Electron resonant tunneling through a circle-ring multicomponent quantum system

We theoretically study resonant tunneling for an electron injected into a multicomponent quantum (QCR) system composed of a quantum circle (QC) and quantum ring (QR). We first solve the time-independent Schrödinger equation numerically to determine the eigenstates of an electron confined in the QCR with an externally applied electrostatic (gate) potential. Several QC and QR local states hybridize mutually to produce the QCR eigenstates, resulting in crossing and/or avoided crossing of the eigenstates. Interestingly, local orbital hybridization is generated commensurately or incommensurately due to the coaxial geometry in the QCR system. The commensurate state produces a rational bonding-antibonding interaction whereas the incommensurate state causes a discrepancy in the position of the nodal planes of the QC and QR local orbitals. We then solve the time-dependent Schrödinger equation for the electron resonant tunneling through this QCR system computationally and study the dynamical properties based on projection analysis. When the electron is injected asymmetrically into the QCR system, quasidegeneracy in the eigenstates induces interstate interference and causes a characteristic "coming-and-going" variation in the electron density ρ. When the electron is injected into the avoided-crossing states produced by the incommensurate local-orbital mixing, the interstate interference induces a "rotational" motion in ρ in spite of the fact that the electrostatic gate potential is uniformly applied to the system.