Aharanov-Bohm oscillations of conductance in two-dimensional rings

Abstract

Transport properties of mesoscopic rings with applied external magnetic field are considered numerically. Rings have square and circular forms and a finite aspect ratio $d/L$ where $L$ is the ring size and $d$ is the width of ring arms. The type of the Aharonov-Bohm oscillations (ABO's) of the transmission substantially depends on the number of channels participating in the electron transmission. Moreover the aspect ratio and the geometrical form of the ring are important for the ABO's. In square rings with a small aspect ratio $(d/L=1/10)$ the transmission displays periodic ABO's in the region of applied magnetic field defined by the inequality $\ensuremath{\infty}>{l}_{B}=(\ensuremath{\Elzxh}{c/eB)}^{1/2}>~d$, while for rings with a large aspect ratio $(d/L=1/3)$ only the single-channel transmission has quasiperiodical ABO's. For the circular rings with small aspect ratios the quasiperiodic ABO's are observed all over the region of the applied magnetic field while for the rings with moderate aspect ratios only the multichannel transmission displays irregular ABO's. The probability current flow patterns demonstrate fine correspondence between the transmission and the vortex structure of current distributions in the rings. For single-channel transmission, electron currents are laminar. For multichannel transport, current flow patterns display a complicated convection pattern in the form of a vortex lattice. An elementary cell of the vortex lattice consists of a few vortices and antivortices and has a size of $\ensuremath{\sim}d/f$, where $f$ is the number of channels of electron transmission in the ring. Application of the flux distorts the vortex lattice enormously, partially destroying it. Correspondingly the Aharonov-Bohm oscillations of the transmission become irregular.