Broken time-reversal symmetry detected by tunneling spectroscopy of superconducting Pd-doped CaAgP

TL;DR

This work reports evidence for broken time-reversal symmetry in superconducting Pd-doped CaAgP, a nodal-line semimetal with surface superconductivity. Using normal/insulator/superconductor tunneling junctions, the authors observe broad zero-bias peaks and, on side surfaces, small asymmetric features that reverse exactly when the magnetic field direction is flipped. The asymmetries are analyzed within an extended BTK framework that accounts for TRSB and asymmetric tunneling current distributions; simulations with a chiral p-wave–like pair potential reproduce the observed field-driven chirality flip. The results demonstrate a novel TRS-sensitive capability of tunneling spectroscopy in topological materials and point to a TRSB superconducting state possibly arising from surface–bulk band interactions or anapole-type order, motivating further multi-probe studies and Pd-doping tuning to elucidate the mechanism.

Abstract

The appearance of broken time-reversal symmetry (TRS) in superconducting states is an intriguing issue in solid-state physics because of the incompatibility of the spontaneous magnetic field and the Meissner effect. We identify broken TRS in Pd-doped CaAgP (CaAg$_{0.9}$Pd$_{0.1}$P) by tunneling spectroscopy through the magnetic field response of conductance spectra. CaAg$_{0.9}$Pd$_{0.1}$P is a nodal-line semimetal with exotic electronic states such as drumhead surface states and surface superconductivity. Tunneling conductance spectra acquired at the side surfaces of CaAg$_{0.9}$Pd$_{0.1}$P under an applied magnetic field exhibit broad zero-bias peaks with small asymmetric structures. Surprisingly, the asymmetric structures are reversed exactly by flipping the field direction. On the basis of an analysis which stands on the formula of tunneling junctions for unconventional superconductors, these results are consistent with the pair potential of the superconductivity breaks the TRS and is strongly coupled to an external magnetic field. We reveal the novel character of superconducting nodal-line semimetals by developing the TRS sensitivity of tunneling spectroscopy. Our results serve as an exploration of broken TRS in superconducting states realized in topological materials.

Figures (4)

• Figure 1: (a) Schematic of the band structure and Fermi surface of $\mathrm{CaAg_{0.9}Pd_{0.1}P}$ with $E_\mathrm{F} \sim -0.14~\mathrm{eV}$ below the Dirac node. Red indicates the surface electron state, and green and purple show the bulk band. The Fermi surface is composed of the bulk toroid and the surface flat-dispersive plane. (b) Schematic of a $\mathrm{CaAg_{0.9}Pd_{0.1}P}$ crystal and the soft point contacts formed at the top and side surfaces. (c--f) The temperature dependences of conductance spectra obtained at four junctions (#1-Top(c), #1-Side(d), #2-Side(e), and #3-Side(f)) in the absence of an applied field. Here, #i-Top (Side) indicates the junction formed on the top (side) surface of crystal #i ($1\le i\le 3$). In all cases, broad zero-bias conductance peaks appear below $T_\mathrm{c} \sim 1.8~\mathrm{K}$, indicating unconventional superconductivity of $\mathrm{CaAg_{0.9}Pd_{0.1}P}$ .
• Figure 2: (a--d) The magnetic field dependences of conductance spectra for (a) #1-Top, (b)#1-Side, (c) #2-Side, and (d) #3-Side junctions. The fine structures in (a)#1-Top are simply smeared by application of the field. However, asymmetric small structures that appear in side junctions exhibit peculiar responses. Flipping the field direction exactly reverses the structures of positive and negative bias, as indicated by the red arrows. (e,f) The asymmetric factor $\gamma (B)$ defined by equation (1) for (e) #1-Side and (f) #2-Side are plotted.
• Figure 3: (a) Schematics of a normal metal/insulator/superconductor junction assumed in the extended BTK formula. The superconductor has an anisotropic gap amplitude, as illustrated on the right side. The blue arrows indicate the group velocity of injected quasiparticles and transmitted electron (hole)-like quasiparticles. (b) Three types of tunneling current distribution $\sigma_\mathrm{N}(\theta)$ used in the simulation. Compared with the symmetric $\sigma_\mathrm{N}(\theta)$ for the $\delta$-function barrier model, blue and red curves contain the weighting factors described in equation (7). (c--h) Results of the simulation of the tunneling conductance $\sigma_\mathrm{T}(E)$ with $\Delta(\theta) = \Delta_0 (1+\alpha\cos(6\theta)+\beta\cos(12\theta))(\mathrm{cos}\theta+i~\mathrm{sin}\theta)$. (c--e) for $\alpha=\beta=0$, (f--h) for $\alpha=\beta=0.02$. The color of each plot corresponds to the color of $\sigma_\mathrm{N}(\theta)$ shown in (b). The solid and dotted lines correspond to the results for $\Delta(\theta)$ and $\Delta^*(\theta)$, respectively. The exact reversing relation of the two curves reflects the relation $\sigma_\mathrm{T}(E)=\sigma_\mathrm{T}^\mathrm{C}(-E)$ of iv) in Table I.
• Figure 4: (a) Schematic of a tunneling junction with a $\delta$-function potential. (b) A tunneling junction model with broken inversion symmetry to $\theta$. An isotropic Fermi surface shape for the left electrode and an anisotropic shape with tilting angle $\alpha$ for the right electrode are assumed. The $y$ component of wavelength is conserved. The direction of the wave vector and group velocity are not equal in the right electrode. (c) Plots of calculated $\sigma_\mathrm{N}(\theta )$ for $\alpha$=0 and $\pi$/8.