Identifying topological excitonic insulators via bulk-edge correspondence

Abstract

Excitonic insulator remains elusive and there has been a lack of reliable identification methods. In this work, we demonstrate the promise of topological excitonic insulators for identification due to their unique bulk-edge correspondence, as illustrated by the LiFe$X$ ($X$ = S, Se, and Te) family. First-principles Bethe-Salpeter equation calculations reveal excitonic instabilities in these spin-orbit coupling quantum anomalous Hall insulators. Effective Hamiltonian analyses indicate that spontaneous exciton condensation does not disrupt the gapless edge state but reconstructs the bulk-gap to be almost independent of the spin-orbit coupling strength. This change in the bulk-edge correspondence can be experimentally inspected by angle-resolved photoelectron spectroscopy or electron compressibility measurements, providing observational evidence for the identification of topological excitonic insulators. Moreover, exciton condensation raises the critical temperature of the topological nontrivial phase above room temperature.

Figures (4)

• Figure 1: (a) Top and side views of the monolayer LiFe$X$ structure, which contains an out-of-plane Li-$X$-Fe-$X$-Li quintuple layer and an in-plane tetragonal lattice. The unit cell (black dashed rectangle) has two sets of Li, $X$ and Fe atoms. The $M_x$ and $M_y$ lines represent the two mirror symmetries. (b) Spin-resolved band structure of LiFeSe without considering the SOC, as well as the orbital-projection of the linear Dirac-cone. Red and blue lines denote spin-majority and spin-minority, respectively. (c) Three-dimensional Dirac-cone band structure of LiFeSe in the entire Brillouin zone with the SOC included. In (b) and (c), the Fermi levels are set to zero.
• Figure 2: (a) Exciton formation energy spectra of LiFeS, LiFeSe and LiFeTe obtained from solving the BSE. Each horizontal line represents an exciton state, and the one with the lowest energy is labeled as the $X_1$-exciton. An excitonic instability occurs if the $X_1$-exciton has a negative energy. All shown here are zero-momentum excitons, since our exciton dispersion calculations indicate that the ground-state exciton has q = 0 (see Fig. S3SI). (b) Wavefunction modulus of the $X_1$-exciton in the reciprocal space for LiFeSe. (c) Plots of decomposed charge density for electrons and holes that make up the $X_1$-excitons in LiFeSe with an isosurface of 0.1 e/$\rm {\AA}^3$. (d) Wavefunction modulus of the $X_1$-exciton in the real space for LiFeSe, with the hole fixed at the center (black dot). In (b) and (d), the maximum modulus has been renormalized to unity.
• Figure 3: (a) Band structures derived from $H$($\vec{k}$) under different scenarios, namely, $H_0$ (black lines), $H_0$$+$$H_{\rm {soc}}$ (blue dots), and $H_0$$+$$H_{\rm {soc}}$$+$$H_{\rm {eh}}$ (red dashes). See the Supplementary MaterialSI for more details. (b) Edge modes obtained from $H_0$$+$$H_{\rm {soc}}$$+$$H_{\rm {eh}}$, where there are two gapless edge states (bright yellow lines) connecting the conduction and valence bands. The Fermi levels are set to zero.
• Figure 4: (a) Bulk-gaps of the LiFe$X$ as a function of SOC strength in the SOC and excitonic QAH phases, respectively. The SOC bulk-gaps are obtained by first-principles (Blue balls), while the excitonic ones (Red diamonds) are obtained by self-consistently solving for $E(\vec{k})$ in Eqs. (3). Dependence curves are established by linearly interpolating the first-principles results of LiFeS, LiFeSe, and LiFeTe in order to simulate the effect of possible $S$-group atom alloyingXuSY. See the Supplemental MaterialsSI for more details. The blue and orange regions indicate that the system ground-state is in the SOC and excitonic QAH phase, respectively. Comparison between the band spectra of (b) LiFeS and (c) LiFeSe in the SOC (black solid) and excitonic (red dotted) QAH phases. The black dashed vertical line distinguishes the left and right excitonic QAH regions, in which the exciton reformulated band spectra have a Mexican-hat and a flattened shape, respectively. (d) Band-edge spectrum of LiFeTe in the SOC QAH phase.