# Possible two-component pairings in electron-doped Bi$_{2}$Se$_{3}$ based on a tight-binding model

## TL;DR

This paper systematically explores possible two-component pairing symmetries in electron-doped Bi2Se3 superconductors using a tight-binding model, highlighting the potential for complex, multichannel, and symmetry-breaking pairings.

## Contribution

It provides an exhaustive classification of two-component pairing channels in MxBi2Se3 superconductors based on a detailed tight-binding analysis, including their properties and experimental implications.

## Key findings

- Multiple pairing channels are possible, including nematic, chiral, and mixed states.
- Some pairings may be nonunitary and exhibit spontaneous magnetization.
- The true pairing likely involves multichannel combinations consistent with experimental data.

## Abstract

Recent experiments show the spontaneous breaking of rotational symmetry in the superconducting topological insulators M$_{x}$Bi$_{2}$Se$_{3}$ (M represents Cu, Sr, or Nd), suggesting that the pairing belongs to a two-dimensional representation of the $D_{3d}$ symmetry group of the crystal. Motivated by these progresses, we construct an exhaustive list of possible two-component pairings of the M$_{x}$Bi$_{2}$Se$_{3}$ superconductors, both for the odd-parity $E_{u}$ representation and for the even-parity $E_{g}$ representation. Starting from a tight-binding model for the normal phase of Bi$_{2}$Se$_{3}$ and M$_{x}$Bi$_{2}$Se$_{3}$, we firstly construct the pairing channels in the spin-orbital basis, up to second-nearest-neighbor pairing correlations in the basal plane. We then infer the properties of these pairings by transforming them to the band (pseudospin) basis for the conduction band. A comparison with the key experimental consensuses on M$_{x}$Bi$_{2}$Se$_{3}$ superconductors shows that the true pairings should also be multichannel. Besides a nematic and time-reversal symmetric pairing combination, the other pairings that we have identified are chiral and nematic at the same time, which may be nonunitary and have a spontaneous magnetization. A complementary set of experiments are proposed to identify the true pairing symmetries of these superconductors and their evolution with the doping concentration $x$.