Theory of the time-resolved spectral function of high-temperature superconductors

We have recently developed a three-temperature model to simulate the time evolution of the electron and phonon temperatures in high-temperature superconductors. This is the first model that is valid in the superconducting state. Based on this model, we calculated the time-resolved spectral function via the double-time Green's functions. Our calculations show that the theory not only reveals the familiar dip-hump structure in the normal state, but also a new signature of the electron-phonon coupling in the superconducting state. We further show that this signature can only be observed when the phonons are pumped directly. In this proceedeing, we provide detailed derivation of our theory.