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The theory of inelastic electron resonant tunneling through a double-barrier nanostructure is extended to establish a theory of phonon-assisted resonant magnetotunneling when a magnetic field is applied parallel to the tunneling current. At higher temperatures we have discovered an interesting characteristic oscillation of the width and height of the main peak in the I-Y curve when the ratio ω 0 /ω c changes between integer (double resonant) and half integer (single resonant), where ω 0 is the LO phonon frequency and ω c is the cyclotron frequency in the well. If confirmed experimentally, our theoretical prediction provides an additional method to determine the electronic effective mass in the well

The lifetime τ e of an electron occupying the quasibound state in an Al x Ga 1-x As/GaAs doublebarrier structure has been calculated with both the tunneling Hamiltonian approach and the complex eigenvalue method. It is found that τ e is dominated by the barrier width, but is insensitive to the well width and the bias. We have also investigated the effect of the electron-LO-phonon interaction on the dynamics of the electron in the quasibound state

The inelastic scattering effect on electron tunneling through a double-barrier resonant tunneling device has been studied with a cumulant expansion on the electron transmission probability and the I-V characteristics using the Frohlich Hamiltonian which allows electron recoil enhances the incoherence process and so broadens the phonon replica, which is also shifted towards the main peak

We consider electrons tunneling through a double-barrier resonant-tunneling structure (DBRTS) and interacting with a defect which has internal degrees of freedom. Usually such a defect has two (or more) metastable configurations and can switch between them due to its interaction with a thermal bath. Interaction between the tunneling electron and the dynamic defect creates a noisy environment surrounding the DBRTS, and leads to fluctuations in time of the resonant level. Such fluctuations result in inelastic tunneling and low-frequency noise. This paper is focused on the problem of inelastic resonant tunneling. We have calculated the average transparency for various relations between the switching rate of the dynamic defect, the escape rate of the electron from the resonant level in the well, the coupling strength between the electron and the dynamic defect, and the temperature. The results derived here are entirely different from those found in phonon-assisted resonant tunneling, because phonons obey the Bose statistics but a two-level fluctuator behaves as an effective spin.

Although there may exist a large intrasite Coulomb repulsion, the local mode can still induce a attractive interaction between electrons through oxygen breathing mode. This interaction plays an imporatnt role in raising Tc. The result approaches that of experiment by a combination of the local mode and the Van Hove singularity.

We proposed that BCS-like Hamiltonian with quasi-two-dimensional tight-binding electrons describe the Ba-La-Cu-O system approximately. Tc was calculated under the cases both negligible and non-negligible weak coupling between neighbor layers. It is found that the results we obtained approach that of experiments.