Topological Lifshitz transitions

Физика Низких Температур: Том 43, Выпуск 1 (Январь 2017), c. 57-67 ( к оглавлению , назад )

Topological Lifshitz transitions

G.E. Volovik

Low Temperature Laboratory, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland

Landau Institute for Theoretical Physics, 1a Acad. Semyonov Ave., Chernogolovka 142432, Russia

P.N. Lebedev Physical Institute, RAS, Moscow 119991, Russia
E-mail: volovik@boojum.hut.fi

Received July 4, 2016

Abstract

Different types of Lifshitz transitions are governed by topology in momentum space. They involve the topological transitions with the change of topology of Fermi surfaces, Weyl and Dirac points, nodal lines, and also the transitions between the fully gapped states.

PACS: 03.65.Vf Topological phases (quantum mechanics);
PACS: 64.70.Tg Quantum phase transitions.

Key words: Lifshitz transitions, Fermi surface, Weyl and Dirac points.

Published online: November 25, 2016

References

1. I. M. Lifshitz , Sov. Phys. JETP 11, 1130 (1960). Google Scholar

2. G. E. Volovik , Lect. Notes Phys. 718, 31 (2007); e-print arXiv:cond-mat/0601372. CrossRef Google Scholar

3. V. A. Khodel and V. R. Shaginyan , JETP Lett. 51, 553 (1990). Google Scholar

4. G. E. Volovik , JETP Lett. 53, 222 (1991). Google Scholar

5. P. Nozieres , J. Phys. (Paris) 2, 443 (1992). Google Scholar

6. S. Ryu and Y. Hatsugai , Phys. Rev. Lett. 89, 077002 (2002). CrossRef Google Scholar

7. A. P. Schnyder and S. Ryu , Phys. Rev. B 84, 060504(R) (2011). CrossRef Google Scholar

8. T. T. Heikkilä and G. E. Volovik , Pis'ma ZhETF 93, 63 (2011) T. T. Heikkilä and G. E. Volovik , [JETP Lett. 93, 59 (2011)]; e-print arXiv:1011.4185. CrossRef Google Scholar

9. T. T. Heikkilä , N. B. Kopnin , and G. E. Volovik , Pis'ma ZhETF 94, 252 (2011) T. T. Heikkilä , N. B. Kopnin , and G. E. Volovik , [JETP Lett. 94, 233 (2011)]; e-print arXiv:1012.0905. CrossRef Google Scholar

10. A. P. Schnyder and P. M. R. Brydon , J. Phys.: Condens. Matter 27, 243201 (2015). CrossRef Google Scholar

11. G. E. Volovik , Pis'ma ZhETF 59, 798 (1994)CAS G. E. Volovik , [JETP Lett. 59, 830 (1994)]. Google Scholar

12. D. Yudin , D. Hirschmeier , H. Hafermann , O. Eriksson , A. I. Lichtenstein , and M. I. Katsnelson , Phys. Rev. Lett. 112, 070403 (2014). CrossRef Google Scholar

13. A. P. Drozdov , M. I. Eremets , I. A. Troyan , V. Ksenofontov , and S. I. Shylin , Nature 525, 73 (2015). CrossRef Google Scholar

14. Y. Quan and W. E. Pickett , Phys. Rev. B 93, 104526 (2016). CrossRef Google Scholar

15. A. Bianconi and T. Jarlborg , Novel Supercond. Mater. 1, 37 (2015); e-print arXiv:1507.01093. CrossRef Google Scholar

16. X. Shi , Z.-Q. Han , X.-L. Peng , P. Richard , T. Qian , X.-X. Wu , M.-W. Qiu , S. C. Wang , J. P. Hu , Y.-J. Sun , and H. Ding , “Enhanced superconductivity accompanying a Lifshitz transition in electron-doped FeSe monolayer,” e-print arXiv:1606.01470. CrossRef Google Scholar

17. P. Esquinazi , T. T. Heikkila , Y. V. Lysogorskiy , D. A. Tayurskii , and G. E. Volovik , Pis'ma ZhETF 100, 374 (2014). Google Scholar

18. P. Esquinazi , Pap. Phys. 5, 050007 (2013). Google Scholar

19. A. Ballestar , J. Barzola-Quiquia , T. Scheike , and P. Esquinazi , New J. Phys. 15, 023024 (2013). CrossRef Google Scholar

20. A. Ballestar , T. T. Heikkila , and P. Esquinazi , Supercond. Sci. Technol. 27, 115014 (2014). CrossRef Google Scholar

21. G. E. Volovik , JETP Lett. 46, 98 (1987). Google Scholar

22. G. E. Volovik , The Universe in a Helium Droplet (Clarendon Press, Oxford, 2003). Google Scholar

23. F. R. Klinkhamer and G. E. Volovik , Int. J. Mod. Phys. A 20, 2795 (2005). CrossRef Google Scholar

24. L.-K. Lim and R. Moessner , “A pseudospin vortex-ring with a nodal line in three dimensions,” e-print arXiv:1606.00982. CrossRef Google Scholar

25. J. L. Manes , F. Guinea , and M. A. H. Vozmediano , Phys. Rev. B 75, 155424 (2007). CrossRef Google Scholar

26. G. E. Volovik and V. A. Konyshev , JETP Lett. 47, 250–254 (1988). Google Scholar

27. A. Shtyk , G. Goldstein , and C. Chamon , “Electrons at the monkey saddle: A multicritical Lifshitz point,” e-print arXiv:1606.04950. CrossRef Google Scholar

28. G. P. Mikitik and Yu. V. Sharlai , Phys. Rev. B 73, 235112 (2006). CrossRef Google Scholar

29. G. P. Mikitik and Yu. V. Sharlai , Fiz. Nizk. Temp. 34, 1012 (2008) G. P. Mikitik and Yu. V. Sharlai , [Low Temp. Phys. 34, 794 (2008)]. CrossRef Google Scholar

30. G. P. Mikitik and Yu. V. Sharlai , Phys. Rev. B 90, 155122 (2014). CrossRef Google Scholar

31. T. T. Heikkilä and G. E. Volovik , New J. Phys. 17, 093019 (2014), e-print arXiv:1505.03277. CrossRef Google Scholar

32. E. I. Rashba and V. I. Sheka , Fiz. Tverd. Tela II, 162 (1959) (in Russian);English translation: Supplemental material to the paper by G. Bihlmayer , O. Rader , and R. Winkler , “Focus on the Rashba effect,” New J. Phys. 17, 050202 (2015). Google Scholar

33. I. I. Boiko and E. I. Rashba , Fiz. Tverd. Tela 2, 1874 (1960).CAS Google Scholar

34. C. H. Ho , C. P. Chang , W. P. Su , and M. F. Lin , New J. Phys. 15, 053032 (2013). CrossRef Google Scholar

35. A. A. Soluyanov , D. Gresch , Z. Wang , Q. S. Wu , M. Troyer , X. Dai , and B. A. Bernevig , Nature 527, 495 (2015). CrossRef Google Scholar

36. P. Huhtala and G. E. Volovik , ZhETF 121, 995 (2002) P. Huhtala and G. E. Volovik , [JETP 94, 853 (2002)]. CrossRef Google Scholar

37. G. E. Volovik and M. A. Zubkov , Nucl. Phys. B 881, 514 (2014). CrossRef Google Scholar

38. G. E. Volovik , Pis'ma ZhETF 104, 660 (2016), e-print arXiv:1610.00521. CrossRef Google Scholar

39. M. O. Goerbig , J.-N. Fuchs , G. Montambaux , and F. Piechon , Phys. Rev. B 78, 045415 (2008). CrossRef Google Scholar

40. A. P. Schnyder , S. Ryu , A. Furusaki , and A. W. W. Ludwig , Phys. Rev. B 78, 195125 (2008). CrossRef Google Scholar

41. A. P. Schnyder , S. Ryu , A. Furusaki , and A. W. W. Ludwig , AIP Conf. Proc. 1134, 10 (2009).Scitation Google Scholar

42. P. Horava , Phys. Rev. Lett. 95, 016405 (2005). CrossRef Google Scholar

43. A. M. Essin and V. Gurarie , Phys. Rev. B 84, 125132 (2011). CrossRef Google Scholar

44. C. Caroli , P. G. de Gennes , and J. Matricon , Phys. Lett. 9, 307 (1964). CrossRef Google Scholar

45. Yu. G. Makhlin and G. E. Volovik , JETP Lett. 62, 737 (1995); e-print arXiv:cond-mat/9510075. CrossRef Google Scholar

46. M. A. Silaev and G. E. Volovik , JETP 119, 1042 (2014), e-print arXiv:1405.1007. CrossRef Google Scholar