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n this article we study the Friedel phase of the electron transport in two different systems of quantum dots which exhibit bound states in the continuum (BIC). The Friedel phase jumps abruptly in the energies of the BICs, which is associated to the vanishing width of these states, as shown by Friedrich and Wintgen in Phys. Rev. A textbf{31}, 3964 (1985). This odd behavior of the Friedel phase has consequences in the charge through the Friedel sum rule. Namely, if the energy of the BIC drops under the Fermi energy the charge changes abruptly in a unity. We show that this behavior closely relates with discontinuities in the conductance predicted for interacting quantum dot systems.
We consider a square lattice configuration of circular gate-defined quantum dots in an unbiased graphene sheet and calculate the electronic, particularly spectral properties of finite albeit actual sample sized systems by means of a numerically exact
We present a distinct mechanism for the formation of bound states in the continuum (BICs). In chiral quantum systems there appear zero-energy states in which the wave function has finite amplitude only in one of the subsystems defined by the chiral s
We study the low-energy physics of a one-dimensional array of superconducting quantum dots realized by proximity coupling a semiconductor nanowire to multiple superconducting islands separated by narrow uncovered regions. The effective electrostatic
We study transport through a Weyl semimetal quantum dot sandwiched between an $s$-wave superconductor and a normal lead. The conductance peaks at regular intervals and exhibits double periodicity with respect to two characteristic frequencies of the
We report the formation of bound states in the continuum for Dirac-like fermions in structures composed by a trilayer graphene flake connected to nanoribbon leads. The existence of this kind of localized states can be proved by combining local densit