Light-Induced Type-II Band Inversion and Quantum Anomalous Hall State in Monolayer FeSe

Coupling a quantum anomalous Hall (QAH) state with a superconducting state offers an attractive approach to detect the signature alluding to a topological superconducting state [Q. L. He et al., Science 357, 294 (2017)], but its explanation could be clouded by disorder effects in magnetic doped QAH materials. On the other hand, an antiferromagnetic (AFM) quantum spin Hall (QSH) state is identified in the well-known high-temperature 2D superconductor of monolayer FeSe [Z. F. Wang et al., Nat. Mater. 15, 968 (2016)]. Here, we report a light-induced type-II band inversion (BI) and a QSH-to-QAH phase transition in the monolayer FeSe. Depending on the handedness of light, a spin-tunable QAH state with a high Chern number of $\pm 2$ is realized. In contrast to the conventional type-I BI resulting from intrinsic spin-orbital coupling (SOC), which inverts the band an odd number of times and respects time reversal symmetry, the type-II BI results from a light-induced handedness-dependent effective SOC, which inverts the band an even number of times and does not respect time reversal symmetry. The interplay between these two SOC terms makes the spin-up and -down bands of an AFM QSH state respond oppositely to a circularly polarized light, leading to the type-II BI and an exotic topological phase transition. Our finding affords an exciting opportunity to detect Majorana fermions in one single material without magnetic doping.

Figure 1

(a) Type-I BI for a NI-to-QSH phase transition with increasing intrinsic SOC. (b) Type-II BI for a QSH-to-QAH phase transition with increasing light-induced ESOC. The red and blue colors denote spin-up (up arrow) and spin-down (down arrow) bands, respectively. The corresponding Chern numbers for the spin-up and spin-down bands are labeled before and after BI.

Figure 2

(a)–(e) Band structure evolution of FeSe under the irradiation of left-handed circularly polarized light with a light intensity $eA/\hslash$ of 0, 0.1, 0.2, 0.24, and $0.3{\AA }^{-1}$, respectively. The red and blue colors in (b)–(e) denote the up and down spin-$z$ component, respectively. (f) The band gap evolution under the light irradiation. The inset is the enlarged band gap around the $M$ point in (e) and the definition of $E_g^1$ and $E_g^2$. In our calculations, the light energy $\hslash \omega$ is set to 8 eV, which is chosen to be larger than the band width of FeSe, so that the Floquet bands do not cross each other.

Figure 3

(a)–(c),(e)–(g) Projected band structure of a FeSe ribbon with a ferromagnetic edge under the irradiation of left-handed circularly polarized light before and after BI with a light intensity $eA/\hslash$ of 0.2 and $0.3{\AA }^{-1}$, respectively. (a),(e) Spin-$z$ component projection. (b),(f) Left edge projection. (c),(g) Right edge projection. The red and blue colors denote the up and down spin-$z$ component, respectively. The circle size denotes the weighting factor of the edge states. (d),(f) Schematic plot of the topological edge states for the QSH and QAH state shown in (a)–(c) and (e)–(g), respectively.

Figure 4

(a),(b) Spin Hall and Hall conductivity under the irradiation of left-handed circularly polarized light before and after BI with a light intensity $eA/\hslash$ of 0.2 and $0.3{\AA }^{-1}$, respectively. (c) and (d) are the same as (a) and (b), respectively, but under the irradiation of right-handed circularly polarized light. The insets show the handedness of the light, and the Chern number for the spin-up and -down band.