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Potential energy entangler8/5/2023 One prime example is Bose–Einstein condensation, whose onset in a quantum liquid leads to phenomena such as superfluidity and superconductivity. The effect of quantum statistics in quantum gases and liquids results in observable collective properties among many-particle systems. We find for the hexagonal ring that the orbital degeneracy can still be controlled via the flux, similar to the ring with the mass confinement.Ĭoherent zero-state and pi-state in an exciton–polariton condensate arrayĬ. For the latter case, we study a ring of hexagonal form with lattice-terminated zigzag edges numerically. We compare our analytical model to another type of ring with strong intervalley scattering. The tunable breaking of the valley degeneracy by the flux allows for the controlled manipulation of valley isospins. This model describes rings with zero or weak intervalley scattering so that the valley isospin is a good quantum number. We explicitly confirm this prediction analytically for a circular ring with a smooth boundary modelled by a space-dependent mass term in the Dirac equation. The phenomenon has observable consequences on the persistent current circulating around the closed graphene ring, as well as on the ring conductance. We show that the combined effect of the ring confinement and applied magnetic flux offers a controllable way to lift the orbital degeneracy originating from the two valleys, even in the absence of intervalley scattering. We analyze theoretically the electronic properties of Aharonov-Bohm rings made of graphene. It also implies that nonelectronic systems with the same band structure as graphene, such as honeycomb-lattice photonic crystals, can exhibit pseudo-superconducting behavior.Īharonov-Bohm effect and broken valley-degeneracy in graphene rings This correspondence implies that bipolar junctions in graphene may have zero density of states at the Fermi level and carry a current in equilibrium, analogously to superconducting Josephson junctions. We derive that the energy spectra in the two systems are identical, at low energies E << Delta and for an antisymmetric potential profile U(-x,y)=-U(x,y). TworzydloĪndreev reflection at a superconductor and Klein tunneling through an n-p junction in graphene are two processes that couple electrons to holes - the former through the superconducting pair potential Delta and the latter through the electrostatic potential U. We discuss the applicability of such QDs to control and measure the valley isospin and their potential use for hosting and controlling spin qubits.Ĭorrespondence between Andreev reflection and Klein tunneling in bipolar grapheneĬ.W.J. The tunability of the gap in the bilayer case allows us to observe different regimes of level spacings directly related to the formation of a pronounced "Mexican hat" in the bulk bandstructure. Striking in the case of bilayer graphene is the anomalous bulk Landau level (LL) that crosses the gap which results in crossings of QD states with this bulk LL at large magnetic fields in stark contrast to the single-layer case where this LL is absent. We also point out the similarities and differences in the spectrum between single- and bilayer graphene quantum dots. This opens up a feasible route to create well-defined and well controlled spin- and valley-qubits in graphene QDs. We show that its degeneracy is efficiently and controllably broken by a magnetic field applied perpendicular to the graphene plane. Due to the absence of sharp edges in these types of QDs, the valley degree of freedom is a good quantum number. The magnetic field dependence of energy levels in gapped single- and bilayer graphene quantum dots (QDs) defined by electrostatic gates is studied analytically in terms of the Dirac equation.
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