Gap Generation in Weyl Semimetals in a Model with Local Four-Fermion Interaction
DOI:
https://doi.org/10.15407/ujpe59.07.0696Keywords:
Weyl semimetals, gap generation, quasiparticle energy spectrumAbstract
We study the gap generation in Weyl semimetals in a model with local four-fermion interaction. It is shown that there exists a critical value of coupling constant separating the symmetric and broken symmetry phases, and the corresponding phase diagram is described. The gap generation in a more general class of Weyl materials with small bare gap is studied, and the quasiparticle energy spectrum is determined. It is found that, in this case, the dynamically generated gap leads to the additional splitting of the quasiparticle energy bands.
References
X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 831057 (2011).
https://doi.org/10.1103/RevModPhys.83.1057
M.Z. Hasan and C. L. Kaney Rev. Mod. Phys. 82, 823045 (2010).
https://doi.org/10.1103/RevModPhys.82.3045
Y. Ando J. Phys. Soc. Jpn. 82, 102001 (2013).
https://doi.org/10.7566/JPSJ.82.102001
M.H. Cohen and E.I. Blount, Phil. Mag. 5, 115 (1960).
https://doi.org/10.1080/14786436008243294
P.A. Wolff, J. Phys. Chem. Solids 25, 1057 (1964).
https://doi.org/10.1016/0022-3697(64)90128-3
L.A. Fal'kovskii, Sov. Phys. Usp. 11, 1 (1968).
https://doi.org/10.1070/PU1968v011n01ABEH003721
V.S. Edel'man, Adv. Phys. 25, 555 (1976);
https://doi.org/10.1080/00018737600101452
Sov. Phys. Usp. 20, 819 (1977).
https://doi.org/10.1070/PU1977v020n10ABEH005467
Z. Wang, Y. Sun, X. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, and Z. Fang, Phys. Rev. B 85, 195320 (2012).
https://doi.org/10.1103/PhysRevB.85.195320
Z. Wang, H. Weng, Q. Wu, X. Dai, and Z. Fang, Phys. Rev. B 88, 125427 (2013).
https://doi.org/10.1103/PhysRevB.88.125427
Z.K. Liu, B. Zhou, Z.J. Wang, H.M. Weng, D. Prabhakaran, S.-K. Mo, Y. Zhang, Z.X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y.L. Chen, Science 343, 864 (2013).
https://doi.org/10.1126/science.1245085
M. Neupane, SuY. Xu, R. Sankar, N. Alidoust, G. Bian, C. Liu, I. Belopolski, T.-R. Chang, H.-T. Jeng, H. Lin, A. Bansil, F. Chou, and M.Z. Hasan, e-print arXiv:1309.7892v1 (2013).
S. Borisenko, Q. Gibson, D. Evtushinsky, V. Zabolotnyy, B. Buechner, and R. J. Cava, e-print arXiv:1309.7978v1 (2013).
H.-J. Kim, Ki-S. Kim, J.F. Wang, M. Sasaki, N. Satoh, A. Ohnishi, M. Kitaura, M. Yang, and L. Li, Phys. Rev. Lett. 111, 246603 (2013).
https://doi.org/10.1103/PhysRevLett.111.246603
E.V. Gorbar, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. B 88, 165105 (2013).
https://doi.org/10.1103/PhysRevB.88.165105
Z. Wang and S.-C. Zhang, Phys. Rev. B 87, 161107(R) (2013).
H. Wei, S.-Po Chao, and V. Aji, Phys. Rev. Lett. 109, 196403 (2012).
https://doi.org/10.1103/PhysRevLett.109.196403
K.-Y. Yang, Y.-M. Lu, and Y. Ran, Phys. Rev. B 84, 075129 (2011).
https://doi.org/10.1103/PhysRevB.84.075129
H.B. Nielsen and M. Ninomiya, Phys. Lett. B 130, 389 (1983).
https://doi.org/10.1016/0370-2693(83)91529-0
E.V. Gorbar, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. C 80, 032801(R) (2009).
E.V. Gorbar, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. D 83, 085003 (2011).
https://doi.org/10.1103/PhysRevD.83.085003
A.A. Zyuzin and A.A. Burkov, Phys. Rev. B 86, 115133 (2012).
https://doi.org/10.1103/PhysRevB.86.115133
J.M. Cornwall, R. Jackiw, and E. Tomboulis, Phys. Rev. D 10, 8, 2428 (1974).
https://doi.org/10.1103/PhysRevD.10.2428
A.I. Larkin and Y.N. Ovchinnikov, Sov. Phys. JETP 20, 762 (1965).
P. Fulde and R.A. Ferrell, Phys. Rev. 135, A550 (1964).
https://doi.org/10.1103/PhysRev.135.A550
K. Malik, D. Das, D. Mondal, D. Chattopadhyay, A.K. Deb, S. Bandyopadhyay, A. Banerjee, J. of Applied Physics 112, 083706 (2012).
https://doi.org/10.1063/1.4759137
J. Ziman, Principles of the Theory of Solids (Cambridge Univ. Press, Cambridge, 1972).
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