Triplet superconductivity supported by an X9 high-order Van Hove singularity
Abstract
We study a four-fold symmetric dispersion relation of a quantum material, which exhibits a single high-order Van Hove singularity of X9 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 Tc 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 Sr3Ru2O7 which has been shown to exhibit this type of singularity.
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