Fingerprints of transverse and longitudinal coupling between induced open quantum dots in the longitudinal magnetoconductance through antidot lattices

Abstract

We propose numerical simulations of longitudinal magnetoconductance through a finite antidot lattice located inside an open quantum dot with a magnetic field applied perpendicular to the plane. The system is connected to reservoirs using quantum point contacts. We discuss the relationship between the longitudinal magnetoconductance and the generation of transversal couplings between the induced open quantum dots in the system. The system presents longitudinal magnetoconductance maps with crossovers ͑between transversal bands͒ and closings ͑longitudinal decoupling͒ of fundamental quantum states related to the open quantum dots induced by the antidot lattice. A relationship is observed between the distribution of antidots and the formed conductance bands, allowing a systematic follow up of the bands as a function of the applied magnetic field and quantum point-contact width. We observed a high conductance intensity ͓between n and ͑n +1͒ quantum of conductance, n =1,2,. . .͔ in the regions of crossover and closing of states. This suggests transversal couplings between the induced open quantum dots of the system that can be modulated by varying both the antidots potential and the quantum point-contact width. A new continuous channel ͑not expected͒ is induced by the variation in the contact width and generate Fano resonances in the conductance. These resonances can be manipulated by the applied magnetic field.

Exclusive sub-lattices for extended and localized states in graphene ribbons: their role in Klein tunneling, disorder and magnetic field effects

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Magneto-conductance fingerprints of purely quantum states in the open quantum dot limit

“…This will not be analyzed in this work, since we are interested in the low magnetic field limit for emulating a bona fide mesoscopic system, in which the host lattice effects are not important. Note that mesoscopic effects can modify the electronic structure associated with the tight binding host lattice [43]. This suggests that the results of the QW-OQD transition for both low energies (E < 20 meV) and magnetic fields (φ/φ 0 < 0.05) cannot be extrapolated to the high energy and magnetic field regimes.…”

Dedução da Matriz do Hamiltoniano Tight Binding usando a discretização da Equação de Schrödinger

“…Assim, a matriz Tight Binding (para o caso 2D) deduzida a partir da equação de Schrödinger é uma matriz de blocos tridiagonais [7,22]. Nesta matriz, o bloco diagonal é formado pelas cadeias transversais e os blocos secundarios são as submatrizes que conectam longitudinalmente às cadeias transversais.…”

“…Na seção seguinte, partindo da equação de Schrödinger, equação (1), e utilizando-se de um procedimento de discretização, deduziremos a matriz Tight Binding mostrada na equação (2). Posteriormente faremos uma extensão deste procedimento e deduziremos a matriz Tight Binding para o caso 2D [7,22].…”