- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Superconductivity of repulsive spinless fermions with sublattice potentials

Yuchi He1,*, Kang Yang2,†, Jonas B. Profe1,‡, Emil J. Bergholtz2,§, and Dante M. Kennes1,3,¶

  • 1Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA—Fundamentals of Future Information Technology, 52056 Aachen, Germany
  • 2Department of Physics, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden
  • 3Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761 Hamburg, Germany

  • *yuchi.he@rwth-aachen.de
  • †kang.yang@fu-berlin.de
  • ‡jonas.hauck@rwth-aachen.de
  • §emil.bergholtz@fysik.su.se
  • dante.kennes@mpsd.mpg.de
PDF

Phys. Rev. Research 5, L012009 – Published 26 January, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L012009

Abstract

We explore unconventional superconductivity of repulsive spinless fermions on square and honeycomb lattices with staggered sublattice potentials. The two lattices can exhibit staggered d-wave and f-wave pairing, respectively, at low doping stemming from an effective two-valley band structure. At higher doping, in particular, the square lattice displays a much richer phase diagram including topological p+ip superconductivity which is induced by a qualitatively different mechanism compared to the d-wave pairing. We illuminate this from several complementary perspectives: We analytically perform sublattice projection to analyze the effective continuum low-energy description and we numerically calculate the binding energies for pair and larger bound states for few-body doping near half filling. Furthermore, for finite doping, we present phase diagrams based on extensive functional renormalization group and and density matrix renormalization group calculations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (51)

  1. W. Kohn and J. M. Luttinger, New Mechanism for Superconductivity, Phys. Rev. Lett. 15, 524 (1965).
  2. P. A. Lee, N. Nagaosa, and X.-G. Wen, Doping a Mott insulator: Physics of high-temperature superconductivity, Rev. Mod. Phys. 78, 17 (2006).
  3. M. R. Norman, The challenge of unconventional superconductivity, Science 332, 196 (2011).
  4. G. R. Stewart, Unconventional superconductivity, Adv. Phys. 66, 75 (2017).
  5. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
  6. W. A. Little, Possibility of synthesizing an organic superconductor, Phys. Rev. 134, A1416 (1964).
  7. X. Chen, S. Maiti, A. Linscheid, and P. J. Hirschfeld, Electron pairing in the presence of incipient bands in iron-based superconductors, Phys. Rev. B 92, 224514 (2015).
  8. Z. Dong and L. Levitov, Activating superconductivity in a repulsive system by high-energy degrees of freedom, arXiv:2103.08767.
  9. V. Crépel and L. Fu, New mechanism and exact theory of superconductivity from strong repulsive interaction, Sci. Adv. 7, eabh2233 (2021).
  10. V. Crépel and L. Fu, Spin-triplet superconductivity from excitonic effect in doped insulators, Proc. Natl. Acad. Sci. USA 119, e2117735119 (2022).
  11. V. Crépel, T. Cea, L. Fu, and F. Guinea, Unconventional superconductivity due to interband polarization, Phys. Rev. B 105, 094506 (2022).
  12. Y. Nakagawa, Y. Kasahara, T. Nomoto, R. Arita, T. Nojima, and Y. Iwasa, Gate-controlled BCS-BEC crossover in a two-dimensional superconductor, Science 372, 190 (2021).
  13. V. Fatemi, S. Wu, Y. Cao, L. Bretheau, Q. D. Gibson, K. Watanabe, T. Taniguchi, R. J. Cava, and P. Jarillo-Herrero, Electrically tunable low-density superconductivity in a monolayer topological insulator, Science 362, 926 (2018).
  14. E. Sajadi, T. Palomaki, Z. Fei, W. Zhao, P. Bement, C. Olsen, S. Luescher, X. Xu, J. A. Folk, and D. H. Cobden, Gate-induced superconductivity in a monolayer topological insulator, Science 362, 922 (2018).
  15. S. Zhang, M. Tanaka, E. Watanabe, H. Zhu, K. Inumaru, and S. Yamanaka, Superconductivity of alkali metal intercalated TiNBr with α-type nitride layers, Supercond. Sci. Technol. 26, 122001 (2013).
  16. M. Sigrist and K. Ueda, Phenomenological theory of unconventional superconductivity, Rev. Mod. Phys. 63, 239 (1991).
  17. M. Cheng, K. Sun, V. Galitski, and S. Das Sarma, Stable topological superconductivity in a family of two-dimensional fermion models, Phys. Rev. B 81, 024504 (2010).
  18. S. Hesselmann, D. D. Scherer, M. M. Scherer, and S. Wessel, Bond-ordered states and f-wave pairing of spinless fermions on the honeycomb lattice, Phys. Rev. B 98, 045142 (2018).
  19. K.-H. Ma and N.-H. Tong, Interacting spinless fermions on the square lattice: Charge order, phase separation, and superconductivity, Phys. Rev. B 104, 155116 (2021).
  20. N. Gneist, D. Kiese, R. Henkel, R. Thomale, L. Classen, and M. M. Scherer, Functional renormalization of spinless triangular-lattice fermions: N-patch vs. truncated-unity scheme, Europ. Phys. J. B 95, 157 (2022).
  21. S. R. White, Density Matrix Formulation for Quantum Renormalization Groups, Phys. Rev. Lett. 69, 2863 (1992).
  22. I. P. McCulloch, Infinite size density matrix renormalization group, revisited, arXiv:0804.2509.
  23. W. Metzner, M. Salmhofer, C. Honerkamp, V. Meden, and K. Schönhammer, Functional renormalization group approach to correlated fermion systems, Rev. Mod. Phys. 84, 299 (2012).
  24. N. Read and D. Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect, Phys. Rev. B 61, 10267 (2000).
  25. A. H. MacDonald, S. M. Girvin, and D. Yoshioka, tU expansion for the Hubbard model, Phys. Rev. B 37, 9753 (1988).
  26. A. L. Chernyshev, D. Galanakis, P. Phillips, A. V. Rozhkov, and A.-M. S. Tremblay, Higher order corrections to effective low-energy theories for strongly correlated electron systems, Phys. Rev. B 70, 235111 (2004).
  27. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L012009 for details.
  28. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009).
  29. N. Dupuis, L. Canet, A. Eichhorn, W. Metzner, J. Pawlowski, M. Tissier, and N. Wschebor, The nonperturbative functional renormalization group and its applications, Phys. Rep. 910, 1 (2021).
  30. L. Markhof, B. Sbierski, V. Meden, and C. Karrasch, Detecting phases in one-dimensional many-fermion systems with the functional renormalization group, Phys. Rev. B 97, 235126 (2018).
  31. J. B. Hauck and D. M. Kennes, TU2FRG: a scalable approach for truncated unity functional renormalization group in generic fermionic models, Eur. Phys. J. B 95, 60 (2022).
  32. J. Beyer, J. B. Hauck, and L. Klebl, Reference results for the momentum space functional renormalization group, Eur. Phys. J. B 95, 65 (2022).
  33. S. B. Sinnott and R. Andrews, Carbon nanotubes: Synthesis, properties, and applications, Crit. Rev. Solid State Mater. Sci. 26, 145 (2001).
  34. C. Peng, Y. Wang, J. Wen, Y. Lee, T. Devereaux, and H.-C. Jiang, Enhanced superconductivity by near-neighbor attraction in the doped Hubbard model, arXiv:2206.03486.
  35. V. Zauner, D. Draxler, L. Vanderstraeten, M. Degroote, J. Haegeman, M. M. Rams, V. Stojevic, N. Schuch, and F. Verstraete, Transfer matrices and excitations with matrix product states, New J. Phys. 17, 053002 (2015).
  36. Y. He, D. Pekker, and R. S. K. Mong, One-dimensional repulsive Hubbard model with mass imbalance: Orders and filling anomaly, Phys. Rev. B 104, 195126 (2021).
  37. F. Pollmann, S. Mukerjee, A. M. Turner, and J. E. Moore, Theory of Finite-Entanglement Scaling at One-Dimensional Quantum Critical Points, Phys. Rev. Lett. 102, 255701 (2009).
  38. T. Fukui, Y. Hatsugai, and H. Suzuki, Chern numbers in discretized Brillouin zone: Efficient method of computing (spin) Hall conductances, J. Phys. Soc. Jpn. 74, 1674 (2005).
  39. D. J. Scalapino, E. Loh, and J. E. Hirsch, Fermi-surface instabilities and superconducting d-wave pairing, Phys. Rev. B 35, 6694 (1987).
  40. C. L. Kane, A. Stern, and B. I. Halperin, Pairing in Luttinger Liquids and Quantum Hall States, Phys. Rev. X 7, 031009 (2017).
  41. Y. He, B. Tian, D. Pekker, and R. S. K. Mong, Emergent mode and bound states in single-component one-dimensional lattice fermionic systems, Phys. Rev. B 100, 201101(R) (2019).
  42. L. Gotta, L. Mazza, P. Simon, and G. Roux, Pairing in spinless fermions and spin chains with next-nearest neighbor interactions, Phys. Rev. Res. 3, 013114 (2021).
  43. L.-Y. Xiao, S.-L. Yu, W. Wang, Z.-J. Yao, and J.-X. Li, Possible singlet and triplet superconductivity on honeycomb lattice, Europhys. Lett. 115, 27008 (2016).
  44. M. Messer, R. Desbuquois, T. Uehlinger, G. Jotzu, S. Huber, D. Greif, and T. Esslinger, Exploring Competing Density Order in the Ionic Hubbard Model with Ultracold Fermions, Phys. Rev. Lett. 115, 115303 (2015).
  45. K. Bouadim, N. Paris, F. Hébert, G. G. Batrouni, and R. T. Scalettar, Metallic phase in the two-dimensional ionic Hubbard model, Phys. Rev. B 76, 085112 (2007).
  46. T. Watanabe and S. Ishihara, Band and Mott insulators and superconductivity in honeycomb-lattice ionic-Hubbard model, J. Phys. Soc. Jpn. 82, 034704 (2013).
  47. A. Chattopadhyay, S. Bag, H. R. Krishnamurthy, and A. Garg, Phase diagram of the half-filled ionic Hubbard model in the limit of strong correlations, Phys. Rev. B 99, 155127 (2019).
  48. A. Chattopadhyay, H. R. Krishnamurthy, and A. Garg, Unconventional superconductivity in a strongly correlated band-insulator without doping, SciPost Phys. Core 4, 009 (2021).
  49. P. Weinberg and M. Bukov, QuSpin: A Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: Bosons, fermions and higher spins, SciPost Phys. 7, 020 (2019).
  50. J. Hauschild and F. Pollmann, Efficient numerical simulations with tensor networks: Tensor Network Python (TeNPy), SciPost Phys. Lect. Notes 5, 1 (2018).
  51. P. Thörnig, JURECA: Data centric and booster modules implementing the modular supercomputing architecture at Jülich Supercomputing Centre, J. Large-Scale Res. Facilities 7, A182 (2021).

Outline

Information

Phys. Rev. Research 5, L012009– Published 26 January, 2023
  • Received 13 August 2022
  • Revised 6 January 2023
  • Accepted 10 January 2023
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation