry-breaking transitions in Sr2RuO4 under stress, Nat. Phys. 17, 748 (2021).
  4. A. Pustogow, Y. Luo, A. Chronister, Y. S. Su, D. A. Sokolov, F. Jerzembeck, A. P. Mackenzie, C. W. Hicks, N. Kikugawa, S. Raghu, E. D. Bauer, and S. E. Brown, Constraints on the superconducting order parameter in Sr2RuO4 from oxygen-17 nuclear magnetic resonance, Nature (London) 574, 72 (2019).
  5. K. Ishida, M. Manago, K. Kinjo, and Y. Maeno, Reduction of the O17 knight shift in the superconducting state and the heat-up effect by NMR pulses on Sr2RuO4, J. Phys. Soc. Jpn. 89, 034712 (2020).
  6. C. Kallin, Chiral p−wave order in Sr2RuO4, Rep. Prog. Phys. 75, 042501 (2012).
  7. A. P. Mackenzie, T. Scaffidi, C. W. Hicks, and Y. Maeno, Even odder after twenty-three years: The superconducting order parameter puzzle of Sr2RuO4, npj Quantum Mater. 2, 40 (2017).
  8. A. P. Mackenzie, A personal perspective on the unconventional superconductivity of Sr2RuO4, J. Supercond. Novel Magn. 33, 177 (2020).
  9. M. D. Bachmann, G. Ferguson, F. Theuss, T. Meng, C. Putzke, T. Helm, K. Shirer, Y. S. Li, K. Modic, M. Nicklas et al., Spatial control of heavy-fermion superconductivity in CeIrIn5, Science 366, 221 (2019).
  10. A. Bouhon and M. Sigrist, Current inversion at the edges of a chiral p−wave superconductor, Phys. Rev. B 90, 220511(R) (2014).
  11. A variation of td would not lead to any qualitative change in the essential behavior discussed here. As mentioned in section “Topology of Superconducting Phase,” the primary effects of nonzero td are to shift Lifshitz transition points and to remove the chemical potential inversion symmetry.
  12. A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Classification of topological insulators and superconductors in three spatial dimensions, Phys. Rev. B 78, 195125 (2008).
  13. S. Ryu, A. P. Schnyder, A. Furusaki, and A. W. Ludwig, Topological insulators and superconductors: Tenfold way and dimensional hierarchy, New J. Phys. 12, 065010 (2010).
  14. M. Sato, Topological properties of spin-triplet superconductors and Fermi surface topology in the normal state, Phys. Rev. B 79, 214526 (2009).
  15. D. Asahi and N. Nagaosa, Topological indices, defects, and Majorana fermions in chiral superconductors, Phys. Rev. B 86, 100504(R) (2012).
  16. In this study, we restrict ourselves to cases where coherence lengths of Cooper pairs are small enough relative to the periodicity of the strain modulation. This is motivated by [9], in which the electronic structure of slab samples of the heavy-fermion superconductor CeIrIn5 is studied under spatially inhomogeneous strain fields on a submicro scale.
  17. M. Sigrist and K. Ueda, Phenomenological theory of unconventional superconductivity, Rev. Mod. Phys. 63, 239 (1991).
  18. W. Huang, S. Lederer, E. Taylor, and C. Kallin, Nontopological nature of the edge current in a chiral p-wave superconductor, Phys. Rev. B 91, 094507 (2015).
  19. J. R. Kirtley, C. Kallin, C. W. Hicks, E. A. Kim, Y. Liu, K. A. Moler, Y. Maeno, and K. D. Nelson, Upper limit on spontaneous supercurrents in Sr2RuO4, Phys. Rev. B 76, 014526 (2007).
  20. P. J. Curran, S. J. Bending, W. M. Desoky, A. S. Gibbs, S. L. Lee, and A. P. Mackenzie, Search for spontaneous edge currents and vortex imaging in Sr2RuO4 mesostructures, Phys. Rev. B 89, 144504 (2014).
  21. S. B. Etter, A. Bouhon, and M. Sigrist, Spontaneous surface flux pattern in chiral p−wave superconductors, Phys. Rev. B 97, 064510 (2018).
  22. R. Bianco and R. Resta, Mapping topological order in coordinate space, Phys. Rev. B 84, 241106(R) (2011).
  23. T. Morimoto, A. Furusaki, and C. Mudry, Anderson localization and the topology of classifying spaces, Phys. Rev. B 91, 235111 (2015).
  24. M. D. Caio, G. Möller, N. R. Cooper, and M. Bhaseen, Topological marker currents in Chern insulators, Nat. Phys. 15, 257 (2019).
  25. B. Irsigler, J. H. Zheng, and W. Hofstetter, Microscopic characteristics and tomography scheme of the local Chern marker, Phys. Rev. A 100, 023610 (2019).

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