Orbital-Selective Mott Transition Effects and Nontrivial Topology of Iron Chalcogenide

The iron-based superconductor ${\mathrm{FeSe}}_{1-x}{\mathrm{Te}}_x$ has recently gained significant attention as a host of two distinct physical phenomena: (i) Majorana zero modes that can serve as potential topologically protected qubits, and (ii) a realization of the orbital-selective Mott transition. In this Letter, we connect these two phenomena and provide new insights into the interplay between strong electronic correlations and nontrivial topology in ${\mathrm{FeSe}}_{1-x}{\mathrm{Te}}_x$. Using linearized quasiparticle self-consistent $GW$ plus dynamical mean-field theory, we show that the topologically protected Dirac surface state has substantial $\mathrm{Fe}(d_{xy})$ character. The proximity to the orbital-selective Mott transition plays a dual role: it facilitates the appearance of the topological surface state by bringing the Dirac cone close to the chemical potential but destroys the $Z_2$ topological superconductivity when the system is too close to the orbital-selective Mott phase. We derive a reduced effective Hamiltonian that describes the topological band. Its parameters capture all the chemical trends found in the first principles calculation. Our findings provide a framework for further study of the interplay between strong electronic correlations and nontrivial topology in other iron-based superconductors.

Figure 1

Structural inversion symmetry, and the band inversion in experiments [8, 44, 45] and the present theory. (a),(b) The present structural model for FST and the atomic coordinate in the unit cell. The Cn indicates a chalcogen atom, and the inversion center is [0,0,0]. (c) Experimental quasiparticle dispersions in the $\mathrm{\Gamma }-Z$ $k$ point line, adapted from P. D. Johnson et al. (ARPES1 from Ref. [44]), H. Lohani et al. (ARPES2 from Ref. [45]), and Z. Wang et al. (ARPES3 from Ref. [8]). (d) Theoretical quasiparticle dispersions in the $\mathrm{\Gamma }-Z$ $k$ point line in the present $\mathrm{LQS}GW+\mathrm{DMFT}+\mathrm{SOC}$ framework. Parity eigenvalues for each band are denoted in (d), as ${\alpha }^{\prime }$ ($+$), $\alpha$ ($+$), $\beta$ ($+$), and $x{y}^{-}$ ($-$). The band has the $z^2$ orbital character is also denoted in (c) and (d).

Figure 2

Theoretical (001) surface state electronic structure in the $\mathrm{LQS}GW+\mathrm{DMFT}+\mathrm{SOC}$ near $\overline{\mathrm{\Gamma }}$, compared with the experimental surface electronic structure in the ARPES of Ref. [14]. The black horizontal dashed line is the original chemical potential in the present theory. The purple horizontal dashed line is the chemical potential for the electron doping of 0.035 (electrons/formula unit), $+6\mathrm{meV}$ in the present theory.

Figure 3

OSMT effects on the electronic structure of FST. (a) Band structure of FST in the $\mathrm{LQS}GW+\mathrm{DMFT}$ framework. (b) Band structure of FST in the OSMP by forcing $Z_{xy}$ to zero from the $\mathrm{LQS}GW+\mathrm{DMFT}$ result. (c) and (d) are the same as (a) and (b) in a wide energy window, respectively. The size of green, red, blue, and orange circles present $\mathrm{Fe}(d_{xz/yz})$, $\mathrm{Fe}(d_{xy})$, $\mathrm{Se}(p_z)$, and $\mathrm{Fe}(s)$ orbital contributions, respectively. For (a) and (b), the size of blue circles for the $\mathrm{Se}(p_z)$ orbital is multiplied by the factor of 1.6. The parity for $\alpha$, ${\alpha }^{\prime }$, $\beta$, and $x{y}^{-}$ bands are denoted in (a) and (b). The characterization of $p_z^{-}$ majority and $p_z^{+}$ majority bands are denoted for (c) and (d) [see Eq. (2)].

Figure 4

The $Z_{\mathrm{Se}}$ dependent phase diagram of the band inversion condition for the nontrivial $Z_2$ bulk topology and the energy position of the Dirac surface band. (a) The $Z_{\mathrm{Se}}$ dependent variation of (i) the $\alpha /{\alpha }^{\prime }$ bands top and bottom energy positions [${\epsilon }_{\alpha /{\alpha }^{\prime }}(\mathrm{Z})$ and ${\epsilon }_{\alpha /{\alpha }^{\prime }}(\mathrm{\Gamma })$], and (ii) the $x{y}^{-}$ band top and bottom energy positions [${\epsilon }_{x{y}^{-}}(\mathrm{\Gamma })$ and ${\epsilon }_{x{y}^{-}}(\mathrm{Z})$]. The $\alpha /{\alpha }^{\prime }$ bands degenerate along the $\mathrm{\Gamma }-Z$ momentum path in computations without SOC. Linear lines are for the interpolating from the given data (dots) in the LDA. [$Z_{\mathrm{Se},\min }$, $Z_{\mathrm{Se},\max }$] indicate the range of the $Z_{\mathrm{Se}}$ for the band inversion. (b) Same as (a) in the $\mathrm{LQS}GW$. (c) Same as (a) in the $\mathrm{LQS}GW+\mathrm{DMFT}$. (d) A schematic diagram for the band inversion condition and the energy position (${\omega }_{\text{Dirac}}$) for the Dirac surface band.