Direct detection of odd-frequency superconductivity via time- and angle-resolved photoelectron fluctuation spectroscopy

We propose a measurement scheme to directly detect odd-frequency superconductivity via time- and angle-resolved photoelectron fluctuation spectroscopy. The scheme includes two consecutive nonoverlapping probe pulses applied to a superconducting sample. The photoemitted electrons are collected in a momentum-resolved fashion. Correlations between signals with opposite momenta are analyzed. Remarkably, these correlations are directly proportional to the absolute square of the time-ordered anomalous Green's function of the superconductor. This setup allows for the direct detection of the “hidden order parameter” of odd-frequency pairing. We illustrate this general scheme by analyzing the signal for the prototypical case of a two-band superconductor.

Figure 1

Schematic of the setup. The superconducting sample is subjected to two separate probe pulses $A$ and $B$ with their temporal envelopes centered at times $t_A$ and $t_B$, respectively. One possible detection event is the following one: The electron emitted due to pulse $A$ has momentum $\mathit{p}$ and is registered by detector 1, whereas the electron with momentum ${\mathit{p}}^{\prime }$ emitted due to the pulse $B$ is registered by detector 2.

Figure 2

Momentum dependence of odd (red), even (blue), and full signal (black) for the model of a two-band superconductor for (a) $t_B-t_A=10$ and (b) $t_B-t_A=40$. The odd part of the signal has one peak, whereas the even part has two peaks.

Figure 3

Time dependence of odd (red), even (blue), and full signal (black) for the model of a two-band superconductor at $p=p_{\max }+\delta p,\delta p/\tilde{p}=0.04$. The full signal is different for a different ordering of pulses $A$ and $B$ since they address different bands. The odd component changes its sign with the order of the band indices, whereas the even one does not.

Figure 4

The contour for integration over frequency.