Systematic study of superconductivity in few-layer $T_d$-MoTe$_2$

Abstract

We present a systematic investigation of superconductivity in a topological superconductor candidate $T_{\rm d}$-MoTe$_2$ in the few-layer limit. By examining multiple mechanically exfoliated samples with different thicknesses, substrates and crystal qualities, we quantitatively correlate superconducting temperature ($T_c$) with disorder, carrier density, carrier type and mobility. By integrating these experimental findings with first-principles calculations, we reveal the relationship between the band structure and superconductivity in this material. Notably, in 2 L samples we access a highly hole-doped regime that has not been systematically explored in previous experiments, providing a complementary perspective to earlier studies. In this regime, we demonstrate that superconductivity can be realized in a manner consistent with a conventional phonon-mediated $s_{(++)}$-wave pairing.

Figures (6)

• Figure 1: (a) Typical temperature ($T$) dependence of resistance ($R$) for samples with different numbers of layers. Inset: $T$-$R$ from a bulk sample for reference, where $T_c$ = 150 mK. (b) Thickness dependence of the superconducting critical temperature ($T_c$), showing a rapid increase with decreasing thickness, particularly for $t <$ 5 nm (approximately 7 L). The error bars represent the variation among samples. The horizontal dashed line indicates $T_c \sim$ 150 mK for the bulk sample with $t >$ 100 nm.
• Figure 2: (a) $T_c$ as a function of the residual resistivity ratio (RRR) for three different 2 L samples (MTS10, MTS18 and MTS4 from left to right, the same for (b) and (c)). (b) Electron ($n_e$) and hole ($n_h$) carrier density dependence of $T_c$ from different 2 L samples. (c) Electron ($\mu_e$) and hole ($\mu_h$) mobility dependence of $T_c$ from different 2 L samples.
• Figure 3: (a) Gate voltage dependence of resistance in the normal state for a 2 L sample (MTS4). The gate voltage ($V_g$) is converted to $\Delta n = C_gV_g$ with the gate capacitance $C_g$. (b) Temperature dependence of resistance for the 2 L sample, normalized by the value at 4.0 K with different $V_g$. (c) $T_c$ as a function of $\Delta n$ for different 2 L samples (Sample#1: MTS4, Sample#2: MTS18), showing the monotonic increase of $T_c$ as the Fermi level moves toward the CNP. The CNP is located in the positive side beyond the range of $x$-axis in (a) and (c) (see arrows).
• Figure 4: (a) RRR for four different 4 L samples (MTS3, MTS5, MTS9 and MTS19). (b) Electron ($n_e$) and hole ($n_h$) carrier density dependence of $T_c$ from different 4 L samples (MTS14, MTS5, MTS19 and MTS3). (c) Electron ($\mu_e$) and hole ($\mu_h$) mobility dependence of $T_c$ from different 4 L samples. (d) Gate dependence of resistance in the normal state for a 4 L sample (MTS3). (e) Temperature dependence of resistance for the 4 L sample (MTS3), normalized by the value at 1.4 K, taken at different $V_g$. (f) $T_c$ plotted as a function of $\Delta n$ for the 4 L sample (MTS3). Similarly to the 2 L case, $T_c$ monotonically increases with electron doping. The CNP is located in the negative side beyond the range of $x$-axis in (d) and (f) (see arrows).
• Figure 5: (a) and (b) Band structures for the 2 L and 4 L obtained from first-principles calculations. (c) Density of states (DOS) per formula unit for the 2 L estimated from (a). (d) Similar DOS per formula unit shown for the 4 L. The light-blue-shaded (orange-shaded) rectangles in (a) and (b) express the energy range where the Fermi level moves by modulating the gate voltage for Sample#1 (Sample#2, see Figs. 3) for the 2 L samples. The light-green-shaded rectangle in (c) and (d) is similar for one of the 4 L samples.