Amplitude mode oscillations in pump-probe photoemission spectra from a d -wave superconductor

Abstract

Recent developments in the techniques of ultrafast pump-probe photoemission have made possible the search for collective modes in strongly correlated systems out of equilibrium. Including inelastic scattering processes and a retarded interaction, we simulate time-and angle-resolved photoemission spectroscopy (trARPES) to study the amplitude mode of a d -wave superconductor, a collective mode excited through the nonlinear light-matter coupling to the pump pulse. We find that the amplitude mode oscillations of the d -wave order parameter occur in phase at a single frequency that is twice the quasi-steady-state maximum gap size after pumping. We comment on the necessary conditions for detecting the amplitude mode in trARPES experiments.The amplitude mode of the superconducting order parameter, also known as the Higgs mode, is fundamental to superconductivity and arises because of the broken gauge symmetry of the superconducting state. Observing this mode is interesting from the perspective of understanding the collective behavior of a macroscopic quantum state out of equilibrium and has been the subject of several experimental studies performed on s-wave superconductors using Raman and THz pump-probe spectroscopy [1][2][3]. However, these experimental techniques are most likely not as well-suited as the quickly advancing technique of time-and angle-resolved photoemission spectroscopy (trARPES) for studying the Higgs mode in materials such as the high-T c cuprate superconductors which have a superconducting order parameter with dwave symmetry. We demonstrate that future trARPES experiments may be an ideal candidate to address the question of whether the Higgs mode of a d -wave superconductor appears as a single amplitude mode associated with the value of the superconducting gap maximum or as a spectrum of modes arising from the nodal nature of the superconducting order.Since the Higgs mode is a scalar boson without charge or spin, it does not couple linearly to electromagnetic fields and is difficult to observe via the standard experimental probes of the equilibrium state [4,5]. Traditionally the Higgs mode has been detected indirectly through Raman spectroscopy which relies on the interpretation that the observed 2∆ excitations borrow Raman activity from the coexisting charge density wave via electronphonon coupling [1,2]. As an alternative to probing the equilibrium state, recent advancements in time-domain spectroscopies make possible the direct detection of amplitude modes by driving systems out of equilibrium [6]. In a pump-probe experiment, an ultrashort pump pulse excites the system to a nonequilibrium state for which the original magnitude of the order parameter in the equilibrium state is no longer a minimum of the free energy. Because the order is partially melted by a pump pulse, the amplitude mode appears as the oscillation of the order parameter about a new, smaller value due to the decrease in quasiparticles involved in ordering [7].The first time-domain experiment to successfully detect the Higgs mode...

Higgs Mode in Superconductors

“…Possible collective modes have been classified based on the point group symmetry of the lattice [91], and the relaxation behavior of the A 1g mode induced by a quench has been discussed [92]. A theoretical proposal has been made to observe the Higgs mode in a d-wave superconductor through a time-and angle-resolved photoemission spectroscopy [80].…”

Identifying a forward-scattering superconductor through pump-probe spectroscopy

“…3a). These amplitude mode, or Higgs mode oscillations have been proposed and seen before in literature [28,[34][35][36][37] for pumped superconductors. In forward scattering, we observe similar oscillations for low fluences.…”

Theoretical understanding of photon spectroscopies in correlated materials in and out of equilibrium

“…With fine control of the ultrafast pump, the 'Higgs' mode, or amplitude mode, in superconductors has been identified in NbN (Refs. [113][114][115] and validated by comparison with mean-field theory 116,117 and by microscopic calculation of photoemission spectroscopy in the superconducting state 118,119 . Additional theoretical work has demonstrated how ultrafast approaches can not only separate equilibrium modes for cleaner detection, but can also be used to characterize the intertwined nature of the degrees of freedom near a quantum phase transition where fermionic and bosonic excitations become entangled 120 .…”