Theory of Electron-phonon Couplings in 3D Quantum Hall Effects

The 3D quantum Hall effect modulated by electron-phonon interactions has been observed recently and has aroused many theoretical discussions. In 3D, because the Landau levels in x-y plane have dispersions in z direction, the bulk state is metallic unless the charge-density-wave (CDW) opens the gaps at Fermi energy. In this research, we developed a numerical way to approach the ground states of the system by considering all possible phonon modes and minimizing the ground state energy. In the process of modulating the effective magnetic field and the effective electron-phonon coupling strength, we demonstrated the ground state phase transitions from (n+1)-levels to n-levels. More importantly, we discovered a novel metallic phase within the transitions, which may account for the plateau in 3D quantum Hall resistance.