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  • Letter
  • Open Access

Pairing of composite electrons and composite holes in νT=1 quantum Hall bilayers

Luca Rüegg*, Gaurav Chaudhary†, and Robert-Jan Slager

  • TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom

  • *lr537@cam.ac.uk
  • †gc674@cam.ac.uk

Phys. Rev. Research 5, L042022 – Published 8 November, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L042022

Abstract

Motivated by recent experimental indications of preformed electron-hole pairs in νT=1 quantum Hall bilayers at relatively large separation, we formulate a Chern-Simons (CS) theory of the coupled composite electron liquid (CEL) and composite hole liquid (CHL). We show that the effective action of the CS gauge field fluctuations around the saddle point leads to stable pairing between CEL and CHL. We find that the CEL-CHL pairing theory leads to a dominant s-wave channel in contrast to the dominant p-wave channel found in the CEL-CEL pairing theory. Moreover, the CEL-CHL pairing is generally stronger than the CEL-CEL pairing across the whole frequency spectrum. Finally, we discuss possible differences between the two pairing mechanisms that may be probed in experiments.

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References (47)

  1. J. P. Eisenstein, G. S. Boebinger, L. N. Pfeiffer, K. W. West, and S. He, New fractional quantum Hall state in double-layer two-dimensional electron systems, Phys. Rev. Lett. 68, 1383 (1992).
  2. J. P. Eisenstein, Exciton condensation in bilayer quantum Hall systems, Annu. Rev. Condens. Matter Phys. 5, 159 (2014).
  3. I. B. Spielman, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Resonantly enhanced tunneling in a double layer quantum Hall ferromagnet, Phys. Rev. Lett. 84, 5808 (2000).
  4. J. P. Eisenstein and A. H. MacDonald, Bose–Einstein condensation of excitons in bilayer electron systems, Nature (London) 432, 691 (2004).
  5. M. Kellogg, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Vanishing Hall resistance at high magnetic field in a double-layer two-dimensional electron system, Phys. Rev. Lett. 93, 036801 (2004).
  6. D. Nandi, A. D. K. Finck, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Exciton condensation and perfect Coulomb drag, Nature (London) 488, 481 (2012).
  7. B. I. Halperin, Theory of the quantized Hall conductance, Helv. Phys. Acta 56, 75 (1983).
  8. H. A. Fertig, Energy spectrum of a layered system in a strong magnetic field, Phys. Rev. B 40, 1087 (1989).
  9. X.-G. Wen and A. Zee, Neutral superfluid modes and “magnetic” monopoles in multilayered quantum Hall systems, Phys. Rev. Lett. 69, 1811 (1992).
  10. X.-G. Wen and A. Zee, Tunneling in double-layered quantum Hall systems, Phys. Rev. B 47, 2265 (1993).
  11. B. I. Halperin, P. A. Lee, and N. Read, Theory of the half-filled Landau level, Phys. Rev. B 47, 7312 (1993).
  12. N. Shibata and D. Yoshioka, Ground state of ν=1 bilayer quantum Hall systems, J. Phys. Soc. Jpn. 75, 043712 (2006).
  13. R. L. Doretto, A. O. Caldeira, and C. M. Smith, Bosonization approach for bilayer quantum Hall systems at νT=1, Phys. Rev. Lett. 97, 186401 (2006).
  14. Z. Zhu, L. Fu, and D. N. Sheng, Numerical study of quantum Hall bilayers at total filling νT=1: A new phase at intermediate layer distances, Phys. Rev. Lett. 119, 177601 (2017).
  15. B. Lian and S.-C. Zhang, Wave function and emergent SU(2) symmetry in the νT=1 quantum Hall bilayer, Phys. Rev. Lett. 120, 077601 (2018).
  16. S. H. Simon, E. H. Rezayi, and M. V. Milovanovic, Coexistence of composite bosons and composite fermions in ν=12+12 quantum Hall bilayers, Phys. Rev. Lett. 91, 046803 (2003).
  17. T. Morinari, Composite-fermion pairing in bilayer quantum Hall systems, Phys. Rev. B 59, 7320 (1999).
  18. Y. B. Kim, C. Nayak, E. Demler, N. Read, and S. Das Sarma, Bilayer paired quantum Hall states and Coulomb drag, Phys. Rev. B 63, 205315 (2001).
  19. G. Möller, S. H. Simon, and E. H. Rezayi, Paired composite fermion phase of quantum Hall bilayers at ν=12+12, Phys. Rev. Lett. 101, 176803 (2008).
  20. I. Sodemann, I. Kimchi, C. Wang, and T. Senthil, Composite fermion duality for half-filled multicomponent Landau levels, Phys. Rev. B 95, 085135 (2017).
  21. N. E. Bonesteel, Compressible phase of a double-layer electron system with total Landau-level filling factor 1/2, Phys. Rev. B 48, 11484 (1993).
  22. N. E. Bonesteel, I. A. McDonald, and C. Nayak, Gauge fields and pairing in double-layer composite fermion metals, Phys. Rev. Lett. 77, 3009 (1996).
  23. R. Cipri and N. E. Bonesteel, Gauge fluctuations and interlayer coherence in bilayer composite fermion metals, Phys. Rev. B 89, 085109 (2014).
  24. H. Isobe and L. Fu, Interlayer pairing symmetry of composite fermions in quantum Hall bilayers, Phys. Rev. Lett. 118, 166401 (2017).
  25. G. Wagner, D. X. Nguyen, S. H. Simon, and B. I. Halperin, s-wave paired electron and hole composite fermion trial state for quantum Hall bilayers with ν=1, Phys. Rev. Lett. 127, 246803 (2021).
  26. J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Precursors to exciton condensation in quantum Hall bilayers, Phys. Rev. Lett. 123, 066802 (2019).
  27. X. Liu, J. I. A. Li, K. Watanabe, T. Taniguchi, J. Hone, B. I. Halperin, P. Kim, and C. R. Dean, Crossover between strongly coupled and weakly coupled exciton superfluids, Science 375, 205 (2022).
  28. D. T. Son, Is the composite fermion a Dirac particle?, Phys. Rev. X 5, 031027 (2015).
  29. D. Bohm and D. Pines, A collective description of electron interactions: III. Coulomb interactions in a degenerate electron gas, Phys. Rev. 92, 609 (1953).
  30. A. L. Fetter, C. B. Hanna, and R. B. Laughlin, Anyons and superconductivity: Random phase approximation, Int. J. Mod. Phys. B 05, 2751 (1991).
  31. G. Möller, S. H. Simon, and E. H. Rezayi, Trial wave functions for ν=12+12 quantum Hall bilayers, Phys. Rev. B 79, 125106 (2009).
  32. M. Barkeshli, M. Mulligan, and M. P. A. Fisher, Particle-hole symmetry and the composite Fermi liquid, Phys. Rev. B 92, 165125 (2015).
  33. A. Lopez and E. Fradkin, Fractional quantum Hall effect and Chern-Simons gauge theories, Phys. Rev. B 44, 5246 (1991).
  34. D. Kamburov, Y. Liu, M. A. Mueed, M. Shayegan, L. N. Pfeiffer, K. W. West, and K. W. Baldwin, What determines the fermi wave vector of composite fermions? Phys. Rev. Lett. 113, 196801 (2014).
  35. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L042022 for the derivation of the Euclidean CEL-CHL action, the full effective propagator and effective interaction, the details of the Eliashberg theory, the numerical calculation of the effective couplings, and a discussion of the impact of a density imbalance on the level of the Lagrangian.
  36. F. Marsiglio, Eliashberg theory: A short review, Ann. Phys. 417, 168102 (2020).
  37. W. Pan, W. Kang, M. P. Lilly, J. L. Reno, K. W. Baldwin, K. W. West, L. N. Pfeiffer, and D. C. Tsui, Particle-hole symmetry and the fractional quantum Hall effect in the lowest Landau level, Phys. Rev. Lett. 124, 156801 (2020).
  38. J. Schliemann, S. M. Girvin, and A. H. MacDonald, Strong correlation to weak correlation phase transition in bilayer quantum Hall systems, Phys. Rev. Lett. 86, 1849 (2001).
  39. Y. Zou, G. Refael, A. Stern, and J. P. Eisenstein, Clausius-Clapeyron relations for first-order phase transitions in bilayer quantum Hall systems, Phys. Rev. B 81, 205313 (2010).
  40. J. K. Jain, Composite-fermion approach for the fractional quantum Hall effect, Phys. Rev. Lett. 63, 199 (1989).
  41. B. S. Chandrasekhar, A note on the maximum critical field of high-field superconductors, Appl. Phys. Lett. 1, 7 (1962).
  42. A. M. Clogston, Upper limit for the critical field in hard superconductors, Phys. Rev. Lett. 9, 266 (1962).
  43. I. B. Spielman, M. Kellogg, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Onset of interlayer phase coherence in a bilayer two-dimensional electron system: Effect of layer density imbalance, Phys. Rev. B 70, 081303(R) (2004).
  44. A. R. Champagne, A. D. K. Finck, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Charge imbalance and bilayer two-dimensional electron systems at νT=1, Phys. Rev. B 78, 205310 (2008).
  45. J. P. Eisenstein, T. Khaire, D. Nandi, A. D. K. Finck, L. N. Pfeiffer, and K. W. West, Spin and the Coulomb gap in the half-filled lowest Landau level, Phys. Rev. B 94, 125409 (2016).
  46. D. Chowdhury, B. Skinner, and P. A. Lee, Effect of magnetization on the tunneling anomaly in compressible quantum Hall states, Phys. Rev. Lett. 120, 266601 (2018).
  47. G. Chaudhary, D. K. Efimkin, and A. H. MacDonald, Tunneling density of states, correlation energy, and spin polarization in the fractional quantum Hall regime, Phys. Rev. B 100, 085107 (2019).

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