Effective Mass of Bound Electron Pairs in Two-Dimensional Materials with a Gapped Band Spectrum

TL;DR

This paper investigates the effective mass of bound electron pairs in two-dimensional gapped materials, revealing a relationship between mass sign and energy position within the band gap, with implications for charge and spin transport.

Contribution

It provides a theoretical analysis of the effective mass of bound pairs in Bernevig-Hughes-Zhang model materials, highlighting the sign change across the band gap.

Findings

Mass sign changes at the band gap midpoint.

Effective mass depends on bound pair energy.

Distinct mass-energy relationships for different pair types.

Abstract

Bound electron pairs formed due to the peculiarities of the band dispersion of electrons in crystals attract much interest because they can carry charge and spin even in the absence of band conductivity. However, such an important parameter of bound pairs as the effective mass is still poorly understood. We carry out this study for materials described by the Bernevig-Hughes-Zhang model in the electron-hole symmetric case and find a clear relationship between the effective mass and the energy of a bound pair at rest. The dependence of mass on energy has a specific form for each of different types of pairs, but a common feature is the change of the mass sign when energy passes through the middle of the band gap. The sign is negative when the energy is in the lower half of the gap, and positive in the upper half.