Observing unconventional superconductivity via kinetic inductance in Weyl semimetal MoTe$_2$

TL;DR

The work tackles the problem of identifying pairing symmetry in unconventional superconductors by studying MoTe2, a Weyl semimetal with van der Waals bonding. It introduces a high-precision microwave resonator technique to measure the kinetic inductance $L_K$ and infer the London penetration depth $\lambda$, achieving parts-per-million sensitivity. The authors observe a $T^2$-type power law in the temperature dependence of $\lambda$ and detect an anomalous nonlinear Meissner effect with $\delta\lambda^2_I \propto |I|$ at low $T$, crossing to $\propto I^2$ with temperature, which together signal nodal superconductivity. Across multiple devices, these findings provide strong evidence for nodal pairing in MoTe2 and demonstrate a robust, sensitive approach to determine gap symmetry in topological or strongly correlated materials.

Abstract

Identifying the pairing symmetry of unconventional superconductors plays an essential role in the ongoing quest to understand correlated electronic matter. A long-standing approach is to study the temperature dependence of the London penetration depth $λ$ for evidence of nodal points where the superconducting gap vanishes. However, experimental reports can be ambiguous due to the requisite low-temperature resolution, and the similarity in signatures of nodal quasiparticles and impurity states. Here we study the pairing symmetry of Weyl semimetal $T_d$-MoTe$_2$, where previous measurements of $λ$ have yielded conflicting results. We utilize a novel technique based on a microwave resontor to measure the kinetic inductance of MoTe$_2$, which is directly related to $λ$. The high precision of this technique allows us to observe power-law temperature dependence of $λ$, and to measure the anomalous nonlinear Meissner effect -- the current dependence of $λ$ arising from nodal quasiparticles. Together, these measurements provide smoking gun signatures of nodal superconductivity.

Figures (9)

• Figure 1: Measuring the kinetic inductance of superconducting MoTe$_2$.(A) Schematic of the quarter-wave resonator experiment. The transmission-line --- represented by a coaxial cable (cylinder) --- is terminated to the ground through the MoTe$_2$ sample. When the magnitude of the complex impedance $Z_{MoTe_2}$ --- represented by the resistor and inductor in series --- is small compared to the characteristic impedance of the transmission line, the transmission line and sample form a quarter-wave resonance with the sample located at the current antinode. (B-D) Optical micrographs of the resonator. (B) The meandering coplanar-waveguide made of niobium is capacitively coupled to the horizontal feedline for transmission measurement at microwave frequencies. (C) The resonator terminates to the niobium ground plane through (D) an exfoliated flake of MoTe$_2$ (pink rectangle), connected galvanically with sputtered niobium nitride. The MoTe$_2$ flake, shown in pink false-coloring, is oriented such that the long edge of the pink rectangle is along the $a$-axis of the MoTe$_2$ crystal. (E) Measured $|S_{21}|$ of the MoTe$_2$ hybrid resonator at various temperatures.
• Figure 2: Resonance frequency shift under thermal excitation.(A) Measured frequency shift, $\delta f_{res}$, versus temperature normalized to the superconducting transition temperature; $\delta f_{res}$ is referenced to 3.519420 and 3.258497 GHz for MoTe$_2$ and Al, respectively. As $T\rightarrow 0$, the frequency rises as the kinetic inductance of MoTe$_2$ (blue dots) decreases. In contrast to the aluminum data (green crosses), which saturate at around $0.3T_c$ in accordance with BCS theory (pink solid line). The double $x$-axes at the top of the plot denote the absolute temperatures for the MoTe$_2$ (blue) and Al (green) data. (B) The normalized frequency shift is plotted against $(T/T_c)^2$ and fit to a linear trend (solid pink line). Exponential or linear scaling data would feature a systematic drift away from the best fit as $T\rightarrow0$, yet the residual plot (bottom) shows no such trend. The scaling behavior is precisely characterized by plotting $\delta L_K$ (left axis) or equivalently $\delta \lambda^2_T$ (right axis) on a log-log plot, with quadratic scaling (pink dashed line) contrasted with linear scaling (black dashed line); the slope of best fit is $n=2.12 \pm 0.15$. The change in kinetic inductance along the $a$-axis of the MoTe$_2$ flake is on the order of a few fH in this low-temperature regime. The magnitude of $\delta L_K$ and the error bar underscores the stringent sensitivity required and achieved in this experiment.
• Figure 3: Anomalous nonlinear Meissner effect in MoTe$_2$. Density of states (DOS) under an applied current for (A) gapped and (B) nodal superconductors. The applied current shifts the quasiparticle momenta by an amount $p_s$; current dependence of $\lambda^2$ results from a difference in the DOS for forward ($+$) and backward ($-$) moving quasiparticles (shaded region). Impurity-induced DOS near $E\approx 0$ for unconventional, fully gapped superconductors do not shift in energy when the momenta shift by $p_s$, and so do not produce a contribution to the shaded region, whereas nodal quasiparticles with a linear dispersion produce a contribution to the shaded region inside the gap $\propto$$p_s|p_s|$. The shaded areas are given approximately by a rectangle, and difference of two triangles, in the two respective cases. (C) The current dependence of $\lambda^2$ for a fully gapped superconductor at zero (blue) and finite (red) temperature. (D) The current dependence of the superfluid density for a nodal superconductor at zero (blue) and finite (red) temperature. In the nodal case, a current dependent shift $\propto$$|I|$ appears at small $I$. (E) Measured frequency change of an Al hybrid resonator compared to (F) that of an MoTe$_2$ hybrid sample resonator at the same range of input powers, taken at $T \simeq 10$ mK. (G) Measured $\delta \lambda_I^2$ as a function of current across various temperatures, shown on a log-log scale to illustrate power-law behavior. The power law $n$ of best fit as a function of temperature is plotted in inset.
• Figure 4: Cryogenic microwave transmission measurement setup. Schematic of the vector network analyzer (VNA)-based measurement chain used to probe superconducting resonators at millikelvin temperatures. The VNA output is attenuated by 60--80 dB using attenuators that are distributed at room temperature outside the cryostat and at various temperature stages inside the cryostat. The signal is routed through a coaxial line to the mixing chamber stage, where it excites a hanger-type resonator mounted inside a heavily shielded sample enclosure. The transmitted signal is amplified by a cryogenic low-noise amplifier (LNA) at 4 K, followed by additional room-temperature amplification, and is then returned to the VNA for readout. A circulator at the base stage isolates the sample from the noise generated by the amplifier and ensures unidirectional signal routing. The measurement chain was optimized to minimize thermal loading, eliminate electromagnetic noise, and maximize the measurement sensitivity of the resonator at powers down to the single-photon level.
• Figure 5: Temperature dependent kinetic inductance in MoTe$_2$ devices. Fine-temperature measurements display reproducible non-saturating kinetic inductance at low temperatures $T < 0.3T_c$.