Kagome metals $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K}$, Rb, and Cs) exhibit intriguing superconductivity below $0.9\ensuremath{\sim}2.5\text{ }\text{ }\mathrm{K}$, a charge density wave (CDW) transition around $80\ensuremath{\sim}100\text{ }\text{ }\mathrm{K}$, and ${\mathbb{Z}}_{2}$ topological surface states. The nature of the CDW phase and its relation to superconductivity remains elusive. In this work, we investigate the electronic and structural properties of CDW by first-principles calculations. We reveal an inverse Star of David deformation as the $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ CDW ground state of the kagome lattice. The kagome lattice shows softening breathing-phonon modes, indicating the structural instability. However, electrons play an essential role in the CDW transition via Fermi surface nesting and van Hove singularity. The inverse Star of David structure agrees with recent experiments by scanning tunneling microscopy (STM). The CDW phase inherits the nontrivial ${\mathbb{Z}}_{2}$-type topological band structure. Further, we find that the electron-phonon coupling is too weak to account for the superconductivity ${T}_{c}$ in all three materials. It implies the existence of unconventional pairing of these kagome metals. Our results provide essential knowledge toward understanding the superconductivity and topology in kagome metals.

Charge Density Waves and Electronic Properties of Superconducting Kagome Metals.

The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology1–18, which continues to bear surprises. Here, using spectroscopic imaging scanning tunnelling microscopy, we discover a temperature-dependent cascade of different symmetry-broken electronic states in a new kagome superconductor, CsV3Sb5. We reveal, at a temperature far above the superconducting transition temperature Tc ~ 2.5 K, a tri-directional charge order with a 2a0 period that breaks the translation symmetry of the lattice. As the system is cooled down towards Tc, we observe a prominent V-shaped spectral gap opening at the Fermi level and an additional breaking of the six-fold rotational symmetry, which persists through the superconducting transition. This rotational symmetry breaking is observed as the emergence of an additional 4a0 unidirectional charge order and strongly anisotropic scattering in differential conductance maps. The latter can be directly attributed to the orbital-selective renormalization of the vanadium kagome bands. Our experiments reveal a complex landscape of electronic states that can coexist on a kagome lattice, and highlight intriguing parallels to high-Tc superconductors and twisted bilayer graphene. A study reveals a temperature-dependent cascade of different symmetry-broken electronic states in the kagome superconductor CsV3Sb5, and highlights intriguing parallels between vanadium-based kagome metals and materials exhibiting similar electronic phases.

Cascade of correlated electron states in the kagome superconductor CsV3Sb5.

Charge-density-wave-driven electronic nematicity in a kagome superconductor

Recently discovered kagome superconductors AV3Sb5 (A=K, Rb, Cs) provide a fresh opportunity to realize and study correlation-driven electronic phenomena on a kagome lattice. The observation of a 2a0 by 2a0 charge density wave (CDW) in the normal state of all members of AV3Sb5 kagome family has generated an enormous amount of interest, in an effort to uncover the nature of this CDW state, and identify any "hidden" broken symmetries. We use spectroscopic-imaging scanning tunneling microscopy to reveal a pronounced intensity anisotropy between different 2a0 CDW directions in KV3Sb5. In particular, by examining the strength of ordering wave vectors as a function of energy in Fourier transforms of differential conductance maps, we find that one of the CDW directions is distinctly different compared to the other two. This observation points towards an intrinsic rotation symmetry broken electronic ground state, where the symmetry is reduced from C6 to C2. Furthermore, in contrast to previous reports, we find that the CDW phase is insensitive to magnetic field direction, regardless of the presence or absence of atomic defects. Our experiments, combined with earlier observations of a stripe 4a0 charge ordering in CsV3Sb5, establish correlation-driven rotation symmetry breaking as a unifying feature of AV3Sb5 kagome superconductors.

Rotation symmetry breaking in the normal state of a kagome superconductor KV3Sb5

The electronic band structure of the 2D kagome net hosts two different types of van Hove singularities (vHs) arising from an intrinsic electron-hole asymmetry. The distinct sublattice flavors (pure and mixed, p-type and m-type) and pairing instabilities associated to the two types of vHs are key to understand the unconventional many-body phases of the kagome lattice. Here, in a recently discovered kagome metal CsV3Sb5 exhibiting charge order and superconductivity, we have examined the vHs, Fermi surface nesting, and many-body gap opening. Using high-resolution angle-resolved photoemission spectroscopy (ARPES), we identify multiple vHs coexisting near the Fermi level of CsV3Sb5, including both p- and m-types of vHs emerging from dxz/dyz kagome bands and a p-type vHs from dxy/dx2-y2 kagome bands. Among the multiple vHs, the m-type vHs is located closest to the Fermi level and is characterized by sharp Fermi surface nesting and gap opening across the charge order transition. Our work reveals the essential role of kagome-derived vHs as a driving mechanism for the collective phenomena realized in the AV3Sb5 family (A = K, Rb, Cs) and paves the way for a deeper understanding of strongly correlated topological kagome systems.

Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5

The recently discovered family of vanadium-based kagome metals with topological band structures offer a new opportunity to study frustrated, correlated and topological quantum states. These layered compounds are nonmagnetic and undergo charge density wave (CDW) transitions before developing superconductivity at low temperatures. Here we report the observation of unconventional superconductivity and pair density wave (PDW) in the vanadium-based kagome lattice CsV3Sb5 using scanning tunneling microscope/spectroscopy (STM/STS) and Josephson STS. The differential conductance exhibits a V-shaped pairing gap about 0.5 meV below a transition temperature Tc about 2.3 K. Superconducting phase coherence is observed by Josephson effect and Cooper-pair tunneling to a superconducting tip. We find that CsV3Sb5 is a strong-coupling superconductor (2delta/kBTc about 5) and coexists with 4a0 unidirectional and 2x2 charge order. Remarkably, we discover a 4a0/3 bidirectional PDW accompanied by spatial modulations of the coherence peak and gap-depth in the tunneling conductance. We term the latter as a roton-PDW that can produce a commensurate vortex-antivortex lattice to account for the observed conductance modulations. Above Tc, we observe long-range ordered 4a0 unidirectional and 2a0 bidirectional CDW and a large V-shaped pseudogap in the density of state. Electron-phonon calculations attribute the 2x2 CDW to phonon softening induced structural reconstruction, but the phonon mediated pairing cannot describe the observed strong-coupling superconductor. Our findings show that electron correlations in the charge sector can drive the 4a0 unidirectional CDW, unconventional superconductivity, and roton-PDW with striking analogies to the phenomenology of cuprate high-Tc superconductors, and provide the groundwork for understanding their microscopic origins in the vanadium-based kagome superconductors.

Roton pair density wave and unconventional strong-coupling superconductivity in a topological kagome metal

The transition-metal kagome lattice materials host frustrated, correlated, and topological quantum states of matter1–9. Recently, a new family of vanadium-based kagome metals AV3Sb5 (A=K, Rb, and Cs) with topological band structures has been discovered10,11. These layered compounds are nonmagnetic and undergo charge density wave transitions before developing superconductivity at low temperatures11–19. Here we report the observation of unconventional superconductivity and pair density wave (PDW) in CsV3Sb5 using scanning tunneling microscope/spectroscopy (STM/STS) and Josephson STS. We find that CsV3Sb5 exhibits a V-shaped pairing gap Δ~0.5 meV and is a strong-coupling superconductor (2∆/kBTc~5) that coexists with 4a0 unidirectional and 2a0×2a0 charge order. Remarkably, we discover a 3Q PDW accompanied by bidirectional 4a0/3 spatial modulations of the superconducting gap, coherence peak and gap-depth in the tunneling conductance. We term this novel quantum state a roton-PDW associated with an underlying vortex-antivortex lattice that can account for the observed conductance modulations. Probing the electronic states in the vortex halo in an applied magnetic field, in strong-field that suppresses superconductivity, and in zero-field above Tc reveals that the PDW is a primary state responsible for an emergent pseudogap and intertwined electronic order. Our findings show striking analogies and distinctions to the phenomenology of high-Tc cuprate superconductors, and provide groundwork for understanding the microscopic origin of correlated electronic states and superconductivity in vanadium-based kagome metals.

Roton pair density wave in a strong-coupling kagome superconductor.

The control of the Kondo effect is of great interest in single-molecule junction due to its potential applications in spin based electronics. Here, we demonstrate that the Kondo effect is reversibly switched on and off in an iron phthalocyanine (FePc) single-molecule junction by using a superconducting Nb tip. In a scanning tunneling microscope-based Nb-insulator-FePc-Au junction, we achieve a reversible switching between the Kondo dip and inelastic electronic tunneling spectra by simply adjusting the tip-sample distance to tune the tunnel coupling at low temperature. Further approaching the tip leads to the picking up of the molecule to the tip apex, which transfers the geometry of the single-molecule junction into a Nb-FePc-insulator-Au type. As the molecule forms an effective magnetic impurity embedded into the superconducting ground states of the Nb tip, the out-gap Kondo dip switched to an in-gap Yu-Shiba-Rusinov state. Our results open up a new route for manipulating the Kondo effect within a single-molecule junction.

Yuhan Ye

Papers

Roton pair density wave and unconventional strong-coupling superconductivity in a topological kagome metal

Roton pair density wave in a strong-coupling kagome superconductor.

Reversible switching of Kondo resonance in a single-molecule junction