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Register a new userZero Energy States for a Class of Two-Dimensional Potentials in Graphene
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The excitations in graphene and some other materials are described by two-dimensional massless Dirac equation with applied external potential of some kind. Solutions of this zero energy equation are built analytically for a wide class of scalar potentials. In contrast to most publications on analytical solutions of massless two-dimensional Dirac equation, our potentials really depend on both spatial coordinates in some bounded domain. Several examples of such construction are given explicitly.
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The Su-Schrieffer-Heeger (SSH) model on a two-dimensional square lattice has been considered as a significant platform for studying topological multipole insulators. However, due to the highly-degenerate bulk energy bands protected by $ C_{4v} $ and chiral symmetry, the discussion of the zero-energy topological corner states and the corresponding physical realization have been rarely presented. In this work, by tuning the hopping terms to break $ C_{4v} $ symmetry down to $ C_{2v} $ symmetry but with the topological phase invariant, we show that the degeneracies can be removed and a complete band gap can be opened, which provides robust protection for the spectrally isolated zero-energy corner states. Meanwhile, we propose a rigorous acoustic crystalline insulator and therefore these states can be observed directly. Our work reveals the topological properties of the robust zero-energy states, and provides a new way to explore novel topological phenomena.
We present a tight-binding theory of triangular graphene quantum dots (TGQD) with zigzag edge and broken sublattice symmetry in external magnetic field. The lateral size quantization opens an energy gap and broken sublattice symmetry results in a shell of degenerate states at the Fermi level. We derive a semi-analytical form for zero-energy states in a magnetic field and show that the shell remains degenerate in a magnetic field, in analogy to the 0th Landau level of bulk graphene. The magnetic field closes the energy gap and leads to the crossing of valence and conduction states with the zero-energy states, modulating the degeneracy of the shell. The closing of the gap with increasing magnetic field is present in all graphene quantum dot structures investigated irrespective of shape and edge termination.
We investigate zero-bias conductance peaks that arise from coalescing subgap Andreev states, consistent with emerging Majorana zero modes, in hybrid semiconductor-superconductor wires defined in a two-dimensional InAs/Al heterostructure using top-down lithography and gating. The measurements indicate a hard superconducting gap, ballistic tunneling contact, and in-plane critical fields up to $3$~T. Top-down lithography allows complex geometries, branched structures, and straightforward scaling to multicomponent devices compared to structures made from assembled nanowires.
We study the energy level structures of the defective graphane lattice, where a carbon dimer defect is created by removing the hydrogen atoms on two nearest-neighbor carbon sites. Robust defect states emerge inside the bulk insulating gap of graphane. While for the stoichiometric half-filled system there are two doubly degenerate defect levels, there are four nondegenerate and spin-polarized in-gap defect levels in the system with one electron less than half filling. A universal set of quantum gates can be realized in the defective graphane lattice, by triggering resonant transitions among the defect states via optical pulses and emph{ac} magnetic fields. The sizable energy separation between the occupied and the empty in-gap states enables precise control at room temperature. The spatial locality of the in-gap states implies a qubit network of extremely high areal density. Based on these results, we propose that graphane as a unique platform could be used to construct the future all-purpose quantum computers.
The intertwining relations between superpartner Hamiltonians are the main ingredients of well known Supersymmetrical Quantum Mechanics (SUSY QM). In the present paper, the generalized form of intertwining is used for investigation of a massless (zero energy) two-dimensional Dirac equation with scalar external potential. This equation is related to the description of graphene and some other materials in the field of external electrostatic potential. The use of modified intertwining relations allows to find analytically solutions for the wave functions in the field of some external scalar potentials which depend on both space coordinates. A few examples of this construction are given explicitly.
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