Correlation-driven Lifshitz transition in electron-doped iron selenides (Li,Fe)OHFeSe

Effects of electronic correlation and spin-orbit coupling (SOC) on electronic structure of iron selenides (${\mathrm{Li}}_{1-x}{\mathrm{Fe}}_x$)OHFeSe have been investigated with the combination of density functional theory (DFT) and dynamical mean-field theory. It is found that the electronic correlation substantially changes the Fermi surface topology for $x=0.2$, resulting in a tiny electron pocket around the zone center $\mathrm{\Gamma }$ and two large electron pockets around the zone corner $M$, respectively. Moreover, the SOC also considerably affects the low-energy electronic structure near the Fermi level, especially inducing a gap in the Dirac-like dispersion around $\mathrm{\Gamma }$ for $x=0.2$. Our calculations show a correlation-driven Lifshitz transition from FeSe to the heavily electron-doped compound, leading to a transition of the nesting wave vector from ($\pi$, 0) to ($\pi$, $0.5\pi \pm \delta$) accompanied by an orbital-weight redistribution between the $d_{xy}$ and $d_{xz}/d_{yz}$ orbitals. These correlation-driven electronic structures enrich the understanding of different DFT and experimental results, suggesting a quite distinct superconducting state of (${\mathrm{Li}}_{0.8}{\mathrm{Fe}}_{0.2}$)OHFeSe in comparison with FeSe.

Figure 1

Crystal structure of (${\mathrm{Li}}_{1-x}{\mathrm{Fe}}_x$)OHFeSe at $x=0$, drawn by vesta software [37].

Figure 2

Band structures of (${\mathrm{Li}}_{1-x}{\mathrm{Fe}}_x$)OHFeSe without (blue solid line) and with (red dash line) SOC within DFT. The Fermi levels at $x=0$ and $x=0.2$ are presented, respectively.

Figure 3

(a) Total and (b) Fe $3d$ orbital-resolved density of states of (Li,Fe)OHFeSe without SOC within $\mathrm{DFT}+\mathrm{DMFT}$. The vertical dashed and solid lines denote the Fermi level at $x=0$ and 0.2, respectively.

Figure 4

Momentum-resolved spectral function of (${\mathrm{Li}}_{1-x}{\mathrm{Fe}}_x$)OHFeSe without SOC within $\mathrm{DFT}+\mathrm{DMFT}$. The two horizontal lines correspond to $x=0$ and 0.2, respectively.

Figure 5

Orbital-resolved spectral function of (${\mathrm{Li}}_{1-x}{\mathrm{Fe}}_x$)OHFeSe without SOC within $\mathrm{DFT}+\mathrm{DMFT}$. The $d_{xy}$ (red), $d_{xz}/d_{yz}$ (green), $d_{x^2-y^2}$ and $d_{3z^2-r^2}$ (blue) orbital characters are highlighted in colors. The two horizontal lines correspond to $x=0$ and 0.2, respectively.

Figure 6

Momentum-resolved spectral function of (${\mathrm{Li}}_{1-x}{\mathrm{Fe}}_x$)OHFeSe with SOC within $\mathrm{DFT}+\mathrm{DMFT}$. The two horizontal lines correspond to $x=0$ and 0.2, respectively.

Figure 7

Three-dimensional Fermi surface of (${\mathrm{Li}}_{1-x}{\mathrm{Fe}}_x$)OHFeSe within DFT [panels (a) and (d)], $\mathrm{DFT}+\mathrm{DMFT}$ [panels (b) and (e)], and DFT+DMFT+SOC [panels (c) and (f)] at $x=0$ (LiOHFeSe) and $x=0.2$ [(${\mathrm{Li}}_{0.8}{\mathrm{Fe}}_{0.2}$)OHFeSe], respectively.

Figure 8

Two-dimensional cut of the Fermi surface and the corresponding ${\chi }_0\left(q\right)$ of (${\mathrm{Li}}_{1-x}{\mathrm{Fe}}_x$)OHFeSe within DFT [panels (a) and (d)], $\mathrm{DFT}+\mathrm{DMFT}$ [panels (b) and (e)], and $\mathrm{DFT}+\mathrm{DMFT}+\mathrm{SOC}$ [panels (c) and (f)] at $x=0$ (LiOHFeSe), respectively. The symbols $e$ and $h$ represent the electron and hole pockets, respectively.

Figure 9

Two-dimensional cut of the Fermi surface and the corresponding ${\chi }_0\left(q\right)$ of (${\mathrm{Li}}_{1-x}{\mathrm{Fe}}_x$)OHFeSe within DFT [panels (a) and (d)], $\mathrm{DFT}+\mathrm{DMFT}$ [panels (b) and (e)], and $\mathrm{DFT}+\mathrm{DMFT}+\mathrm{SOC}$ [panels (c) and (f)] at $x=0.2$ [(${\mathrm{Li}}_{0.8}{\mathrm{Fe}}_{0.2}$)OHFeSe], respectively. The symbols $e$ and $h$ represent the electron and hole pockets, respectively.

Figure 10

Real part of in-plane (a) and out-plane (b) optical conductivities of (Li,Fe)OHFeSe obtained by both DFT and $\mathrm{DFT}+\mathrm{DMFT}$ methods. Insets: Magnified views of the optical conductivity at low frequencies.