We develop a variational approach to an extended Holstein model, comprising both local and nonlocal electron-phonon coupling. The approach is based on the minimization of a Bogoliubov bound to the Helmholtz free energy. The ambivalent character of nonlocal coupling, which both promotes and hinders transport, is clearly observed. Furthermore, a salient feature of our results is that the local and nonlocal couplings can compensate each other, leading to a reduction of polaronic effects and a quasi-free character of the excitation. Our findings have implications for organic crystals of p-conjugated molecules, where this electron-phonon coupling mechanism plays an important role.
Stojanovic, V. M., Bobbert, P. A., & Michels, M. A. J. (2004). Nonlocal electron-phonon coupling: consequences for the nature of polaron states. Physical Review B, 69(14), 144302-1/13. . https://doi.org/10.1103/PhysRevB.69.144302