Nature of Unconventional Pairing in the Kagome Superconductors $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K},\mathrm{Rb},\mathrm{Cs}$)

The recent discovery of $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K},\mathrm{Rb},\mathrm{Cs}$) has uncovered an intriguing arena for exotic Fermi surface instabilities in a kagome metal. Among them, superconductivity is found in the vicinity of multiple van Hove singularities, exhibiting indications of unconventional pairing. We show that the sublattice interference mechanism is central to understanding the formation of superconductivity in a kagome metal. Starting from an appropriately chosen minimal tight-binding model with multiple van Hove singularities close to the Fermi level for $A{\mathrm{V}}_3{\mathrm{Sb}}_5$, we provide a random phase approximation analysis of superconducting instabilities. Nonlocal Coulomb repulsion, the sublattice profile of the van Hove bands, and the interaction strength turn out to be the crucial parameters to determine the preferred pairing symmetry. Implications for potentially topological surface states are discussed, along with a proposal for additional measurements to pin down the nature of superconductivity in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$.

Figure 1

Generic three-band kagome dispersion exhibits two van Hove singularities with distinct sublattice ($A$, $B$, $C$) decoration. Whereas the upper van Hove filling at $E=0$ has a pure sublattice makeup ($p$ type, left inset), the lower van Hove filling at $E=-2t$ mixes different sublattice states ($m$ type, right inset). Energy is measured in units of the NN hybridization $t$.

Figure 2

(a) Fermi surfaces of the minimal two-orbital tight-binding model [Eq. (1)] for a vanadium kagome net. Both a $p$-type and $m$-type van Hove filling are present nearby the Fermi level, indicated by their respective orbital color. (b) Real-space structure of the kagome V planes. The sign structure (blue or red) and spatial orientation of the $B_{2g}$ and $B_{3g}$ orbitals is sketched on different lattice sites. The red, yellow, and orange coloring indicates the three kagome sublattices. (c) Band structure along the high-symmetry path depicted by the dashed line in (a). The band coloring indicates the sublattice support of the momentum eigenstates.

Figure 3

Pairing-strength eigenvalues $\lambda$ for the dominant instabilities as a function of $U$ ($V=0.3U$, $J=0.1U$) in Eq. (2). Continuous (dashed) lines indicate triplet (singlet) pairing. Two distinct $f$-wave solutions, $B_{1u}$ (blue dots) and $B_{2u}$ (large orange dots), dominate for smaller interaction scales. The $d$-wave $E_{2g}$ solution dominates for larger $U$. The $p$-wave $E_{2u}$ solution (gray triangles) is subleading, but competitive at all $U$. The upper left inset depicts the largest eigenvalue trajectory of the bare susceptibility ${\chi }_0(\mathit{q})$ along the high-symmetry path indicated in Fig. 2.

Figure 4

The intersublattice triplet $f_{x^3-3x{y}^2}$-wave pairing function in (a) momentum and (b) real space, where the superconducting order parameter changes sign under 60° rotation. (c) Edge spectra for open boundary conditions along $x$ direction; zero-energy Andreev bound states appear between the projections of nodal points in the $f$-wave pairing. (d) Density of states for the bulk $f$-wave pairing (black) and local density of states at edges from Andreev bound states (red).