Pressure induced Lifshitz transition in ThFeAsN

In this paper, we present pressure dependent structural parameters and electronic structure of the ThFeAsN superconductor. There are no anomalies in the structural parameters as well as elastic constants with hydrostatic pressure which is consistent with the experiments. We study the electronic structure of this compound at different external pressures in terms of density of states, band structure, and Fermi surface. Density of states at the Fermi level, coming from $\mathrm{Fe}\text{−}d$ orbitals, follows the same trend as that of the superconducting transition temperature $\left(T_c\right)$ as a function of hydrostatic pressure. We also observe a pressure induced orbital selective Lifshitz transition in ThFeAsN compound which is quite different from the Lifshitz transitions observed in the other families of Fe-based superconductors. Fermi surfaces of ThFeAsN especially holelike Fermi surfaces at the $\mathrm{\Gamma }$ point are altered significantly with pressure. This modification of Fermi surface topology with pressure seems to play a major role in the reduction of $T_c$ with pressure in ThFeAsN superconductor. Spin-orbit coupling does not affect the Lifshitz transition but it modifies the energy ordering of bands near the $\mathrm{\Gamma }$ point at higher pressure.

Figure 1

(a) Crystal structure and (b) Brillouin zone of tetragonal ThFeAsN.

Figure 2

Pressure dependencies of lattice parameters (a) $a$, (b) $c$, (c) volume of unit cell, (d) anion height (distance of As atom from Fe plane) and As-Fe-As bond angle $\alpha$.

Figure 3

(a) Fe-Fe bond length, (b) Fe-As bond length, (c) in-plane and out of plane As-As bond length, (d) Th-As bond length of ThFeAsN as a function of hydrostatic pressure.

Figure 4

Pressure variation of elastic constants of tetragonal ThFeAsN.

Figure 5

Calculated total density of states of tetragonal ThFeAsN at (a) ambient, (b) 4 GPa, (c) 10 GPa, (d) 15 GPa, (e) 20 GPa, and (f) 25 GPa pressure. Fermi level is denoted by a vertical line at $E=0$ eV.

Figure 6

Calculated atom projected density of states of tetragonal ThFeAsN at (a) ambient, (b) 4 GPa, (c) 10 GPa, (d) 15 GPa, (e) 20 GPa, and (f) 25 GPa pressure.

Figure 7

Fe-$d$ orbital-projected density of states at the Fermi level (blue circle) and experimentally measured superconducting $T_c$ [48] (red square) as a function of pressure.

Figure 8

Calculated orbital-projected density of states of tetragonal ThFeAsN at (a)–(d) ambient, (e)–(h) 15 GPa, and (i)–(l) 25 GPa pressure. $d_{xy}$, $d_{yz+xz}$, $d_{z^2}$, and $d_{x^2-y^2}$ orbitals are indicated by red, blue, magenta, and brown colors, respectively.

Figure 9

Calculated band structure of tetragonal ThFeAsN along high symmetry $k$ points at (a) ambient, (b) 4 GPa, (c) 10 GPa, (d) 15 GPa, (e) 20 GPa, and (f) 25 GPa pressure.

Figure 10

Calculated Fe-$d$ orbital-projected low energy band structure of ThFeAsN near the $\mathrm{\Gamma }$ point for (a) ambient, (b) 10 GPa, (c) 20 GPa, and (d) 30 GPa pressure. $d_{yz+xz}$, $d_{z^2}$, $d_{x^2-y^2}$ orbitals are indicated by blue, magenta, and brown colors, respectively. Here the line thickness denotes the weight of the Fe-$d$ orbitals.

Figure 11

Calculated Fe-$d$ orbital-projected low energy band structure of ThFeAsN near the $M$ point for (a) ambient, (b) 10 GPa, (c) 20 GPa, and (d) 30 GPa pressure. $d_{yz+xz}$, $d_{z^2}$, $d_{x^2-y^2}$ orbitals are indicated by blue, magenta, and brown colors, respectively. Here the line thickness denotes the weight of the Fe-$d$ orbitals.

Figure 12

Variation of different band energies of ThFeAsN around the $\mathrm{\Gamma }$ point with pressure.

Figure 13

Calculated Fermi surfaces of tetragonal ThFeAsN at (a) ambient, (b) 5 GPa, (c) 10 GPa, (d) 15 GPa, (e) 20 GPa, and (f) 25 GPa pressure.

Figure 14

Evolution of all the electron- and holelike Fermi surfaces at (a) ambient, (b) 10 GPa, (c) 20 GPa, and (d) 25 GPa pressure.

Figure 15

Calculated band structure of tetragonal ThFeAsN with spin-orbit coupling at (a) ambient pressure and (b) 25 GPa of hydrostatic pressure.

Figure 16

Calculated Fe-$d$ orbital-projected low energy band structure of ThFeAsN at the $\mathrm{\Gamma }$ point with spin-orbit coupling for (a) ambient and (b) 25 GPa pressure. $d_{yz+xz}$ (${\alpha }_1,{\alpha }_2$), $d_{z^2}$ ($\beta$), $d_{x^2-y^2}$ ($\gamma$) orbitals are indicated by blue, magenta, and brown colors, respectively.

Figure 17

Calculated DOS of ThFeAsN at ambient pressure within the $\mathrm{GGA}+U$ formalism with Hubbard $U=0$ eV (a), $U=1$ eV (b), 1.5 eV (c), and 2 eV (d) on $\mathrm{Fe}\text{−}3d$ orbitals.

Figure 18

Calculated band structures of ThFeAsN employing experimental structural parameters (lattice parameters as well as ${\mathrm{z}}_{\text{As}}$) at (a) ambient pressure and (b) 25 GPa of hydrostatic pressure.

Figure 19

Calculated Fe-$d$ orbital-projected band structures of ThFeAsN around the $\mathrm{\Gamma }$ point, using experimental structural parameters (lattice parameters as well as ${\mathrm{z}}_{\text{As}}$) at (a) ambient pressure and (b) 25 GPa of hydrostatic pressure.

Figure 20

Evolution of Fermi surfaces of ThFeAsN, calculated using experimental structural parameters (lattice parameters as well as ${\mathrm{z}}_{\text{As}}$) at (a) ambient pressure and (b) 25 GPa of hydrostatic pressure.