Jahn-Teller Coupled Charge Density Wave in A Two Orbital Double Exchange System

In a two orbital double exchange 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 $Q_2$ or $Q_3$ 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 $Q_2$ distortion mode yields lowest free energy. The calculated heat capacity for each mode shows $T^3$ behavior at low temperature. Effect of electron-lattice interaction on collective mode, such as amplitude mode, is more pronounced when the excited mode is $Q_2$.