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  • Open Access

Universal Transport at Lifshitz Metal-Insulator Transitions in Two Dimensions

Harry Tomlins1 and Jan M. Tomczak1,2

  • 1Department of Physics, King’s College London, Strand, London WC2R 2LS, United Kingdom
  • 2Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria

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Phys. Rev. Lett. 135, 116302 – Published 8 September, 2025

DOI: https://doi.org/10.1103/kc4r-72vj

Abstract

We study the charge transport across a band-tuned metal-insulator transition in two dimensions. For high temperatures T and chemical potentials μ far from the transition point, conduction is ballistic and the resistance R(T) verifies a simple one-parameter scaling relation. Here, we explore the limits of this semiclassical behavior and study the quantum regime beyond, where scaling breaks down. We analytically evaluate the simplest Feynman diagram of the linear-response conductivity σ=1/R of a parabolic band endowed with a finite lifetime. Our formula shows excellent agreement for experiments for a field-tuned MoTe2/WSe2 moiré bilayer, and can capture the quantum effects responsible for breaking the one-parameter scaling. We go on to discuss a fascinating prediction of our model: The resistance at the quantum-critical band-tuned Lifshitz point (μ=T=0) has the universal value, RL=(2πh)/e2, per degree of freedom, in congruence with experiment. Furthermore, we investigate whether two-dimensional metal-insulator transitions driven by strong electron correlations or disorder can also be classified by their quantum-critical resistance and come up with an, in principle, complete assignment of the transition mechanism.

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References (62)

  1. S. V. Kravchenko and M. P. Sarachik, Rep. Prog. Phys. 67, 1 (2003).
  2. A. A. Shashkin and S. V. Kravchenko, Appl. Sci. 9, 1169 (2019).
  3. S. D. Sarma and E. Hwang, Solid State Commun. 135, 579 (2005).
  4. E. Abrahams, S. V. Kravchenko, and M. P. Sarachik, Rev. Mod. Phys. 73, 251 (2001).
  5. N. F. Mott, Metal-Insulator Transitions (Taylor and Francis, London, 1990).
  6. A. Camjayi, K. Haule, V. Dobrosavljević, and G. Kotliar, Nat. Phys. 4, 932 (2008).
  7. A. Amaricci, A. Camjayi, K. Haule, G. Kotliar, D. Tanasković, and V. Dobrosavljević, Phys. Rev. B 82, 155102 (2010).
  8. S. Musser, T. Senthil, and D. Chowdhury, Phys. Rev. B 106, 155145 (2022).
  9. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
  10. P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985).
  11. I. M. Lifshitz, Sov. Phys. JETP 11, 1130 (1960).
  12. G. E. Volovik, Low Temp. Phys. 43, 47 (2017).
  13. G. E. Volovik, Quantum phase transitions from topology in momentum space, in Lecture Notes in Physics (Springer, Berlin, Heidelberg, 2007), p. 31–73.
  14. A. A. Varlamov, Y. M. Galperin, S. G. Sharapov, and Y. Yerin, Low Temp. Phys. 47, 672 (2021).
  15. B. Spivak, S. V. Kravchenko, S. A. Kivelson, and X. P. A. Gao, Rev. Mod. Phys. 82, 1743 (2010).
  16. S. Fratini, S. Ciuchi, V. Dobrosavljević, and L. Rademaker, Phys. Rev. Lett. 131, 196303 (2023).
  17. S. V. Kravchenko, W. E. Mason, G. E. Bowker, J. E. Furneaux, V. M. Pudalov, and M. D’Iorio, Phys. Rev. B 51, 7038 (1995).
  18. A. A. Shashkin, S. V. Kravchenko, and T. M. Klapwijk, Phys. Rev. Lett. 87, 266402 (2001).
  19. M. Y. Melnikov, A. A. Shashkin, V. T. Dolgopolov, A. Y. X. Zhu, S. V. Kravchenko, S.-H. Huang, and C. W. Liu, Phys. Rev. B 99, 081106(R) (2019).
  20. Y. Hanein, U. Meirav, D. Shahar, C. C. Li, D. C. Tsui, and H. Shtrikman, Phys. Rev. Lett. 80, 1288 (1998).
  21. P. Coleridge, P. Zawadzki, A. Sachrajda, R. Williams, and Y. Feng, Physica (Amsterdam) 6E, 268 (2000).
  22. K. Lai, W. Pan, D. C. Tsui, S. A. Lyon, M. Mühlberger, and F. Schäffler, Phys. Rev. B 72, 081313(R) (2005).
  23. S. J. Papadakis and M. Shayegan, Phys. Rev. B 57, R15068 (1998).
  24. B. H. Moon, Emergent Mater. 4, 989 (2021).
  25. A. Ramasubramaniam, D. Naveh, and E. Towe, Phys. Rev. B 84, 205325 (2011).
  26. W. Choi, N. Choudhary, G. H. Han, J. Park, D. Akinwande, and Y. H. Lee, Mater. Today 20, 116 (2017).
  27. T. Li, S. Jiang, L. Li, Y. Zhang, K. Kang, J. Zhu, K. Watanabe, T. Taniguchi, D. Chowdhury, L. Fu, J. Shan, and K. F. Mak, Nature (London) 597, 350 (2021).
  28. Y. Tan, P. K. H. Tsang, and V. Dobrosavljević, Nat. Commun. 13, 7469 (2022).
  29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/kc4r-72vj, which includes Refs. [30–42], for derivations and details on the extraction of critical resistances from experimental data.
  30. J. Hall, N. Ehlen, J. Berges, E. van Loon, C. van Efferen, C. Murray, M. Rösner, J. Li, B. V. Senkovskiy, M. Hell, M. Rolf, T. Heider, M. C. Asensio, J. Avila, L. Plucinski, T. Wehling, A. Grüneis, and T. Michely, ACS Nano 13, 10210 (2019).
  31. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
  32. J. Mitscherling and T. Holder, Phys. Rev. B 105, 085154 (2022).
  33. G. Yu, L. Wen, G. Luo, and Y. Wang, Phys. Scr. 96, 125874 (2021).
  34. J.-X. Li, W.-Q. Li, S.-H. Hung, P.-L. Chen, Y.-C. Yang, T.-Y. Chang, P.-W. Chiu, H.-T. Jeng, and C.-H. Liu, Nat. Nanotechnol. 17, 721 (2022).
  35. A. Punnoose and A. M. Finkel’stein, Phys. Rev. Lett. 88, 016802 (2001).
  36. N. Kharche, S. Kim, T. B. Boykin, and G. Klimeck, Appl. Phys. Lett. 94, 042101 (2009).
  37. K. Vakili, Y. P. Shkolnikov, E. Tutuc, E. P. De Poortere, and M. Shayegan, Phys. Rev. Lett. 92, 226401 (2004).
  38. H. Jin, G. L. Zhao, and D. Bagayoko, Phys. Rev. B 73, 245214 (2006).
  39. N. Fraj, I. Saïdi, S. Ben Radhia, and K. Boujdaria, J. Appl. Phys. 102, 053703 (2007).
  40. T. Whall and E. Parker, Thin Solid Films 367, 250 (2000).
  41. D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Phys. Rev. Lett. 108, 196802 (2012).
  42. Y. Zhang, T. Devakul, and L. Fu, Proc. Natl. Acad. Sci. U.S.A. 118, e2112673118 (2021).
  43. P. Coleman, Introduction to Many-Body Physics (Cambridge University Press, Cambridge, England, 2015).
  44. M. Pickem, E. Maggio, and J. M. Tomczak, Phys. Rev. B 105, 085139 (2022).
  45. M. Pickem, E. Maggio, and J. M. Tomczak, Commun. Phys. 4, 226 (2021).
  46. M. Pickem, E. Maggio, and J. M. Tomczak, SciPost Phys. Codebases 16 (2023).
  47. J. M. Tomczak, K. Haule, T. Miyake, A. Georges, and G. Kotliar, Phys. Rev. B 82, 085104 (2010).
  48. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, (Dover Publications, Inc., New York, USA, 1974).
  49. G. Grissonnanche, Y. Fang, A. Legros, S. Verret, F. Laliberté, C. Collignon, J. Zhou, D. Graf, P. A. Goddard, L. Taillefer, and B. J. Ramshaw, Nature (London) 595, 667 (2021).
  50. M. Gurvitch, Phys. Rev. B 24, 7404 (1981).
  51. K. T. N. E. Hussey and H. Takagi, Philos. Mag. 84, 2847 (2004).
  52. J. M. Tomczak, J. Phys. Condens. Matter 30, 183001 (2018).
  53. J. Pack, Y. Guo, Z. Liu, B. S. Jessen, L. Holtzman, S. Liu, M. Cothrine, K. Watanabe, T. Taniguchi, D. G. Mandrus, K. Barmak, J. Hone, and C. R. Dean, Nat. Nanotechnol. 19, 948 (2024).
  54. J. Yoon, C. C. Li, D. Shahar, D. C. Tsui, and M. Shayegan, Phys. Rev. Lett. 82, 1744 (1999).
  55. J. Huang, L. Pfeiffer, and K. West, Appl. Sci. 9, 80 (2019).
  56. P. Brussarski, S. Li, S. V. Kravchenko, A. A. Shashkin, and M. P. Sarachik, Nat. Commun. 9, 3803 (2018).
  57. R. L. J. Qiu, C.-W. Liu, S. Liu, and X. P. A. Gao, Appl. Sci. 8, 1909 (2018).
  58. S. M. Girvin and K. Yang, Anderson localization, in Modern Condensed Matter Physics (Cambridge University Press, Cambridge, England, 2019), pp. 252–300.
  59. N. Mott, J. Phys. C 20, 3075 (1987).
  60. M. Rahimi, S. Anissimova, M. R. Sakr, S. V. Kravchenko, and T. M. Klapwijk, Phys. Rev. Lett. 91, 116402 (2003).
  61. J. Falson, I. Sodemann, B. Skinner, D. Tabrea, Y. Kozuka, A. Tsukazaki, M. Kawasaki, K. von Klitzing, and J. H. Smet, Nat. Mater. 21, 311 (2022).
  62. M. S. Osofsky, S. C. Hernández, A. Nath, V. D. Wheeler, S. G. Walton, C. M. Krowne, and D. K. Gaskill, Sci. Rep. 6, 19939 (2016).

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Phys. Rev. Lett. 135, 116302– Published 8 September, 2025
  • Received 4 March 2025
  • Accepted 6 August 2025
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