Phonon-mediated excitonic excitations in solids

Abstract

Phonon is probably the most well-known elementary excitation in solid state physics. In the spin-Peierls transition(SP), this phonon interacts with the one-dimensional antiferromagnetic chain of spins and this antiferromagnetc chain becomes nonmagnetic spontaneously because the resulting lattice distortion move ions and electrons to arrange for a dimerization. We investigate the spin-Peierls transition temperature, $T_c$ when ferromagnetic bonds (equivalent to solitons) are doped into the antiferromagnetic chain. A weak ferromagnetic ordering is possible below $T_c^{soliton}$ where $T_c^{soliton}/T_c$ ranges from 1 to 5 when the soliton density is small. In the ferromagnetic system, we derive electron-electron interactions mediated by phonons. Using the Hartree-Fock approximation, we can compute the magnetic susceptibility XK and obtain the ferromagnetic transition temperature which depends significantly on the parameters of the phonon-mediated electron-electron interaction, $V_{ph}$. $T_c$ can be obtained in agreement with the experimental values when $V_{ph}$ is probably chosen. We describe a new Hamiltonian which predicts an electron-hole pair excitation different from that of a coventional exciton in that we include electronphonon interactions in pair with hole-phonon interactions. We can then derive the indirect electron-hole interaction mediated by phonons using the Heisenberg equations and we find a new form of exciton from this indirect interaction. We also investigate the isotope effect in the excitonic high temperature superconductors(HTSC) and we calculate the isotope exponents. We show that the exciton-plasmon interaction is possible in HTSC and we may also have hole-doped exciton states and quasi-plasmons.