We have studied an infinite Hubbard chain with a spin-orbit coupling term, submitted to a uniform magnetic field as well as local phonons. By means of a Lang-Firsov transformation, we show that an effective interacting fermion model emerges. Moreover, a self-consistent mean-field theory of this model,
formulated in terms of thermal Green's functions,
shows that a BCS term emerges, thus leading to a superconducting phase transition at zero temperature. We find analytical expressions for the phase boundary, that agree well with exact numerical diagonalization of the Hamiltonian.
A novel proof of principle prototype for a quantum heat engine is proposed, based on the quasi-static tuning of an external magnetic field, in combination with controlled mechanical strain applied to a single graphene flake. The "working fluid" of this engine is composed by a statistical ensemble of Dirac quasiparticles in Landau levels. The cyclic operation of the engine, whose intermediate states are described through a density matrix, is discussed in detail, and its thermodynamic efficiency is calculated in the quasi-static limit.