Correlation effects in the emergence of Bound Spin State in the Continuum

Bound States in the Continuum (BICs) are states with localized wave-function even though lying in the continuum. Here, we explore theoretically the emergence of a Spin-BIC 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 dot symmetry, we work with the bonding and anti-bonding (AB) levels resulting from the symmetric and antisymmetric combinations of the dot levels. We consider a Two-Impurity Anderson model. In the non-interacting limit (U=0), the AB orbital is decoupled from the conduction band and is hence a BIC. For U≠0, our Numerical Renormalization-Group results show that the interaction couples the bonding and anti-bonding orbitals and hence broadens the latter. The RKKY interaction between the magnetic moments of the two dots can either be ferro- or antiferromagnetic, to form a singlet or a triplet, which affects the formation of the Kondo cloud. In the strongly particle-hole asymmetric coupling limit, the AB orbital is reduced to a singly occupied level that is decoupled from the continuum, i.e., a Spin-BIC.