Cooper Pair Spectroscopy for Odd-Frequency Superconductors

Sammanfattning

In conventional spin-singlet superconductors with even parity, the anomalous pairingamplitude is even in frequency. Odd-frequency superconductivity is an unconventionalsuperconducting state in which the pair amplitude is odd under exchange oftime coordinates. Since superconducting pairing is encoded in two-particle correlations,double photoelectron spectroscopy provides a natural framework for probingsuch states through the simultaneous detection of two photoemitted electrons.When applied to superconducting samples, this approach is commonly referred to asCooper pair spectroscopy. In this thesis, a Green’s-function formulation of Cooperpair spectroscopy for odd-frequency superconductors is developed by extending thetheoretical structure of angle-resolved photoemission spectroscopy to the doublephotoemissioncase.Starting from an expansion of the S-matrix, the double-photoelectron counting rateis derived to second order, which is the lowest order giving a non-vanishing contribution.The result separates into an anomalous contribution, expressed throughgreater anomalous Green’s functions, and a normal contribution, expressed throughlesser normal Green’s functions. The anomalous part describes correlated emissionassociated with a single Cooper pair, while the normal part describes contributionsfrom ordinary single-particle correlations.The main result is that odd-frequency pairing leads to a different momentum structurein the anomalous contribution than conventional even-frequency pairing. Inparticular, the odd-frequency kernel contains a difference of screened Coulomb potentials,whereas the even-frequency case contains their sum. Consequently, for asymmetric screened Coulomb potential, the momentum dependence of the electron–photon coupling becomes essential for obtaining a finite odd-frequency anomalouscontribution. The derived expression therefore identifies a key formal distinctionbetween even- and odd-frequency superconductors in double photoelectron spectroscopyand provides a basis for future numerical and experimental investigations.