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Register a new userBound states in the continuum: localization of Dirac-like fermions
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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 density of states and electronic conductance calculations. By applying a gate voltage, the bound states couple to the continuum, yielding a maximum in the electronic transmission. This feature can be exploited to identify bound states in the continuum in graphene-based structures.
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We theoretically investigate a topological Kitaev chain connected to a double quantum-dot (QD) setup hybridized with metallic leads. In this system we observe the emergence of two striking phenomena: (i) a decrypted Majorana fermion (MF) qubit recorded over a single QD, which is detectable by means of conductance measurements due to the asymmetrical MF-qubit leaked state into the QDs; (ii) an encrypted qubit recorded in both QDs when the leakage is symmetrical. In such a regime, we have a cryptographylike manifestation, since the MF qubit becomes bound states in the continuum, which is not detectable in conductance experiments.
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 symmetry. When the system is coupled to leads with a continuum energy band, part of these states remain bound. We derive some algebraic rules for the number of these states depending on the dimensionality and rank of the total Hamiltonian. We examine the transport properties of such systems including the appearance of Fano resonances in some limiting cases. Finally, we discuss experimental setups based on microwave dielectric resonators and atoms in optical lattices where these predictions can be tested.
Majorana bound states appearing in 1-D $p$-wave superconductor ($cal{PWS}$) are found to result in exotic quantum holonomy of both eigenvalues and the eigenstates. Induced by a degeneracy hidden in complex Bloch vector space, Majorana states are identified with a pair of exceptional point ($cal{EP}$) singularities. Characterized by a collapse of the vector space, these singularities are defects in Hilbert space that lead to M$ddot{rm o}$bius strip-like structure of the eigenspace and singular quantum metric. The topological phase transition in the language of $cal{EP}$ is marked by one of the two exception point singularity degenerating to a degeneracy point with non singular quantum metric. This may provide an elegant and useful framework to characterize the topological aspect of Majorana fermions and the topological phase transition.
We report on a theoretical investigation of the interplay between vacuum fluctuations, Majorana quasiparticles (MQPs) and bound states in the continuum (BICs) by proposing a new venue for qubit storage.BICs emerge due to quantum interference processes as the Fano effect and, since such a mechanism is unbalanced, these states decay as regular into the continuum. Such fingerprints identify BICs in graphene as we have discussed in detail in Phys. Rev. B 92, 245107 and 045409 (2015). Here by considering two semi-infinite Kitaev chains within the topological phase, coupled to a quantum dot (QD) hybridized with leads, we show the emergence of a novel type of BICs, in which MQPs are trapped. As the MQPs of these chains far apart build a delocalized fermion and qubit, we identify that the decay of these BICs is not connected to Fano and it occurs when finite fluctuations are observed in the vacuum composed by electron pairs for this qubit. From the experimental point of view, we also show that vacuum fluctuations can be induced just by changing the chain-dot couplings from symmetric to asymmetric. Hence, we show how to perform the qubit storage within two delocalized BICs of MQPs and to access it when the vacuum fluctuates by means of a complete controllable way in quantum transport experiments.
We calculate the tunneling density-of-states (DOS) of a disorder-free two-dimensional interacting electron system with a massless-Dirac band Hamiltonian. The DOS exhibits two main features: i) linear growth at large energies with a slope that is suppressed by quasiparticle velocity enhancement, and ii) a rich structure of plasmaron peaks which appear at negative bias voltages in an n-doped sample and at positive bias voltages in a p-doped sample. We predict that the DOS at the Dirac point is non-zero even in the absence of disorder because of electron-electron interactions, and that it is then accurately proportional to the Fermi energy. The finite background DOS observed at the Dirac point of graphene sheets and topological insulator surfaces can therefore be an interaction effect rather than a disorder effect.
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