Heavy carrier effective masses in van der Waals semiconductor Sn(SeS) revealed by high magnetic fields up to 150 T

The ${\mathrm{SnSe}}_{2(1-x)}{\mathrm{S}}_{2x}$ alloy is a van der Waals semiconductor with versatile, tunable electronic properties and prospects for future applications ranging from electronics to thermoelectrics and superconductivity. Its band structure and carrier effective masses underlie the quantum behavior of charge carriers and hold great promise in future technologies. However, experimental measurement of these properties remains a challenging task. Here magnetotransmission spectroscopy of ${\mathrm{SnSe}}_{2(1-x)}{\mathrm{S}}_{2x}$ thin films at pulsed magnetic fields $B$ of up to 150 T reveals a large electron-hole reduced cyclotron mass ${\mu }^{*}>$ 0.454 $m_e$ ($m_e$ is the free electron mass). This finding is supported by first-principle calculations of the band structure and by semiclassical Boltzmann transport theory, which predict a pronounced anisotropy of the carrier effective masses and electrical conductivity over two orthogonal directions (namely in the layer plane and out-of-plane) with a different anisotropy for electrons and holes. These properties are unique and important features of this class of compounds and are critical for understanding and using the tunable band structure of ${\mathrm{SnSe}}_{2(1-x)}{\mathrm{S}}_{2x}$ in fundamental and applied research.

Figure 1

(a) Optical images of CVT-grown ${\mathrm{SnSe}}_{2(1-x)}{\mathrm{S}}_{2x}$. (b) Crystal structure for ${\mathrm{MX}}_2$ (M = Sn and X = Se, S) and the orientation of magnetic field B relative to the $a$, $b$, and $c$ axis in the Faraday configuration. The red dashed line shows the semiclassical cyclotron motion of the electron in the $ab$ plane. (c) Photos of single turn coil setup before and after the magnetotransmission measurements. (d) Schematic view of a specially designed liquid-He flow-type cryostat for magnetotransmission measurements.

Figure 2

Normalized transmission spectra measured at $T=293\mathrm{K}$ and 77 K for thin films of ${\mathrm{SnSe}}_2$, ${\mathrm{SnSe}}_{2(1-x)}{\mathrm{S}}_{2x}$ (nominal composition $x=0.5$), and ${\mathrm{SnS}}_2$. The absorption edge energies of the three samples at $T=77\mathrm{K}$ are marked with arrows. Dashed lines are guide to the eye.

Figure 3

[(a) and (d)] Time dependence of the magnetic field $B$ pulse with values sweeping from $B=0\mathrm{T}$ to $B=150\mathrm{T}$. [(b) and (e)] Streak camera image of the optical transmission of ${\mathrm{SnS}}_2$ and ${\mathrm{SnSe}}_{2(1-x)}{\mathrm{S}}_{2x}$ (nominal composition $x=0.5$) at 10 K with magnetic field of up to $B$ = 150 T. Color markers indicate the cross-section positions in the streak camera image at $B$ = 0 T, 50 T, 100 T, and 150 T. [(c) and (f)] Normalized transmission spectra at indicated magnetic field ($T=10\mathrm{K}$).

Figure 4

(a) Schematics of two-dimensional (top) and three-dimensional (bottom) Brillouin zones. [(b) and (c)] The calculated band structure of ${\mathrm{SnS}}_2$ and ${\mathrm{SnSe}}_2$. The valence band maximum (VBM) is set to zero energy. The red dots indicate the conduction band (CB) and VB edges. (d) Three-dimensional band energy isosurfaces and cross sections containing the band-edge $k$ points of ${\mathrm{SnS}}_2$ highlighting several hole and electron pockets. The band energy isosurfaces correspond to an energy of 0.69 eV below the VBM and 0.55 eV above the CB minimum (CBM). D is the $k$ point of the CBM and B-C-D plane is parallel to the $\mathrm{\Gamma }$-K-M plane: B (0.00, 0.00, 0.33), C ($-0.33$, 0.67, 0.33), and D (0.00, 0.50, 0.33). The color bar corresponds to the group velocity $v_g$ from low (blue) to high (red) values.

Figure 5

Calculated values of the ratio between the components of the conductivity tensor, ${\sigma }_{xx}$, ${\sigma }_{yy}$, and ${\sigma }_{zz}$, and the relaxation time $\tau$ versus the carrier concentration $n$ (or $p$) for (a) ${\mathrm{SnS}}_2$ and (b) ${\mathrm{SnSe}}_2$ at 300 K. Solid and dashed lines refer to $p$-type and $n$-type transport, respectively.