Papers
Topics
Authors
Recent
Search
2000 character limit reached

Excitonic quantum criticality: from bilayer graphene to narrow Chern bands

Published 19 Feb 2024 in cond-mat.str-el, cond-mat.stat-mech, and hep-th | (2402.12436v2)

Abstract: We study a family of excitonic quantum phase transitions describing the evolution of a bilayer metallic state to an inter-layer coherent state where excitons condense. We argue that such transitions can be continuous and exhibit a non-Fermi liquid counterflow response ${\rho_{\mathrm{counterflow}}(\omega)\sim\omega{2/z}}$ that directly encodes the dynamical critical exponent $z$. Our calculations are performed within a controlled expansion around $z = 2$. This physics is relevant to any system with spin, valley, or layer degrees of freedom. We consider two contexts for excitonic quantum criticality: (1) a weakly interacting graphene bilayer, and (2) a system of two narrow, half-filled Chern bands at zero external magnetic field, with total Chern number $C_{\mathrm{tot}}=0$, which may soon be realizable in moir\'{e} materials. The latter system hosts a time-reversed pair of composite Fermi liquid states, and the condensation of excitons of the composite fermions leads to an exotic exciton insulator* state with a charge neutral Fermi surface. Our work sheds new light on the physics of inter-layer coherence transitions in 2D materials.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (74)
  1. L. Ma, P. X. Nguyen, Z. Wang, Y. Zeng, K. Watanabe, T. Taniguchi, A. H. MacDonald, K. F. Mak,  and J. Shan, “Strongly correlated excitonic insulator in atomic double layers,” Nature 598, 585–589 (2021).
  2. J. Gu, L. Ma, S. Liu, K. Watanabe, T. Taniguchi, J. C. Hone, J. Shan,  and K. F. Mak, “Dipolar excitonic insulator in a moire lattice,”  (2021), arXiv:2108.06588 [cond-mat.str-el] .
  3. B. Sun, W. Zhao, T. Palomaki, Z. Fei, E. Runburg, P. Malinowski, X. Huang, J. Cenker, Y.-T. Cui, J.-H. Chu, X. Xu, S. S. Ataei, D. Varsano, M. Palummo, E. Molinari, M. Rontani,  and D. H. Cobden, “Evidence for equilibrium exciton condensation in monolayer wte2,” Nature Physics 18, 94–99 (2022).
  4. Y. Zeng, Z. Xia, R. Dery, K. Watanabe, T. Taniguchi, J. Shan,  and K. F. Mak, “Exciton density waves in coulomb-coupled dual moirélattices,” Nature Materials 22, 175–179 (2023a).
  5. P. X. Nguyen, L. Ma, R. Chaturvedi, K. Watanabe, T. Taniguchi, J. Shan,  and K. F. Mak, “Perfect coulomb drag in a dipolar excitonic insulator,”  (2023), arXiv:2309.14940 [cond-mat.mes-hall] .
  6. M. He, Y.-H. Zhang, Y. Li, Z. Fei, K. Watanabe, T. Taniguchi, X. Xu,  and M. Yankowitz, “Competing correlated states and abundant orbital magnetism in twisted monolayer-bilayer graphene,” Nature Communications 12, 4727 (2021).
  7. H. Kim, Y. Choi, E. Lantagne-Hurtubise, C. Lewandowski, A. Thomson, L. Kong, H. Zhou, E. Baum, Y. Zhang, L. Holleis, K. Watanabe, T. Taniguchi, A. F. Young, J. Alicea,  and S. Nadj-Perge, “Imaging inter-valley coherent order in magic-angle twisted trilayer graphene,”  (2023), arXiv:2304.10586 [cond-mat.str-el] .
  8. Z. Dong, L. Levitov,  and A. V. Chubukov, “Superconductivity near spin and valley orders in graphene multilayers,” Phys. Rev. B 108, 134503 (2023b).
  9. Y.-H. Zhang, D. Mao, Y. Cao, P. Jarillo-Herrero,  and T. Senthil, “Nearly flat chern bands in moiré superlattices,” Phys. Rev. B 99, 075127 (2019a).
  10. Y.-H. Zhang, D. Mao,  and T. Senthil, “Twisted bilayer graphene aligned with hexagonal boron nitride: Anomalous hall effect and a lattice model,” Phys. Rev. Res. 1, 033126 (2019b).
  11. M. Serlin, C. L. Tschirhart, H. Polshyn, Y. Zhang, J. Zhu, K. Watanabe, T. Taniguchi, L. Balents,  and A. F. Young, “Intrinsic quantized anomalous hall effect in a moiré heterostructure,” Science 367, 900–903 (2020), https://www.science.org/doi/pdf/10.1126/science.aay5533 .
  12. T. Li, S. Jiang, B. Shen, Y. Zhang, L. Li, Z. Tao, T. Devakul, K. Watanabe, T. Taniguchi, L. Fu, J. Shan,  and K. F. Mak, “Quantum anomalous hall effect from intertwined moirébands,” Nature 600, 641–646 (2021).
  13. A. L. Sharpe, E. J. Fox, A. W. Barnard, J. Finney, K. Watanabe, T. Taniguchi, M. A. Kastner,  and D. Goldhaber-Gordon, “Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene,” Science 365, 605–608 (2019), https://www.science.org/doi/pdf/10.1126/science.aaw3780 .
  14. P. Wilhelm, T. C. Lang,  and A. M. Läuchli, “Interplay of fractional chern insulator and charge density wave phases in twisted bilayer graphene,” Phys. Rev. B 103, 125406 (2021).
  15. A. Abouelkomsan, Z. Liu,  and E. J. Bergholtz, “Particle-hole duality, emergent fermi liquids, and fractional chern insulators in moiré flatbands,” Phys. Rev. Lett. 124, 106803 (2020).
  16. N. Bultinck, S. Chatterjee,  and M. P. Zaletel, “Mechanism for anomalous hall ferromagnetism in twisted bilayer graphene,” Phys. Rev. Lett. 124, 166601 (2020).
  17. C. Repellin and T. Senthil, ‘‘Chern bands of twisted bilayer graphene: Fractional chern insulators and spin phase transition,” Phys. Rev. Res. 2, 023238 (2020).
  18. P. J. Ledwith, G. Tarnopolsky, E. Khalaf,  and A. Vishwanath, “Fractional chern insulator states in twisted bilayer graphene: An analytical approach,” Phys. Rev. Res. 2, 023237 (2020).
  19. Y. Xie, A. T. Pierce, J. M. Park, D. E. Parker, E. Khalaf, P. Ledwith, Y. Cao, S. H. Lee, S. Chen, P. R. Forrester, K. Watanabe, T. Taniguchi, A. Vishwanath, P. Jarillo-Herrero,  and A. Yacoby, “Fractional chern insulators in magic-angle twisted bilayer graphene,” Nature 600, 439–443 (2021).
  20. B. A. Foutty, C. R. Kometter, T. Devakul, A. P. Reddy, K. Watanabe, T. Taniguchi, L. Fu,  and B. E. Feldman, “Mapping twist-tuned multi-band topology in bilayer wse22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT,”  (2023), arXiv:2304.09808 [cond-mat.mes-hall] .
  21. F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong, J. Jia, Z. Shi, S. Jiang, Y. Zhang, X. Liu,  and T. Li, “Observation of integer and fractional quantum anomalous hall effects in twisted bilayer mote2subscriptmote2{\mathrm{mote}}_{2}roman_mote start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT,” Phys. Rev. X 13, 031037 (2023).
  22. J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe, Y. Ran, T. Cao, L. Fu, D. Xiao, W. Yao,  and X. Xu, “Signatures of fractional quantum anomalous hall states in twisted MoTe2,” Nature  (2023), 10.1038/s41586-023-06289-w.
  23. H. Park, J. Cai, E. Anderson, Y. Zhang, J. Zhu, X. Liu, C. Wang, W. Holtzmann, C. Hu, Z. Liu, T. Taniguchi, K. Watanabe, J.-H. Chu, T. Cao, L. Fu, W. Yao, C.-Z. Chang, D. Cobden, D. Xiao,  and X. Xu, “Observation of fractionally quantized anomalous hall effect,” Nature  (2023), 10.1038/s41586-023-06536-0.
  24. Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu,  and L. Ju, “Fractional quantum anomalous hall effect in a graphene moire superlattice,”  (2023), arXiv:2309.17436 [cond-mat.mes-hall] .
  25. Y. Zeng, Z. Xia, K. Kang, J. Zhu, P. Knüppel, C. Vaswani, K. Watanabe, T. Taniguchi, K. F. Mak,  and J. Shan, “Integer and fractional chern insulators in twisted bilayer mote2,” arXiv preprint arXiv:2305.00973  (2023b).
  26. Z. Dong, A. S. Patri,  and T. Senthil, “Theory of fractional quantum anomalous hall phases in pentalayer rhombohedral graphene moir\\\backslash\’e structures,” arXiv preprint arXiv:2311.03445  (2023c).
  27. J. Dong, T. Wang, T. Wang, T. Soejima, M. P. Zaletel, A. Vishwanath,  and D. E. Parker, “Anomalous hall crystals in rhombohedral multilayer graphene i: Interaction-driven chern bands and fractional quantum hall states at zero magnetic field,” arXiv preprint arXiv:2311.05568  (2023d).
  28. H. Goldman, A. P. Reddy, N. Paul,  and L. Fu, “Zero-field composite fermi liquid in twisted semiconductor bilayers,” Phys. Rev. Lett. 131, 136501 (2023).
  29. J. Dong, J. Wang, P. J. Ledwith, A. Vishwanath,  and D. E. Parker, “Composite fermi liquid at zero magnetic field in twisted mote2subscriptmote2{\mathrm{mote}}_{2}roman_mote start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT,” Phys. Rev. Lett. 131, 136502 (2023e).
  30. K. Kang, B. Shen, Y. Qiu, K. Watanabe, T. Taniguchi, J. Shan,  and K. F. Mak, “Observation of the fractional quantum spin hall effect in moiré mote2,”  (2024), arXiv:2402.03294 [cond-mat.mes-hall] .
  31. D. Belitz, T. R. Kirkpatrick,  and T. Vojta, “How generic scale invariance influences quantum and classical phase transitions,” Rev. Mod. Phys. 77, 579–632 (2005).
  32. A. V. Chubukov, C. Pépin,  and J. Rech, “Instability of the quantum-critical point of itinerant ferromagnets,” Phys. Rev. Lett. 92, 147003 (2004).
  33. J. Rech, C. Pépin,  and A. V. Chubukov, “Quantum critical behavior in itinerant electron systems: Eliashberg theory and instability of a ferromagnetic quantum critical point,” Phys. Rev. B 74, 195126 (2006).
  34. D. V. Efremov, J. J. Betouras,  and A. Chubukov, “Nonanalytic behavior of two-dimensional itinerant ferromagnets,” Phys. Rev. B 77, 220401 (2008).
  35. D. L. Maslov and A. V. Chubukov, “Nonanalytic paramagnetic response of itinerant fermions away and near a ferromagnetic quantum phase transition,” Phys. Rev. B 79, 075112 (2009).
  36. I. Ussishkin and A. Stern, “Coulomb drag in compressible quantum hall states,” Phys. Rev. B 56, 4013–4022 (1997).
  37. M. P. Lilly, J. P. Eisenstein, L. N. Pfeiffer,  and K. W. West, “Coulomb drag in the extreme quantum limit,” Phys. Rev. Lett. 80, 1714–1717 (1998).
  38. M. Kellogg, J. P. Eisenstein, L. N. Pfeiffer,  and K. W. West, “Bilayer quantum hall systems at νT=1subscript𝜈𝑇1{\nu}_{T}=1italic_ν start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT = 1: Coulomb drag and the transition from weak to strong interlayer coupling,” Phys. Rev. Lett. 90, 246801 (2003).
  39. 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).
  40. E. Tutuc, M. Shayegan,  and D. A. Huse, “Counterflow measurements in strongly correlated gaas hole bilayers: Evidence for electron-hole pairing,” Phys. Rev. Lett. 93, 036802 (2004).
  41. J. P. Eisenstein and A. H. MacDonald, “Bose–einstein condensation of excitons in bilayer electron systems,” Nature 432, 691–694 (2004).
  42. A. D. K. Finck, J. P. Eisenstein, L. N. Pfeiffer,  and K. W. West, “Exciton transport and andreev reflection in a bilayer quantum hall system,” Phys. Rev. Lett. 106, 236807 (2011).
  43. X. Liu, K. Watanabe, T. Taniguchi, B. I. Halperin,  and P. Kim, “Quantum hall drag of exciton condensate in graphene,” Nature Physics 13, 746–750 (2017).
  44. X. Liu, J. 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, 205–209 (2022), https://www.science.org/doi/pdf/10.1126/science.abg1110 .
  45. M. Sidler, P. Back, O. Cotlet, A. Srivastava, T. Fink, M. Kroner, E. Demler,  and A. Imamoglu, “Fermi polaron-polaritons in charge-tunable atomically thin semiconductors,” Nature Physics 13, 255–261 (2017).
  46. K. F. Mak, D. Xiao,  and J. Shan, “Light–valley interactions in 2d semiconductors,” Nature Photonics 12, 451–460 (2018).
  47. T. Wang, Z. Li, Z. Lu, Y. Li, S. Miao, Z. Lian, Y. Meng, M. Blei, T. Taniguchi, K. Watanabe, S. Tongay, W. Yao, D. Smirnov, C. Zhang,  and S.-F. Shi, “Observation of quantized exciton energies in monolayer wse2subscriptwse2{\mathrm{wse}}_{2}roman_wse start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT under a strong magnetic field,” Phys. Rev. X 10, 021024 (2020).
  48. Y.-H. Zhang, “Composite fermion insulator in opposite-fields quantum hall bilayers,” arXiv preprint arXiv:1810.03600  (2018).
  49. N. Myerson-Jain, C.-M. Jian,  and C. Xu, “The conjugate composite fermi liquid,”  (2023), arXiv:2311.16250 [cond-mat.str-el] .
  50. Y.-H. Zhang, “Vortex spin liquid with neutral fermi surface and fractional quantum spin hall effect at odd integer filling of moiré chern band,”  (2024), arXiv:2402.05112 [cond-mat.str-el] .
  51. K. Moon, H. Mori, K. Yang, S. M. Girvin, A. H. MacDonald, L. Zheng, D. Yoshioka,  and S.-C. Zhang, “Spontaneous interlayer coherence in double-layer quantum hall systems: Charged vortices and kosterlitz-thouless phase transitions,” Phys. Rev. B 51, 5138–5170 (1995).
  52. N. E. Bonesteel, I. A. McDonald,  and C. Nayak, “Gauge fields and pairing in double-layer composite fermion metals,” Phys. Rev. Lett. 77, 3009–3012 (1996).
  53. G. Möller, S. H. Simon,  and E. H. Rezayi, “Paired composite fermion phase of quantum hall bilayers at ν=12+12𝜈1212\nu=\frac{1}{2}+\frac{1}{2}italic_ν = divide start_ARG 1 end_ARG start_ARG 2 end_ARG + divide start_ARG 1 end_ARG start_ARG 2 end_ARG,” Phys. Rev. Lett. 101, 176803 (2008).
  54. M. V. Milovanović and Z. Papić, “Nonperturbative approach to the quantum hall bilayer,” Phys. Rev. B 79, 115319 (2009).
  55. M. V. Milovanović, E. Dobardžić,  and Z. Papić, “Meron deconfinement in the quantum hall bilayer at intermediate distances,” Phys. Rev. B 92, 195311 (2015).
  56. I. Sodemann, I. Kimchi, C. Wang,  and T. Senthil, “Composite fermion duality for half-filled multicomponent landau levels,” Phys. Rev. B 95, 085135 (2017).
  57. H. Isobe and L. Fu, “Interlayer pairing symmetry of composite fermions in quantum hall bilayers,” Phys. Rev. Lett. 118, 166401 (2017).
  58. Z. D. Shi, “Controlled expansion for transport in a class of non-Fermi liquids,”  (2023), arXiv:2311.12922 [cond-mat.str-el] .
  59. Z. D. Shi, H. Goldman, D. V. Else,  and T. Senthil, “Gifts from anomalies: Exact results for Landau phase transitions in metals,” SciPost Phys. 13, 102 (2022).
  60. Z. D. Shi, D. V. Else, H. Goldman,  and T. Senthil, “Loop current fluctuations and quantum critical transport,” SciPost Physics 14 (2023), 10.21468/scipostphys.14.5.113.
  61. D. V. Else, R. Thorngren,  and T. Senthil, “Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals,” Phys. Rev. X 11, 021005 (2021), arXiv:2007.07896 [cond-mat.str-el] .
  62. H. Guo, A. A. Patel, I. Esterlis,  and S. Sachdev, “Large-n𝑛nitalic_n theory of critical fermi surfaces. ii. conductivity,” Phys. Rev. B 106, 115151 (2022).
  63. H. Guo, “Is the migdal-eliashberg theory for 2+ 1d critical fermi surface stable?”  (2023a), arXiv:2311.03455 [cond-mat.str-el] .
  64. H. Guo, ‘‘Fluctuation spectrum of 2+ 1d critical fermi surface and its application to optical conductivity and hydrodynamics,”  (2023b), arXiv:2311.03458 [cond-mat.str-el] .
  65. M. Barkeshli and J. McGreevy, “Continuous transitions between composite fermi liquid and landau fermi liquid: A route to fractionalized mott insulators,” Phys. Rev. B 86, 075136 (2012).
  66. D. T. Son, “Is the Composite Fermion a Dirac Particle?” Phys. Rev. X 5, 031027 (2015), arXiv:1502.03446 [cond-mat.mes-hall] .
  67. B. I. Halperin, P. A. Lee,  and N. Read, “Theory of the half filled Landau level,” Phys. Rev. B 47, 7312–7343 (1993).
  68. C. Nayak and F. Wilczek, “NonFermi liquid fixed point in (2+1)-dimensions,” Nucl. Phys. B 417, 359–373 (1994), arXiv:cond-mat/9312086 .
  69. M. A. Metlitski, D. F. Mross, S. Sachdev,  and T. Senthil, “Cooper pairing in non-Fermi liquids,” Phys. Rev. B 91, 115111 (2015), arXiv:1403.3694 [cond-mat.str-el] .
  70. S. Raghu, G. Torroba,  and H. Wang, “Metallic quantum critical points with finite BCS couplings,” Phys. Rev. B 92, 205104 (2015), arXiv:1507.06652 [cond-mat.str-el] .
  71. Y.-H. Zhang and A. Vishwanath, “Electrical detection of spin liquids in double moir\\\backslash\’e layers,” arXiv preprint arXiv:2005.12925  (2020).
  72. T. Arp, O. Sheekey, H. Zhou, C. L. Tschirhart, C. L. Patterson, H. M. Yoo, L. Holleis, E. Redekop, G. Babikyan, T. Xie, J. Xiao, Y. Vituri, T. Holder, T. Taniguchi, K. Watanabe, M. E. Huber, E. Berg,  and A. F. Young, “Intervalley coherence and intrinsic spin-orbit coupling in rhombohedral trilayer graphene,”  (2023), arXiv:2310.03781 [cond-mat.mes-hall] .
  73. A. P. Reddy, F. Alsallom, Y. Zhang, T. Devakul,  and L. Fu, “Fractional quantum anomalous hall states in twisted bilayer mote2subscriptmote2{\mathrm{mote}}_{2}roman_mote start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT and wse2subscriptwse2{\mathrm{wse}}_{2}roman_wse start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT,” Phys. Rev. B 108, 085117 (2023).
  74. J. Dong, J. Wang, P. J. Ledwith, A. Vishwanath,  and D. E. Parker, “Composite fermi liquid at zero magnetic field in twisted mote2subscriptmote2{\mathrm{mote}}_{2}roman_mote start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT,” Phys. Rev. Lett. 131, 136502 (2023f).
Citations (6)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 2 tweets with 0 likes about this paper.

Sign Up for Free