Collective mode spectroscopy in time-reversal symmetry breaking superconductors

Collective excitations in superconductors provide essential insights into the symmetry of the broken phase, acting as indicators for identifying the ground state gap symmetry. Time-reversal symmetry breaking (TRSB) superconductors exhibit a rich spectrum of collective modes due to the complexity of their order parameters. These modes, known as “generalized clapping modes,” draw analogies to the clapping modes of helium-3 phase A. This study investigates two-dimensional TRSB superconductors with an order parameter of the form <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi mathvariant="normal">Δ</a:mi> <a:mo>=</a:mo> <a:msub> <a:mi mathvariant="normal">Δ</a:mi> <a:mn>1</a:mn> </a:msub> <a:mo>+</a:mo> <a:mi>i</a:mi> <a:msub> <a:mi mathvariant="normal">Δ</a:mi> <a:mn>2</a:mn> </a:msub> </a:mrow> </a:math> , exploring the characteristics of their collective mode spectrum. We begin with a phenomenological Ginzburg-Landau approach to build intuition, then develop a dynamical theory by deriving linearized equations of motion using the pseudospin formalism. Beyond the linear regime, we propose a classification scheme based on the potential to induce (an)isotropic oscillations in the superconducting condensate. By perturbing the system in symmetry channels distinct from the ground state, we aim to selectively enhance or suppress different mode responses. This study analyzes the features of these generalized clapping modes as a function of the ratio between the order parameter components under various excitation schemes. We believe that our findings could help distinguish between different order parameter symmetries in TRSB superconducting condensates and estimate the magnitude of their components.