Masters Thesis Defense by Christian Lukas H Rasmussen

Title: Coexistence of altermagnetism and superconductivity

Abstract:  Altermagnets are a newly discovered class of collinear magnets that exhibit characteristics of both ferromagnets and antiferromagnets. Notably, they display spin-split energy bands while maintaining a vanishing net magnetization, making them highly relevant for both spintronics applications and unconventional superconductivity. Previous studies have primarily investigated simplified toy models to explore the coexistence of superconductivity in such systems. However, as the pool of altermagnetic material candidates continues to grow, this thesis aims to advance the understanding of superconductivity in altermagnetic systems by studying their coexistence within a realistic minimal model. Particular attention is paid to the discrepancy between one- and two-sublattice models.

Focusing on quasi two-dimensional altermagnetic candidates, we examine systems exhibiting d_xy-wave and d_x^2-y^2-wave altermagnetic orders. For these cases, we analyze the fundamental features arising when transforming from sublattice space to band space. The resulting momentum dependence enables formulation of the effective interaction for onsite pairing in sublattice space. Through an expansion in lattice harmonics, we demonstrate that describing the exact momentum dependence observed in the full solution requires terms extending to at least the ninth nearest neighbor, highlighting that two-sublattice models provide a more complete description of the superconducting order parameter. A comprehensive scan of the parameter space offers valuable insight into how tuning the chemical potential can yield regimes where a one-sublattice model may become applicable. The investigation of finite-momentum pairing proved inconclusive, despite expectations for such a phase in a spin-split system like the altermagnet.

Our work offers detailed insights into when the one-sublattice approximation is valid and when a two-sublattice model is essential for capturing physical properties such as the superconducting order parameter.