Strain-sensitive superconductivity in the kagome metals ${\mathrm{KV}}_3{\mathrm{Sb}}_5$ and $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$ probed by point-contact spectroscopy

The kagome lattice is host to flat bands, topological electronic structures, Van Hove singularities, and diverse electronic instabilities, providing an ideal platform for realizing highly tunable electronic states. Here, we report soft and mechanical point-contact spectroscopy (SPCS and MPCS) studies of the kagome superconductors ${\mathrm{KV}}_3{\mathrm{Sb}}_5$ and $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$. Compared to the superconducting transition temperature $T_{\mathrm{c}}$ from specific heat and electrical resistance measurements, significantly enhanced values of $T_{\mathrm{c}}$ are observed via the zero-bias conductance of SPCS, which become further enhanced in MPCS measurements. While the differential conductance curves from SPCS can be described by a two-gap $s$-wave model, a single $s$-wave gap reasonably captures the MPCS data, likely due to a diminishing spectral weight of the other gap. The enhanced superconductivity probably arises from local strain caused by the point contact, which also leads to two-gap or single-gap behaviors observed in different point contacts. Our results demonstrate highly strain-sensitive superconductivity in kagome metals $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$ and ${\mathrm{KV}}_3{\mathrm{Sb}}_5$, which may be harnessed in the manipulation of possible Majorana zero modes.

Figure 1

Temperature dependence of the zero-bias conductance $G(V=0)$ measured using SPCS and MPCS for (a) $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$ and (e) ${\mathrm{KV}}_3{\mathrm{Sb}}_5$. Electrical resistance $R\left(T\right)$ was carried out on the same samples, as shown in (b) for $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$, and (f) for ${\mathrm{KV}}_3{\mathrm{Sb}}_5$. $C_{\mathrm{e}}\left(T\right)/\gamma T$ data for (c) $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$ and (g) ${\mathrm{KV}}_3{\mathrm{Sb}}_5$, respectively from Refs. [18] and [28]. Field dependence of the zero-bias conductance $G(V=0)$ measured using SPCS and MPCS at $T=0.3$ K for (d) $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$ and (h) ${\mathrm{KV}}_3{\mathrm{Sb}}_5$, with the field along the $c$ axis.

Figure 2

Representative SPCS differential conductance curves for (a)–(c) $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$ and (d)–(f) ${\mathrm{KV}}_3{\mathrm{Sb}}_5$ at $T=0.3$ K. Solid red lines are fits to a single-gap $s$-wave model for data with voltages below the peak in $G(V$). The solid blue lines are fits to a two-gap $s$-wave model. The slight deviation of the measured differential conductance from the fits at large bias voltages is due to current heating effects [34].

Figure 3

Normalized differential conductance curves for $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$ from SPCS, as a function of (a) temperature and (b) magnetic field. The solid lines are fits to the two-gap $s$-wave BTK models at finite temperatures or under applied magnetic fields. The extracted superconducting gaps ${\mathrm{\Delta }}_1$ and ${\mathrm{\Delta }}_2$ are shown in (c) as a function of temperature with $H=0$ T and the solid lines are based on the BCS theory with $T_{\mathrm{c}}$ estimated from the zero-bias conductance. The extracted fraction of normal state vortex core excitations $n_1$ and $n_2$ are shown in (d) as a function of magnetic field at $T=0.3$ K.

Figure 4

Normalized differential conductance curves for ${\mathrm{KV}}_3{\mathrm{Sb}}_5$ from SPCS, as a function of (a) temperature and (b) magnetic field. The solid lines are fits to the two-gap $s$-wave BTK model at finite temperatures or under applied magnetic fields. The extracted superconducting gaps ${\mathrm{\Delta }}_1$ and ${\mathrm{\Delta }}_2$ are shown in (c) as a function of temperature with $H=0$ T and the solid lines are based on the BCS theory with $T_{\mathrm{c}}$ estimated from the zero-bias conductance. The extracted fraction of normal state vortex core excitations $n_1$ and $n_2$ is shown in (d) as a function of magnetic field at $T=0.3$ K.

Figure 5

(a)–(d) Representative MPCS differential conductance curves for $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$ at $T=0.3$ K. The red solid line are fits to a single-gap $s$-wave BTK model. (e) Temperature evolution of the MPCS differential conductance curves for $\mathrm{Cs}{\mathrm{V}}_3{\mathrm{Sb}}_5$, fit to a single-gap $s$-wave BTK model (black solid lines). (f) Temperature dependence of the extracted superconducting gap $\mathrm{\Delta }$ from (e); the black line is the expected behavior of the BCS theory, with $\mathrm{\Delta }=0.47$ meV and $T_{\mathrm{c}}=5.0$ K ($2\mathrm{\Delta }/k_{\mathrm{B}}{\mathrm{T}}_{\mathrm{c}}$ = 2.2).

Figure 6

(a)–(d) Representative MPCS differential conductance curves for ${\mathrm{KV}}_3{\mathrm{Sb}}_5$ at $T$ = 0.3 K. The solid red lines are fits to a single-gap $s$-wave BTK model. (e) Temperature evolution of the MPCS differential conductance curves for ${\mathrm{KV}}_3{\mathrm{Sb}}_5$, fit to a single-gap $s$-wave BTK model (black solid lines). (f) Temperature dependence of the extracted superconducting gap $\mathrm{\Delta }$ from (e); the black line is the expected behavior of the BCS theory, with $\mathrm{\Delta }=0.34$ meV and $T_{\mathrm{c}}=3.1$ K ($2\mathrm{\Delta }/k{}_{\mathrm{B}}{T}_{\mathrm{c}}$ = 2.5).