First-principles study of high-pressure phase stability and superconductivity of ${\mathrm{Bi}}_4{\mathrm{I}}_4$

Bismuth iodide ${\mathrm{Bi}}_4{\mathrm{I}}_4$ exhibits intricate crystal structures and topological insulating states that are highly susceptible to influence by environments, making its physical properties highly tunable by external conditions. In this work, we study the evolution of structural and electronic properties of ${\mathrm{Bi}}_4{\mathrm{I}}_4$ at high pressure using an advanced structure search method in conjunction with first-principles calculations. Our results indicate that the most stable ambient-pressure monoclinic $\alpha -{\mathrm{Bi}}_4{\mathrm{I}}_4$ phase in $C2/m$ symmetry transforms to a trigonal $P31c$ structure ($\varepsilon -{\mathrm{Bi}}_4{\mathrm{I}}_4$) at 8.4 GPa, then to a tetragonal $P4/mmm$ structure ($\zeta -{\mathrm{Bi}}_4{\mathrm{I}}_4$) above 16.6 GPa. In contrast to the semiconducting nature of ambient-pressure ${\mathrm{Bi}}_4{\mathrm{I}}_4$, the two high-pressure phases are metallic, in agreement with reported electrical measurements. The $\varepsilon -{\mathrm{Bi}}_4{\mathrm{I}}_4$ phase exhibits distinct ionic states of ${\mathrm{I}}^{\delta -}$ and (${\mathrm{Bi}}_4{\mathrm{I}}_3{)}^{\delta +}$ ($\delta =0.4123$ e), driven by a pressure-induced volume reduction. We show that both $\varepsilon$- and $\zeta -{\mathrm{Bi}}_4{\mathrm{I}}_4$ are superconductors, and the emergence of pressure-induced superconductivity might be intimately linked to the underlying structural phase transitions.

Figure 1

Energetic stability of ${\mathrm{Bi}}_4{\mathrm{I}}_4$ as a function of pressure. Different curves show pressure evolution of the enthalpy of various ${\mathrm{Bi}}_4{\mathrm{I}}_4$ phases. The enthalpy of formation of $\varepsilon -{\mathrm{Bi}}_4{\mathrm{I}}_4$ ($P31c$) is set as the base line. Previously predicted $P{4}_2/mmc$ and $P{6}_3/mmc$ phases are also included for comparison.

Figure 2

Simulated phonon spectra of the newly predicted $\varepsilon -{\mathrm{Bi}}_4{\mathrm{I}}_4$ at 10 GPa (a) and $\zeta -{\mathrm{Bi}}_4{\mathrm{I}}_4$ at 30 GPa (b).

Figure 3

Crystal structures of $\beta -{\mathrm{Bi}}_4{\mathrm{I}}_4$ (a) and $\alpha -{\mathrm{Bi}}_4{\mathrm{I}}_4$ (b) with identical space group $C2/m$ viewed from the b direction, and the crystal structure of the predicted $\varepsilon -{\mathrm{Bi}}_4{\mathrm{I}}_4$ at 10 GPa (c) together with its simplified building block (d) and the crystal structure of $\zeta -{\mathrm{Bi}}_4{\mathrm{I}}_4$ at 30 GPa (e). While $\varepsilon -{\mathrm{Bi}}_4{\mathrm{I}}_4$ is viewed from the $c$ direction, $\zeta -{\mathrm{Bi}}_4{\mathrm{I}}_4$ is viewed from the $b$ direction. Bi: large purple balls; I: small blue balls.

Figure 4

Two-dimensional ELF of $\varepsilon -{\mathrm{Bi}}_4{\mathrm{I}}_4\mathrm{at}$ 10 GPa plotted in the (001) crystalline plane (a) and the enthalpy of formation as a function of the percentage of displacement of the circled iodine atom along the $c$ direction (b).

Figure 5

The simulated synchrotron x-ray diffraction ($\lambda$ = 0.6888 Å) for the high-pressure phases of ${\mathrm{Bi}}_4{\mathrm{I}}_4$ at selected pressure points.

Figure 6

Electronic band structures of $\alpha -{\mathrm{Bi}}_4{\mathrm{I}}_4$ [(a)–(c)] and $\beta -{\mathrm{Bi}}_4{\mathrm{I}}_4$ [(d)–(f)] at 0.0 GPa, 5.0 GPa, and 8.8 GPa in the presence of SOC, respectively.

Figure 7

Electronic band structures of $\varepsilon -{\mathrm{Bi}}_4{\mathrm{I}}_4$ and $\zeta -{\mathrm{Bi}}_4{\mathrm{I}}_4$ with SOC included and using the HSE hybrid functional for (a)–(c) $\varepsilon -{\mathrm{Bi}}_4{\mathrm{I}}_4$ along the $\mathrm{\Gamma }$-A-H, M-L path and [(d) and (e)] $\zeta -{\mathrm{Bi}}_4{\mathrm{I}}_4$ in the entire BZ. The red line indicates the Fermi level.

Figure 8

The calculated phonon dispersion, partial phonon density of states, Eliashberg spectral functions ${\alpha }^{2}F$($\omega$), and integrated EPC constant $\lambda (\omega$) for (a) $\varepsilon -{\mathrm{Bi}}_4{\mathrm{I}}_4$ at 10 GPa and (b) $\zeta -{\mathrm{Bi}}_4{\mathrm{I}}_4$ at 30 GPa. The size of the red circles of the phonon spectra indicates the strength of the partial EPC constant ${\lambda }_{q\nu }$.

Figure 9

Pressure dependence of theoretically predicted $T{}_c$ for $\varepsilon -{\mathrm{Bi}}_4{\mathrm{I}}_4$ and $\zeta -{\mathrm{Bi}}_4{\mathrm{I}}_4$ compared to experimentally measured $T{}_c$.