Superconducting proximity in three-dimensional Dirac materials: Odd-frequency, pseudoscalar, pseudovector, and tensor-valued superconducting orders
Year: 2017
Type: article
Abstract: We find that a conventional $s$-wave superconductor in proximity to a three-dimensional Dirac material (3DDM), to all orders of perturbation in tunneling, induces a combination of $s$- and $p$-wave pairing only. We show that the Lorentz invariance of the superconducting pairing prevents the formation of Cooper pairs with higher orbital angular momenta in the 3DDM. This no-go theorem acquires stronger form when the probability of tunneling from the conventional superconductor to positive and negative energy states of 3DDM are equal. In this case, all the $p$-wave contribution except for the lowest order, identically vanish and hence we obtain an exact result for the induced $p$-wave superconductivity in 3DDM. Fierz decomposing the superconducting matrix we find that the temporal component of the vector superconducting order and the spatial components of the pseudovector order have odd-frequency pairing symmetry. We find that the latter is odd with respect to exchange of position and chirality of the electrons in the Cooper pair and is a spin-triplet, which is necessary for NMR detection of such an exotic pseudovector pairing. Moreover, we show that the tensorial order breaks into a polar vector and an axial vector and both of them have conventional pairing symmetry except for being a spin triplet. According to our study, for gapless 3DDM, the tensorial superconducting order will be the only order that is odd with respect to the chemical potential $\ensuremath{\mu}$. Therefore we predict that a transverse $p\ensuremath{-}n$ junction binds Majorana fermions. This effect can be used to control the neutral Majorana fermions with electric fields.
Authors: Zahra Faraei, S. A. Jafari
Institutions: Sharif University of Technology, University of Duisburg-Essen
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Sharif University of Technology
OpenAlex ID: W2589632573