Higgs mode and tr-ARPES in Non-equilibrium Superconductors with a Moving Condensate

Jianxin Li, Chung‐Yu Mou, T. K. Lee

Yafis Barlas, Chandra Mohan Varma

Z. E. Krix, Daniel Loss

Collective modes in a superconductor correspond to fluctuations in the amplitude (Higgs mode) or the phase (Goldstone mode) of the order parameter. Starting from the BCS Hamiltonian, we derive a microscopic Hamiltonian for the coupled Higgs-Goldstone-electron system that contains all interactions among these degrees of freedom. The Higgs subsystem is a weakly interacting Bose gas: Higgs modes experience a mutual attraction mediated by the virtual exchange of Bogoliubov quasi-particle pairs. They also interact with external electromagnetic-fields with a coupling constant that we derive explicitly. We use this theory to examine whether an optically pumped gas of Higgs modes can undergo Bose-Einstein condensation. We identify a density window, bounded below by the equilibrium condensation criterion and above by collapse due to the attractive interaction, in which condensation can occur and we derive the expected density of Higgs-modes due to external pumping. This pumping depends crucially on non-parabolic corrections to the electron dispersion around the Fermi-energy. We show that the pumped mode density is compatible with condensation for realistic material parameters. We suggest possible experimental signatures of this non-equilibrium condensate.

Alexander F. Kemper

Lukas Schwarz, Benedikt Fauseweh, Dirk Manske

Higgs oscillations in nonequilibrium superconductors provide a unique tool to obtain information about the underlying order parameter. Several properties like the absolute value, existence of multiple gaps, and the symmetry of the order parameter can be encoded in the Higgs oscillation spectrum. Studying Higgs oscillations with time-resolved angle-resolved photoemission spectroscopy (ARPES) has the advantage over optical measurements that a momentum-resolved analysis of the condensate dynamic is possible. In this paper, we investigate the time-resolved spectral function measured in ARPES for different quench protocols. We find that analyzing amplitude oscillations of the ARPES intensity in the whole Brillouin zone allows to understand how the condensate dynamic contributes to the emerging of collective Higgs oscillations. Furthermore, by evaluating the phase of these oscillations, the symmetry deformation dynamic of the condensate can be revealed, which gives insight about the ground state symmetry of the system. With such an analysis, time-resolved ARPES experiments might be used in the future as a powerful tool in the field of Higgs spectroscopy.

D. A. Kirzhnits, Yu. V. Kopaev