Van Hove Singularity as the Driver of Pseudogap Physics in Cuprate High-$T$ Superconductors

Abstract

We propose a new approach to the pseudogap problem in cuprates. Hole-doped cuprates display a broad plateau in the susceptibility centered near $(\pi ,\pi )$. Competition between the softening of different $q$-modes on this plateau leads to anomalously slow growth of magnetic correlations with reducing temperature -- i.e., extended ranges of short-range correlations. The plateau arises from competition between Fermi- surface nesting and a `hidden' Van Hove singularity (VHS) nesting, associated with a bulk contribution to the susceptibility. As such, the VHS contribution is not tied to the Fermi level but rather turns on near $T_{VHS}=(E_F-E_{VHS})/k_B$ [where $E_F$ is the Fermi energy and $E_{VHS}$ the energy of the VHS peak]. Identifying $T^{\ast }\simeq T_{VHS}$ can explain many characteristic features of the pseudogap, including the transport anomalies and the termination of the pseudogap when $E_{VHS}$ crosses the Fermi level.

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• Efficient implementation of the parquet equations -- role of the reducible vertex function and its kernel approximation