Bi-stability in a two-level quantum dot with attracting e-e interaction

By considering a current carrying two-level quantum dot (QD) with e-e attraction, we obtain the current and electron populations as functions of applied bias voltage using a self-consistent Hartree-Fock (HF) approximation and show that the system could be bi-stable and there exist hysteresis loops. Investigating the permanent polarization, we also show that the permanent polarization changes sign and interpret this as a quantum phase transition, since our system is at zero temperature.