Summary of work on Kagome¶

CDW and Superconductivity¶

• Superconductivity at low temperature and unusual CDW at high temperatures.
• Pressure dependent phase diagrams have been observed to show anomaly at specific temperatures. (Read AV3Sb5 anomalies)
• Double dome type phase diagram under moderate pressure has been obtained, which implies two different kinds of CDWcompeting with Superconductivity.
• Multiple SC gaps have been observed.
• Cs shows richer double peak behavior than other members from AV3Sb5 family.

Topology¶

• Presence of multiple Dirac points near the Fermi surface.
• Corresponding topological protected surface states that occur at the M points (a Time-reversal invariant momentum (TRIM) point) in the Brillouin zone, in addition to small Fermi surfaces with low effective mass and non-zero Berry phases.
• Dirac nodal lines and loops near the Fermi level along the \(k_z\) direction and surrounding the H points.
• ARPES has also been shown to reveal topological surface states and flatbands in CsV3Sb5 with implications on electron correlation phenomena.
• Temperature-driven band renormalization (from ARPES).

Anomalous Hall Effect¶

• The extracted values of the Anomalous Hall effect conductivity for AV3Sb5 family of compounds reach extremely high values of \(> 10^4 \Omega^{-1}cm^{-1}\) and large value of anomalous hall ratio of \(\sim 1.8\%\).
• Some authors attribute this giant AHE to enhanced skew scattering that scales quadratically, rather than linearly, with the longitudinal conductivity (\(\sigma_{xx}\)) as a result of highly conductive Dirac quasiparticles within the frustrated magnetic sublattice or due to scattering off of tilted spin clusters, local groups of coupled spins which can result from the magnetic atoms in kagome nets.
• Other studies on KV3Sb5 seem to dispel this possible theoretical explanation for the AHE in this family of kagome metals, as there is no evidence for the existence of V local moments that would underlie the existence of these tilted spin clusters.

TRS Breaking¶

• Evidence of Time reversal symmetry breaking in muon spin relaxation. A noticeable enhancement of the internal field taking place just below the charge ordering temperature.
• Time-reversal symmetry-breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice.

Coexisting Orders¶

• High-resolution STM measurements reveal a robust in-plane 2 × 2 superlattice structure and unconventional charge ordering through intensity reversals of the charge modulation pattern upon the opening of the energy gap near the Fermi level.
• This unusual ordering is found in all members of AV3Sb5 family.

Theoretical Works¶

DFT¶

• Electronic correlations and magnetic properties in the normal state.
• The 2 × 2 CDW ground state of the kagome lattice is an inverse Star of David structure, with the transition being driven by Peierls instability.
• Electron–phonon coupling in the system is too weak to rationalize conventional Superconductivity and there is an absence of an acoustic phonon anomaly.
• A computational study of the system under pressure indicates conventional superconductivity, with a partial suppression at ambient and low pressures due to magnetism from vanadium atoms.
• First-principles calculations of phonon instabilities due to possible structural phase transition near the CDW transition temperature have been performed and reveal phonon softening at the M and L points, which can lead to an emergence of an inverse Star of David pattern.
• CDW in the system is mainly driven by phonon instability and electron–phonon coupling.

Numerical Studies¶

• The effect of tuning the vHs near the Fermi level with applied pressure and hole doping on the electronic structure was numerically studied, displaying a reconstruction of the Fermi surface with respect to the Sb bands.

Models¶

• Variational cluster calculations on the elementary level of the 2D kagome Hubbard model, propose f-, d- and s-wave superconductivity.
• RPA calculations reveal a close competition between two types of f-wave and a chiral d-wave pairing, implying that the superconducting phase may be one of several exotic types, including helical Cooper pairing of the topological surface state.
• Quantum order in Haldane Model.
• Numerous studies demonstrate a rich Haldane model phase diagram of the multi-component hexagonal (3Q) charge density waves, where they find trivial and Chern insulator phases with real or imaginary orders (like the chiral flux phase).

DMFT¶

• Weakly correlated. Good metals with weak local correlations.
• Absence of local moments.
• The result suggests that the local correlation strength in these materials appears to be too weak to generate unconventional superconductivity, and nonlocal electronic correlation might be crucial in this kagome system.