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Nanorod is a unique low-dimensional nanometer structure in which the Landau level arrangement of polaron is essential for understanding its' quasiparticle system. However, the stability of the polaron level is susceptible to external factors, such as changing magnetic fields. In this manuscript, the Pekar variational method is employed to calculate the external magnetic field's effect on the nanorod's polaron Landau level. It was found that different magnetic fields have different effects on the polaron energy levels of the nanorod, which demonstrated that the external environment had critical effects on the polaron energy levels. This study provides a theoretical basis for regulating the interaction between electrons and phonons in low-dimensional nanomaterials.

In this work, the energies and eigenfunctions of ground state and first-excited states (GFES) of a strongly coupled polaron in a quantum pseudo-dot (QPD) were studied by using variational method of Pekar type (VMPT). A single qubit can be realized in this two-level quantum system. Then, we calculated the coherence time of a QPD qubit by employing the Fermi Golden Rule. The temperature effects on the coherence time are taken into account by using the quantum statistics theory (QST) and self-consistent calculation method. According to the obtained results, it is found that the coherence time increases with decreasing temperature. Also, this time is a decaying function of the chemical potential of the two-dimensional electron gas and the zero point of the PHP.

In this research, the existence of an asymmetrical Gaussian confinement potential (AGCP) along the quantum well (QW) growth direction and of a parabolic potential perpendicular to the polar coordinate direction were considered. The magnetic field and temperature properties of the longitudinal optical (LO)-phonon mean number, ground-state energy (GSE), ground-state binding energy (GSBE) and vibrational frequency (VF) of strongly coupled magnetopolarons in triangular confinement potential QWs (TCPQWs) were investigated according to the quantum statistical theory as well as the linear combination operator and unitary transformation methods. We obtained analytical expressions for the GSE, GSBE, VF and LO-phonon mean number as functions of the applied magnetic field, temperature, AGCP barrier height, AGCP range, polar coordinate system’s polar angle and polar coordinate system’s confinement strength. It was demonstrated by the calculated numerical results that the GSE, GSBE, VF and LO-phonon mean number varied with the related physical quantities. The obtained theoretical results are expected to provide a reference for future research on polarons.

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