Repulsion of single-well fundamental edge magnetoplasmons in double quantum wells

A microscopic treatment of fundamental edge magnetoplasmons (EMP’s) along the edge of a double quantum well (DQW) is presented for strong magnetic fields, low temperatures, and total filling factor $\nu =2.\mathrm{}$ It is valid for lateral confining potentials that Landau-level flattening can be neglected. The cyclotron and Zeeman energies are assumed larger than the DQW energy splitting $\sqrt{{\Delta }^2{+4T}^2},$ where $\Delta$ is the splitting of the isolated wells and T the tunneling matrix element. Using a random-phase approximation, which includes local and nonlocal contributions to the current density, it is shown that for negligible tunnel coupling $2T\ll \Delta$ the interwell Coulomb coupling leads to two DQW fundamental EMP’s, which are strongly renormalized in comparison with the decoupled, single-well fundamental EMP. These DQW modes can be modified further upon varying the interwell distance d, along the z axis, and/or the separation of the wells’ edges $\Delta y$ along the y axis. The charge profile of the fast and slow DQW mode varies, respectively, in an acoustic and optical manner along the y axis and is not smooth on the ${\mathcal{l}}_0$ scale. For strong tunneling $\Delta \lesssim 2T$ these DQW modes are essentially modified when $\Delta$ is changed by applying a transverse electric field to the DQW.