Three-dimensional superconductivity induced by an extremely small amount of Li in ${\mathrm{Li}}_{x}{\mathrm{SnSe}}_{2}$ (2024)

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  Figure 1

  (a), (b) Crystal structure of ${\mathrm{SnSe}}_2$ and ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$ (a 5 × 5 × 5 supercell). (c), (d) Single-crystal diffraction patterns of ${\mathrm{SnSe}}_2$, (d) ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$ (c). (e), (f) Zoomed-in (004) peak for the intercalated (e) and unintercalated (f) cases.

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  Figure 2

  (a) Temperature dependence of the in-plane (${\rho }_{ab}$) and out-of-plane (${\rho }_c$) electrical resistivity of ${\mathrm{SnSe}}_2$. The red dashed line is the fit of metallic ${\rho }_{ab}$ to the Bloch-Grüneisen formula. Inset: ${\rho }_{ab}$($T$) plotted as ln(${\rho }_{ab}$) versus 1/$T$, showing the linear relationship. (b) Temperature dependence of the in-plane (${\rho }_{ab}$) and out of plane (${\rho }_c$) electrical resistivity of ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$. (c) Temperature dependence of the normal-state ${\rho }_{ab}$ for ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$ plotted as ${\rho }_{ab}$ versus $T^2$ below 33 K. (d) Temperature dependence of ${\rho }_{ab}$ and ${\rho }_c$ of ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$ between 1.8 and 10 K. (e) Temperature dependence of the magnetic susceptibility for ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$ (black squares) and ${\mathrm{SnSe}}_2$ (red squares) taken by applying $H$ = 1 T along the $c$ direction. (f) Temperature dependence of the magnetic susceptibility for ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$ between 1.8 and 10 K at $H$ = 10 Oe under both zero field cooling (ZFC) and field cooling (FC) modes.

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  Figure 3

  (a) Temperature dependence of the in-plane electrical resistivity measured under indicated applied magnetic fields ($H\left|\right|c$) for ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$. (b) Temperature dependence of the upper critical field (${\mu }_0{H}_{c2}^c$) corresponding to 90% ${\rho }_{ab}$ (blue squares), 50% ${\rho }_{ab}$ (green squares), and 10% ${\rho }_{ab}$ (black squares) for ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$. The dashed red line is the fit of data to the empirical formula (see text); dashed green and blue lines are guide to eyes. (c) Field dependence of the in-plane magnetization at indicated temperatures for ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$. (d) Upper critical field (${\mu }_0{H}_{c2}^{ab}$) and lower critical field (${\mu }_0{H}_{c1}^{ab}$) versus temperature for ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$. The dashed red lines are the fit of data to the empirical formula (see text).

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  Figure 4

  (a), (b) Magnetic field dependence of the Hall resistivity (${\rho }_{xy}$) measured between 1.8 and 300 K for ${\mathrm{SnSe}}_2$ (a) and ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$ (b). (c) Temperature dependence of the Hall coefficient ($R_H$) for ${\mathrm{SnSe}}_2$ (black squares) and ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$ (red squares). (d) Temperature dependence of the carrier concentration for ${\mathrm{SnSe}}_2$ (black squares) and ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$ (red squares).

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  Figure 5

  (a) Low-temperature specific heat (C) plotted as $C$/$T$ versus $T^2$ for as-grown ${\mathrm{SnSe}}_2$ (black filled circles) and intercalated ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$ (blue circles). The brown solid line is the linear fit of $C$/$T$($T^2$) for ${\mathrm{SnSe}}_2$ below 6 K. The red and green lines represent linear fit of $C$/$T$($T^2$) for ${\mathrm{Li}}_x{\mathrm{SnSe}}_2$ below and above $T_c$, respectively. (b) Field dependence of ${\rho }_{ab}$ under different field directions (θ = 0°, 30°, 60°, and 90°) at $T$ = 20 mK. (c) Electronic structure of the 3 × 3 × 3 supercell (1.2% Li concentration). (d) Brillouin zone. (e) Calculated density of states (DOS) versus energy for different Li concentrations, i.e., one Li atom in 2 × 2 × 2 (222), 3 × 3 × 3 (333), and 4 × 4 × 4 (444) supercells, respectively. (f) Calculated $c$-axis lattice parameter and DOS($E_F$) versus Li concentration. Crosses represent data from experiment.

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