The possible frustrated superconductivity in the kagome superconductors

TL;DR

The paper investigates frustrated superconductivity on kagome AV3Sb5 superconductors, proposing a mechanism where on-site $s$-wave pairing coexists with nearest-neighbor pair hopping on a geometrically frustrated lattice. A mean-field Kagome model with a pairing-hopping term $H_{PH}=J\sum_{\langle ij\rangle}(\tilde{\Delta}^{\dag}_i\tilde{\Delta}_j+H.c.)$ yields two competing SC states: conventional $s$-wave for small $J$ and a frustrated SC state for $J$ beyond a critical value, with a $2\\pi/3$ phase difference among the three sublattices and a six-fold modulation of the gap that breaks time-reversal symmetry via a $4\\pi$ winding around the Fermi surface. The frustrated state remains robust to nonmagnetic impurities and exhibits a pronounced Hebel-Slichter peak, while disorder can drive a transition to an isotropic $s$-wave state without nodal points, reconciling divergent experimental results. Overall, the work provides a unified framework for geometry-induced frustration in superconductivity on kagome lattices and suggests new directions for exploring such states in AV3Sb5 materials.

Abstract

Geometric frustration has long been a subject of enduring interest in condensed matter physics. While geometric frustration traditionally focuses on magnetic systems, little attention is paid to the "frustrated superconductivity" which could arise when the superconducting interaction conflicts with the crystal symmetry. The recently discovered kagome superconductors provide a particular opportunity for studying this due to the fact that the frustrated lattice structure and the interference effect between the three sublattices can facilitate the frustrated superconducting interaction. Here, we propose a theory that supports the frustrated superconducting state, derived from the on-site $s$-wave superconducting pairing in conjunction with the nearest-neighbor pairings hoping and the unique geometrical frustrated lattice structure. In this state, whereas the mutual $2π/3$ difference of the superconducting pairing phase causes the six-fold modulation of the amplitude and breaks the time-reversal symmetry with $4π$ phase changes of the superconducting pairing as one following it around the Fermi surface, it is immune to the impurities without the impurity-induced in-gap states and produces the pronounced Hebel-Slichter peak of the nuclear spin-lattice relaxation rate below $T_{c}$. Notably, the theory also reveals a disorder-induced superconducting pairing transition from the frustrated superconducting state to an isotropic $s$-wave superconducting state without traversing the nodal points, recovering and explaining the behavior found in experiment. This study not only serves as a promising proposal to mediate the divergent or seemingly contradictory experimental outcomes regarding superconducting pairing symmetry, but may also pave the way for advancing investigations into the frustrated superconducting state.

Figures (5)

• Figure 1: (a) Structure of the kagome lattice, made out of three sublattices A (green dots), B (red dots), and C (blue dots). (b) The SC pairing amplitude as a function of the pairing hopping strength $J$. The light cyan region with $J<0.11$ indicates the conventional $s$-wave SC state, and the light purple region with $J>0.11$ denotes the frustrated SC state.
• Figure 2: Distributions of the amplitude (a) and phase (b) of the frustrated SC state in the primitive Brillouin zone. (c) Variations of the amplitude and phase of the frustrated SC state following in a counterclockwise direction around the Fermi surface shown as dashed lines in (a) and (b). (d) Same as (b) but with opposite chirality of the SC pairing.
• Figure 3: Temperature dependence of the amplitude of SC pairing $|\Delta|$ and $(T_{1}T)^{-1}$ for $J=0.1$ (a) and $J=0.2$ (b). The energy dependence of the DOS on a series of sites for $J=0.1$ (c), and $J=0.2$ (d). In (c) and (d), $B_{0}$ and $C_{0}$ denote the other two sublattice sites within the same unit cell as the impurity site $A_{0}$, and $A_{1}-A_{5}$ stand for the LDOS at the same sublattice sites as the impurity site $A_{0}$ in different unit cell moving away from $A_{0}$ [See Fig. \ref{['fig1']}(a).].
• Figure 4: Spatial distributions of SC amplitude $|\Delta_{i}|$ and phase $\theta_{i}$ on the $A$-sublattice sites (a), and on the $B$-sublattice sites (b), where a $U_{0}=2$ impurity is embedded at the $A$-sublattice site indicated by the short green arrow in (a). (c) The average phase difference $\varphi$ between the sublattices and the average amplitude of the SC pairings $|\bar{\Delta}|$ as a function of the impurity strength $W$. (d) The energy dependence of the average DOS at different $W$ for $J=0.13$.
• Figure B1: The momentum distribution of the form factors $|u_{2,A}(\mathbf{k})|^{2}$ (a), and $u_{2,B}(\mathbf{k})u_{2,A}^{\ast}(\mathbf{k})$ (b), respectively. Real and imaginary parts of the Green's functions $\hat{G}_{0,ee}^{AA}(\mathbf{r}_{A_{1}}-\mathbf{r}_{A_{0}},\omega+i\delta)$ and $\hat{G}_{0,ee}^{BA}(\mathbf{r}_{B_{0}}-\mathbf{r}_{A_{0}},\omega+i\delta)$ for the normal state (c), and for the SC state (d). $\hat{G}_{0,ee}^{AA}(\mathbf{r}_{A_{1}}-\mathbf{r}_{A_{0}},\omega+i\delta)$ and $\hat{G}_{0,ee}^{BA}(\mathbf{r}_{B_{0}}-\mathbf{r}_{A_{0}},\omega+i\delta)$ have been abbreviated respectively as $\hat{G}_{0}^{AA}$ and $\hat{G}_{0}^{BA}$ in the figures.