NONLOCAL PERIMETER MAGNETOPLASMONS IN A PLANAR ARRAY OF NARROW QUANTUM RINGS

The collective excitations (perimeter magnetoplasmons) for a square-lattice array of quantum rings are calculated in the presence of a perpendicular magnetic field B. These calculations are done for thin rings whose width W is taken to be much smaller than the radius R and also satisfying W much less than L(H) where L(H) = (hcBAR/eB)1/2 is the magnetic length. The Coulomb interaction between electrons produces a depolarization shift and also couples those transitions for which DELTA-m is different, where DELTA-m is the difference between the angular momentum quantum numbers for the initial and final states. This coupling induces a small gap between the DELTA-m and - DELTA-m modes as well as a large gap between the states with different values of \DELTA-m\. This gap decreases as \DELTA-m\ increases. The collective excitation energies are also a periodic function of the magnetic flux PHI = pi-BR2 within a ring, with period equal to one flux quantum phi-0 = hc/e. Only those excitations having the smallest difference +/-hBAR in angular momentum have appreciable dispersion due to strong Coulomb interaction effects on them. There is a peak in the excitation energy spectrum for some value of the lattice constant a due to a competition between screening and the modification in the electron density. Moreover, there is an abrupt change in the slope of the dispersion curve as a function of 1/R2 when the magnetic flux PHI is either an integer or half-odd integer multiple of the flux quantum phi-0.