Jahn–Teller coupled charge density wave in a double exchange system

In a two orbital model, we formulate Jahn–Teller coupled charge density wave in one electron per lattice site limit. Softening of Jahn–Teller phonons corresponding to distortion modes Q2Q2 or Q3Q3 associated with perfect nesting of Fermi surface leads to this instability at low temperature. The gap equation for charge density wave state and its dependences on electron–lattice coupling are calculated explicitly when any one of the Jahn–Teller modes is excited cooperatively. We find that the Q2Q2 distortion mode yields lowest free energy. Effect of electron–lattice interaction on collective mode, such as amplitude mode, is more pronounced when the excited mode is Q2Q2.