Exciton Condensation in Landau Levels of Quantum Spin Hall Insulators (2403.04691v2)
Abstract: We theoretically study the quantum spin Hall insulator (QSHI) in a perpendicular magnetic field. In the noninteracting case, the QSHI with space inversion and/or uniaxial spin rotation symmetry undergoes a topological transition into a normal insulator phase at a critical magnetic field $B_{\rm c}$. The exciton condensation in the lowest Landau levels is triggered by Coulomb interactions in the vicinity of $B_{\rm c}$ at low temperature and spontaneously breaks the inversion and the spin rotation symmetries. We propose that the electron spin resonance spectroscopy with the ac magnetic field also aligned in the perpendicular direction can directly probe the exciton condensation order. Our results should apply to QSHIs such as the InAs/GaSb quantum wells and monolayer transition metal dichalcogenides.
- M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
- X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
- C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
- B. A. Bernevig and S.-C. Zhang, Phys. Rev. Lett. 96, 106802 (2006).
- C. Xu and J. E. Moore, Phys. Rev. B 73, 045322 (2006).
- L. V. Keldysh and Y. V. Kopaev, Sov. Physics1 Solid State 6, 2219 (1965).
- J. P. Eisenstein and A. H. MacDonald, Nature 432, 691 (2004).
- J. Eisenstein, Annu. Rev. Condens. Matter Phys. 5, 159 (2014).
- Y. Naveh and B. Laikhtman, Phys. Rev. Lett. 77, 900 (1996).
- D. I. Pikulin and T. Hyart, Phys. Rev. Lett. 112, 176403 (2014).
- F. Xue and A. H. Macdonald, Phys. Rev. Lett. 120, 186802 (2018).
- A. Blason and M. Fabrizio, Phys. Rev. B 102, 035146 (2020).
- To be precise, neither the spin nor the total angular momentum is conserved in the semiconductor QWs due to the spin-orbit coupling and the lattice anisotropy Bernevig et al. (2006), and the index α=±𝛼plus-or-minus\alpha=\pmitalic_α = ± is only a label of the Kramers doublet in each band. Nonetheless, we use the term “spin” for convenience.
- C. Liu and S. Zhang, in Topological Insulators, edited by M. Franz and L. Molenkamp (Elsevier, Oxford, 2013).
- See the Supplemental Materials for details.
- M. Oshikawa and I. Affleck, Phys. Rev. B 65, 134410 (2002).