Momentum relaxation due to polar optical phonons in AlGaN/GaN heterostructures

Using the dielectric continuum (DC) model, momentum relaxation rates are calculated for electrons confined in quasi-two-dimensional (quasi-2D) channels of AlGaN/GaN heterostructures. Particular attention is paid to the effects of half-space and interface modes on the momentum relaxation. The total momentum relaxation rates are compared with those evaluated by the three-dimensional phonon (3DP) model, and also with the Callen results for bulk GaN. In heterostructures with a wide channel (effective channel width >100 Å), the DC and 3DP models yield very close momentum relaxation rates. Only for narrow-channel heterostructures do interface phonons become important in momentum relaxation processes, and an abrupt threshold occurs for emission of interface as well as half-space phonons. For a 30-Å GaN channel, for instance, the 3DP model is found to underestimate rates just below the bulk phonon energy by 70% and overestimate rates just above the bulk phonon energy by 40% compared to the DC model. Owing to the rapid decrease in the electron-phonon interaction with the phonon wave vector, negative momentum relaxation rates are predicted for interface phonon absorption in usual GaN channels. The total rates remain positive due to the dominant half-space phonon scattering. The quasi-2D rates can have substantially higher peak values than the three-dimensional rates near the phonon emission threshold. Analytical expressions for momentum relaxation rates are obtained in the extreme quantum limits (i.e., the threshold emission and the near subband-bottom absorption). All the results are well explained in terms of electron and phonon densities of states

Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons

The possibility of realizing bosonic fractional quantum Hall effect in ultra-cold atomic systems suggests a new route to producing and manipulating anyons, by introducing auxiliary bosons of a different species that capture quasiholes and thus inherit their non-trivial braiding properties. States with localized quasiholes at any desired locations can be obtained by annihilating the auxiliary bosons at those locations. We explore how this method can be used to generate non-Abelian quasiholes of the Moore-Read Pfaffian state for bosons at filling factor $\nu=1$. We show that a Hamiltonian with an appropriate three-body interaction can produce two-quasihole states in two distinct fusion channels of the topological "qubit." Characteristics of these states that are related to the non-Abelian nature can be probed and verified by a measurement of the effective relative angular momentum of the auxiliary bosons, which is directly related to their pair distribution function. Moore-Read states of more than two quasiholes can also be produced in a similar fashion. We investigate some issues related to the experimental feasibility of this approach, in particular, how large the systems should be for a realization of this physics and to what extent this physics carries over to systems with the more standard two-body contact interaction.Comment: 16 pages, 6 figure