Papers
Topics
Authors
Recent
Search
2000 character limit reached

Effective field theory of Berry Fermi liquid from the coadjoint orbit method

Published 1 Dec 2023 in cond-mat.str-el and cond-mat.mes-hall | (2312.00877v3)

Abstract: We construct an effective field theory for an interacting Fermi liquid with nonzero Berry curvature at zero temperature, called the Berry Fermi liquid. We start with the extended phase space formalism, incorporating physical time into the configuration space. This approach allows us to include the time dependence of the background gauge fields ``covariantly'' into the symplectic structure. Upon restricting to the physical hypersurface, the effective action that lives on the coadjoint orbit becomes the minus free energy on the extended phase space. We also derive the action perturbatively in external fields using the canonical variables. For applications, we compute both linear and nonlinear electrical responses using the Kubo formula, and identify contributions from the electric and magnetic dipole moments, which stem from interactions breaking parity and time-reversal symmetry. The anomalous Hall effect is confirmed using the kinetic theory.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (46)
  1. LD Landau, “On the theory of the fermi liquid,” Sov. Phys. JETP 8, 70 (1959).
  2. R. Shankar, “Renormalization group approach to interacting fermions,” Rev. Mod. Phys. 66, 129–192 (1994), arXiv:cond-mat/9307009 .
  3. Joseph Polchinski, “Effective field theory and the Fermi surface,” in Theoretical Advanced Study Institute (TASI 92): From Black Holes and Strings to Particles (1992) pp. 0235–276, arXiv:hep-th/9210046 .
  4. Subir Sachdev, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, 2011).
  5. A. H. Castro Neto and Eduardo Fradkin, “Bosonization of fermi liquids,” Phys. Rev. B 49, 10877–10892 (1994).
  6. A. Houghton, H. J. Kwon,  and J. B. Marston, “Multidimensional bosonization,” Adv. Phys. 49, 141–228 (2000), arXiv:cond-mat/9810388 .
  7. F. D. M. Haldane, “Luttinger’s theorem and bosonization of the fermi surface,”  (2005), arXiv:cond-mat/0505529 [cond-mat.str-el] .
  8. Sumit R. Das, Avinash Dhar, Gautam Mandal,  and Spenta R. Wadia, “Bosonization of nonrelativistic fermions and W infinity algebra,” Mod. Phys. Lett. A 7, 71–84 (1992), arXiv:hep-th/9111021 .
  9. D. V. Khveshchenko, “Bosonization of current-current interactions,” Phys. Rev. B 49, 16893–16898 (1994).
  10. D. V. Khveshchenko, “Geometrical approach to bosonization of d¿1 dimensional (non)-fermi liquids,” Phys. Rev. B 52, 4833–4841 (1995).
  11. Luca V. Delacretaz, Yi-Hsien Du, Umang Mehta,  and Dam Thanh Son, “Nonlinear bosonization of Fermi surfaces: The method of coadjoint orbits,” Phys. Rev. Res. 4, 033131 (2022), arXiv:2203.05004 [cond-mat.str-el] .
  12. Michael Victor Berry, “Quantal phase factors accompanying adiabatic changes,” Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 392, 45–57 (1984).
  13. Di Xiao, Ming-Che Chang,  and Qian Niu, “Berry phase effects on electronic properties,” Rev. Mod. Phys. 82, 1959–2007 (2010).
  14. Naoto Nagaosa, Jairo Sinova, Shigeki Onoda, A. H. MacDonald,  and N. P. Ong, “Anomalous hall effect,” Rev. Mod. Phys. 82, 1539–1592 (2010).
  15. Inti Sodemann and Liang Fu, “Quantum nonlinear hall effect induced by berry curvature dipole in time-reversal invariant materials,” Phys. Rev. Lett. 115, 216806 (2015).
  16. Dam Thanh Son and Naoki Yamamoto, “Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids,” Phys. Rev. Lett. 109, 181602 (2012), arXiv:1203.2697 [cond-mat.mes-hall] .
  17. Dam Thanh Son and Naoki Yamamoto, “Kinetic theory with Berry curvature from quantum field theories,” Phys. Rev. D 87, 085016 (2013), arXiv:1210.8158 [hep-th] .
  18. D. T. Son and B. Z. Spivak, “Chiral anomaly and classical negative magnetoresistance of weyl metals,” Phys. Rev. B 88, 104412 (2013).
  19. M. A. Stephanov and Y. Yin, “Chiral Kinetic Theory,” Phys. Rev. Lett. 109, 162001 (2012), arXiv:1207.0747 [hep-th] .
  20. A.A. Burkov, “Weyl metals,” Annual Review of Condensed Matter Physics 9, 359–378 (2018), https://doi.org/10.1146/annurev-conmatphys-033117-054129 .
  21. F. D. M. Haldane, “Berry curvature on the fermi surface: Anomalous hall effect as a topological fermi-liquid property,” Phys. Rev. Lett. 93, 206602 (2004).
  22. Ryuichi Shindou and Leon Balents, “Gradient expansion approach to multiple-band fermi liquids,” Phys. Rev. B 77, 035110 (2008).
  23. Jing-Yuan Chen and Dam Thanh Son, “Berry Fermi Liquid Theory,” Annals Phys. 377, 345–386 (2017), arXiv:1604.07857 [cond-mat.str-el] .
  24. Walter Thirring, Classical Mathematical Physics (Springer Science and Business Media, 2013).
  25. Umang Mehta, Postmodern Fermi Liquids, Other thesis (2023), arXiv:2307.02536 [cond-mat.str-el] .
  26. Dominic V. Else, Ryan Thorngren,  and T. Senthil, “Non-fermi liquids as ersatz fermi liquids: General constraints on compressible metals,” Phys. Rev. X 11, 021005 (2021).
  27. A. A. Kirillov, Lectures on the Orbit Method (American Mathematical Soc., 2004).
  28. SangEun Han, Félix Desrochers,  and Yong Baek Kim, “Bosonization of Non-Fermi Liquids,”   (2023), arXiv:2306.14955 [cond-mat.str-el] .
  29. Daniel Bulmash, Pavan Hosur, Shou-Cheng Zhang,  and Xiao-Liang Qi, “Unified topological response theory for gapped and gapless free fermions,” Phys. Rev. X 5, 021018 (2015).
  30. Dominic V. Else and T. Senthil, “Strange metals as ersatz fermi liquids,” Phys. Rev. Lett. 127, 086601 (2021).
  31. Xiao-Gang Wen, “Low-energy effective field theories of fermion liquids and the mixed u⁢(1)×𝕣d𝑢1superscript𝕣𝑑u(1)\times{}{\mathbb{r}}^{d}italic_u ( 1 ) × blackboard_r start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT anomaly,” Phys. Rev. B 103, 165126 (2021).
  32. Ruochen Ma and Chong Wang, “Emergent anomaly of Fermi surfaces: a simple derivation from Weyl fermions,”   (2021), arXiv:2110.09492 [cond-mat.str-el] .
  33. Chong Wang, Alexander Hickey, Xuzhe Ying,  and A. A. Burkov, “Emergent anomalies and generalized luttinger theorems in metals and semimetals,” Phys. Rev. B 104, 235113 (2021).
  34. Da-Chuan Lu, Juven Wang,  and Yi-Zhuang You, “Definition and classification of Fermi surface anomalies,” Phys. Rev. B 109, 045123 (2024), arXiv:2302.12731 [cond-mat.str-el] .
  35. Dominic V. Else, “Holographic models of non-Fermi liquid metals revisited: An effective field theory approach,” Phys. Rev. B 109, 035163 (2024), arXiv:2307.02526 [cond-mat.str-el] .
  36. N. R. Cooper, B. I. Halperin,  and I. M. Ruzin, “Thermoelectric response of an interacting two-dimensional electron gas in a quantizing magnetic field,” Phys. Rev. B 55, 2344–2359 (1997).
  37. Di Xiao, Junren Shi,  and Qian Niu, “Berry phase correction to electron density of states in solids,” Phys. Rev. Lett. 95, 137204 (2005).
  38. Yong Baek Kim, Patrick A. Lee,  and Xiao-Gang Wen, “Quantum boltzmann equation of composite fermions interacting with a gauge field,” Phys. Rev. B 52, 17275–17292 (1995).
  39. Z. Z. Du, Hai-Zhou Lu,  and X. C. Xie, “Nonlinear hall effects,” Nature Reviews Physics 3, 744–752 (2021).
  40. Qiong Ma, Su-Yang Xu, Huitao Shen, David MacNeill, Valla Fatemi, Tay-Rong Chang, Andrés M. Mier Valdivia, Sanfeng Wu, Zongzheng Du, Chuang-Han Hsu, Shiang Fang, Quinn D. Gibson, Kenji Watanabe, Takashi Taniguchi, Robert J. Cava, Efthimios Kaxiras, Hai-Zhou Lu, Hsin Lin, Liang Fu, Nuh Gedik,  and Pablo Jarillo-Herrero, “Observation of the nonlinear hall effect under time-reversal-symmetric conditions,” Nature 565, 337–342 (2019).
  41. Johannes Gooth et al., “Thermal and electrical signatures of a hydrodynamic electron fluid in tungsten diphosphide,” Nature Communications 9 (2018), 10.1038/s41467-018-06688-y.
  42. Uri Vool, Assaf Hamo, Georgios Varnavides, Yaxian Wang, Tony X. Zhou, Nitesh Kumar, Yuliya Dovzhenko, Ziwei Qiu, Christina A. C. Garcia, Andrew T. Pierce, Johannes Gooth, Polina Anikeeva, Claudia Felser, Prineha Narang,  and Amir Yacoby, “Imaging phonon-mediated hydrodynamic flow in wte2,” Nature Physics 17, 1216–1220 (2021).
  43. Takamori Park and Leon Balents, “An exact method for bosonizing the fermi surface in arbitrary dimensions,”  (2024), arXiv:2310.04636 [cond-mat.str-el] .
  44. Jing-Yuan Chen, Berry Phase Physics in Free and Interacting Fermionic Systems, Other thesis (2016), arXiv:1608.03568 [cond-mat.mes-hall] .
  45. C. Duval, Z. Horvath, P. A. Horvathy, L. Martina,  and P. Stichel, “Berry phase correction to electron density in solids and ’exotic’ dynamics,” Mod. Phys. Lett. B 20, 373–378 (2006), arXiv:cond-mat/0506051 .
  46. R Kubo, “The fluctuation-dissipation theorem,” Rep. Prog. Phys. 29, 255–284 (1966).
Citations (1)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Summarize

Paper to Video (Beta)

Whiteboard

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

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Generate

Open Problems

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

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Continue Learning

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

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Authors (1)

  1. Xiaoyang Huang 

Collections

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

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Tweets

Sign up for free to view the 1 tweet with 9 likes about this paper.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up for Free