Polaron effects on an anisotropic quantum dot in a magnetic field

The polaronic effects for an electron confined in a parabolic quantum dot and a uniform magnetic field are calculated, taking into account the electron-bulk LO-phonon interaction. The variational wave function is constructed as a product form of an electronic part and a part of coherent phonons generated by the Lee-Low-Pines transformation from the vacuum. An analytical expression for the polaron energy is found by the minimization procedure, and from this expression the ground- and first-excited-state energies are obtained explicitly. It is shown that the results obtained for the ground-state energy reduce to the existing works in zero magnetic fields. In the presence of a magnetic field, the confinement of the electron is examined in three different limiting cases both for the ground and first excited states, depending on certain parameters, such as the magnetic-field strength, the electron-phonon coupling strength, the polaron radius, and the confinement length.