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Higgs spectroscopy of superconductors : a new method to identify the superconducting gap symmetry

In this thesis we study the response of a BCS superconductor to an external ultra-fast terahertz electromagnetic field, which we choose so as to mimic the setup in a pump-probe experiment. We begin by considering an optical experimental setup and demonstrate that in an optical pumpprobe experiment, the superconducting amplitude Higgs mode can be excited and measured with ultra-fast terahertz pump pulses. Moreover, for an anistropic d-wave superconductor, there are two Higgs mode, one at the usual 2∆ energy and one with a lower energy. The latter can be used to differentiate the d-wave symmetry from isotropic s-wave, by varying the polarization of the pump relative to the sample. For a linearly polarized pump with a vector potential aligned along a d-wave node we find only a single Higgs mode, while for a direction along an antinode we find two Higgs modes. Next, we consider an angle resolved photoemission spectroscopy (ARPES) experiment and derive a new set of equations of motion, for which we can analyze the two-time nonequilibrium Green’s functions. We show that the Higgs mode can also be studied in an ARPES pump-probe experiment. Moreover, we show how an ARPES pump-probe experiment can be used to differentiate between different momentum-dependent nonequilibrium Higgs modes. Our results suggest that in a d-wave superconductor, the second low-energy Higgs mode is of osculating, B1g character, which corresponds to a symmetry breaking along the d-wave nodal lines. Further study of the role of momentum symmetry breaking promises to provide deeper insight into generating new nonequilibrium states.