Condensed Matter Seminar "Correlation effects in the emergence of bound states in the continuum"
Bound states in the continuum (BICs) are states with localized wave-functions even though lying in the continuum. Here, we explore theoretically the emergence of BICs in a system comprising two identical quantum dots side-coupled to a quantum wire. The dots are symmetrically coupled to the site at the center of the wire and to its nearest neighbors. Taking advantage of the parity symmetry, we work with the bonding and the anti-bonding (AB) levels resulting from the symmetric and antisymmetric combinations of the dot levels. Based on the two-impurity Anderson Hamiltonian and the numerical renormalization group method, our results show that the AB orbital is a BIC in the non-interacting limit. The AB orbital is broadened due the spin-spin and spin-flip interactions between the two orbitals. In addition, if the coupling is particle-hole asymmetric, the magnetic moments of the dots can form a triplet or a singlet state due to the RKKY interaction, affecting the formation of the Kondo cloud. In the strong asymmetric coupling limit, the AB orbital is reduced to a singly occupied level that is decoupled from the continuum, i.e., a bound spin states in the continuum.