Pressure-induced topological and structural phase transitions in natural van der Waals heterostructures from the ${\left(\mathrm{SnTe}\right)}_m{\left({\mathrm{Bi}}_2{\mathrm{Te}}_3\right)}_n$ homologous family: Raman spectroscopy, x-ray diffraction, and density functional theory

A new class of van der Waals heterostructures of ${\left(\mathrm{SnTe}\right)}_{\mathrm{m}}{\left({\mathrm{Bi}}_2{\mathrm{Te}}_3\right)}_{\mathrm{n}}$ (with $m=1,2,..$ and $n=1,2,..$), consisting of a topological crystalline insulator SnTe and a topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ are emerging with exciting properties and applications, such as in thermoelectrics. Our study examines the stability of these heterostructures ($m$ = 1 and $n$ = 1,2) under pressure using Raman scattering, synchrotron x-ray diffraction, and density functional theory. Raman studies as a function of pressure carried out at room temperature reveal a phase transition in the pressure regime of 3–5 GPa for both the compounds, which is shown to be associated with an electronic topological transition involving change in the ${\mathrm{Z}}_2$ topological invariant. In addition to the electronic changes, our Raman experiments indicate that rhombohedral ($R\overline{3}m$) ${\mathrm{SnBi}}_2{\mathrm{Te}}_4$ undergoes structural transition at $\sim 6.0$ to a possible monoclinic phase and another transition at $\sim 12.0$ GPa. Raman and x-ray diffraction experiments on trigonal ($P\overline{3}m1$) ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$ show two structural transitions at $\sim 9.5$ GPa to a monoclinic phase followed by one to cubic phase at $\sim 14.1$ GPa. Our analysis of electronic structure reveals that the phase transition at 9.5 GPa in ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$ is accompanied by an insulator to semimetal transition.

Figure 1

(a) Crystal structure of ${\mathrm{SnBi}}_2{\mathrm{Te}}_4$ showing the 1.13- nm-thick seven atomic layers of ${\mathrm{SnBi}}_2{\mathrm{Te}}_4$. (b) Crystal structure of ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$ showing a quintuple layer of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and a septuple layer of ${\mathrm{SnBi}}_2{\mathrm{Te}}_4$. Red, Yyellow, and blue atoms represent Sn, Bi, and Te, respectively.

Figure 2

Pressure evolution of Raman spectra of ${\mathrm{SnBi}}_2{\mathrm{Te}}_4$ in the increasing pressure run. Disappearance/appearance of new modes at different pressures are marked by arrows. Black solid lines are the experimental data. The solid red lines are Lorentzian fit to the experimental data. The blue solid lines are individual fits of the Raman modes.

Figure 3

(a) Raman shift of ${\mathrm{SnBi}}_2{\mathrm{Te}}_4$ is plotted against applied pressure for the increasing pressure run. The error bars are obtained from the fitting procedure. The solid red lines are the linear fits to the frequencies of the Raman modes in the increasing pressure run. The numbers depict the value of the slope $d\omega /d\mathrm{P}$ in ${\mathrm{cm}}^{-1}$ obtained from linear fits. The black dashed lines indicate the pressure where the transitions are taking place. (b) Pressure dependence of linewidth of the strong Raman modes of ${\mathrm{SnBi}}_2{\mathrm{Te}}_4$. The phase transition at $\sim 4.0$ GPa is marked by the anomalous evolution of the full width at half maximum (FWHM) of the mode M5. The brown dashed lines indicate the pressure where the transitions are taking place. The solid red lines are the linear fits to the linewidths of the Raman modes in the two pressure regions below and above 4 GPa.

Figure 4

Electronic structure of the low-pressure rhombohedral ($R\overline{3}m$) phase of ${\mathrm{SnBi}}_2{\mathrm{Te}}_4$ at P = 0 GPa calculated (a) without and (b) with the inclusion of effects of the spin orbit coupling at its optimized lattice parameter.

Figure 5

Electronic structure of rhombohedral ${\mathrm{SnBi}}_2{\mathrm{Te}}_4$ at (a) P = 3 GPa and (b) 4 GPa. (c) Isosurfaces of charge densities associated with VBM and CBM in the Z-F region reveal inversion at the transition pressure. (Red, yellow, and blue atoms represent Sn, Bi, and Te, respectively).

Figure 6

${\nu }_0$ topological invariant of rhombohedral ($R\overline{3}m$) ${\mathrm{SnBi}}_2{\mathrm{Te}}_4$ calculated as a function of pressure ranging from $-1$ GPa to 10 GPa. NI and TI are normal insulator and topological insulator, respectively.

Figure 7

Electronic structure of rhombohedral ($R\overline{3}m$) phase of ${\mathrm{SnBi}}_2{\mathrm{Te}}_4$ at (a) P = 5 GPa, (b) 8 GPa, (c) 10 GPa, and (d) 12 GPa calculated including the effects of spin-orbit coupling showing metallization at P $\sim 11\mathrm{GPa}$.

Figure 8

(a) The image of Debye-Scherrer diffraction rings collected on the detector at ambient 0 GPa. The small red-polygons are drawn to mask the spots due to cosmic rays. (b) x-ray diffraction pattern of of ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$ with the Rietveld refinement at 0.2 GPa.

Figure 9

(a) Pressure dependence of the lattice parameters of ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$ under compression. The figure inset shows the pressure dependence of the axial c/a ratio. (b) Pressure dependence of the experimental volume of the ambient phase. The pressure-volume data is fitted using third-order Birch-Murnaghan equation.

Figure 10

X-ray diffraction patterns of ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$ as a function of pressure. The new peaks appearing at 9.1 and 14.3 GPa are marked by star symbols. The changes in diffraction pattern at different pressures can be observed.

Figure 11

Schematic representation of different phases of ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$ as a function of pressure.

Figure 12

Pressure evolution of Raman spectra of ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$ in the increasing pressure run. Disappearance/appearance of new modes at different pressures are marked by arrows. Black solid lines are the experimental data. The solid red lines are Lorentzian fit to the experimental data. The blue solid lines are individual fits of the Raman modes.

Figure 13

Raman shift of ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$ is plotted against applied pressure for the increasing pressure run. The error bars are obtained from the fitting procedure. The solid red lines are the linear fits to the frequencies of the Raman modes in the increasing pressure run. The numbers depict the value of the slope $d\omega /d\mathrm{P}$ in ${\mathrm{cm}}^{-1}$ obtained from linear fits. The black dashed lines indicate the pressure where the transitions are taking place. (b) Pressure dependence of linewidth of the strong Raman modes of ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$. The phase transition at $\sim 4.0$ GPa is marked by the anomalous evolution of the FWHM of the mode M5. The brown dashed lines indicate the pressure where the transitions are taking place. The solid red lines are the linear fits to the linewidths of the Raman modes in the two pressure regions below and above 4 GPa.

Figure 14

Electronic structure of the low-pressure trigonal ($P\overline{3}m1$) structure of ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$ at P = 0 GPa calculated (a) without and (b) with the inclusion of effects of the spin orbit coupling at its optimised lattice parameter.

Figure 15

Electronic structure of trigonal ($P\overline{3}m1$) structure of ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$ calculated with spin-orbit coupling at (a) 1 GPa, (b) 3 GPa and (c) 5 GPa and (d) variation in VBM and CBM with pressure in $\mathrm{\Gamma }$-M region of the Brillouin zone showing the opening and closing of gap at the critical pressure $\sim 3$ GPa.

Figure 16

(a) ${\nu }_0$ topological invariant of trigonal ($P\overline{3}m1$) ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$ evaluated as a function of pressure ranging from 0 GPa to 6 GPa. NI and TI are normal insulator and topological insulator respectively. (b) Isosurface of charge densities associated with VBM and CBM in the $\mathrm{\Gamma }$-M region reveal inversion at the critical pressure P $\sim 3$ GPa. (Red, yellow, and blue atoms represent Sn, Bi, and Te, respectively).

Figure 17

(a) Electronic structure of the trigonal ($P\overline{3}m1$) structure of ${\mathrm{SnBi}}_4{\mathrm{Te}}_7$ at (a) P = 6 GPa, (b) 8 GPa, (c) 10 GPa, and (d) 12 GPa calculated with the inclusion of effects of the spin-orbit coupling showing a insulating to semimetallic transition with increasing pressure resulting from valence band maxima (VBM) and conduction band minima (CBM) crossing Fermi level at P = 10 GPa.