Triplet superconductivity supported by an X$_9$ high-order Van Hove singularity

TL;DR

This paper investigates how a high-order Van Hove singularity of type X$_9$ in a four-fold symmetric dispersion can support triplet superconductivity, with implications for materials like Sr$_3$Ru$_2$O$_7$.

Contribution

It demonstrates that a single X$_9$ Van Hove singularity can induce triplet superconductivity with a power-law T$_c$ dependence, expanding understanding of high-order singularity effects.

Findings

Triplet superconductivity can emerge near the X$_9$ Van Hove singularity.

The critical temperature T$_c$ shows a power-law dependence on interaction strength.

An upper bound for T$_c$ in Sr$_3$Ru$_2$O$_7$ is provided.

Abstract

We study a four-fold symmetric dispersion relation of a quantum material, which exhibits a single high-order Van Hove singularity of X$_9$ type at the Fermi energy. First, we analyze in detail its form, type and density of states when the energy dispersion is in its canonical form. Subsequently, we study the possibility of a superconducting state when Hubbard repulsive interactions are taken into account. By solving the gap equation, it is shown that triplet state superconductivity with power-law dependence of the critical temperature T$_c$ on the interaction strength can be formed when a single singularity is present in the Brillouin zone. We discuss the effects of fluctuations and provide an upper bound of a possible superconducting critical temperature for the ruthenate Sr$_3$Ru$_2$O$_7$ which has been shown to exhibit this type of singularity.