Competing electronic orders on Kagome lattices at van Hove filling

TL;DR

This study uses the singular-mode functional renormalization group to explore diverse electronic orders in Hubbard models on Kagome lattices at van Hove filling, revealing complex phase diagrams influenced by interactions and lattice geometry.

Contribution

It provides a comprehensive analysis of electronic instabilities and superconducting states in Kagome lattices, highlighting the effects of interactions and geometrical frustration.

Findings

Successive development of ferromagnetism, antiferromagnetism, and charge bond order with increasing U.

Emergence of charge density wave, s-wave, and charge density wave orders with varying V.

Identification of spin bond order and chiral d+id superconductivity regimes.

Abstract

The electronic orders in Hubbard models on a Kagome lattice at van Hove filling are of intense current interest and debate. We study this issue using the singular-mode functional renormalization group theory. We discover a rich variety of electronic instabilities under short range interactions. With increasing on-site repulsion $U$, the system develops successively ferromagnetism, intra unit-cell antiferromagnetism, and charge bond order. With nearest-neighbor Coulomb interaction $V$ alone (U=0), the system develops intra-unit-cell charge density wave order for small $V$, s-wave superconductivity for moderate $V$, and the charge density wave order appears again for even larger $V$. With both $U$ and $V$, we also find spin bond order and chiral $d_{x^2 - y^2} + i d_{xy}$ superconductivity in some particular regimes of the phase diagram. We find that the s-wave superconductivity is a result of charge density wave fluctuations and the squared logarithmic divergence in the pairing susceptibility. On the other hand, the d-wave superconductivity follows from bond order fluctuations that avoid the matrix element effect. The phase diagram is vastly different from that in honeycomb lattices because of the geometrical frustration in the Kagome lattice.