Resonant transmission through electronic quantum states that exist at the zero points of a magnetic field gradient inside a ballistic quantum wire is reported. Since the semiclassical motion along such a line of zero magnetic field takes place in form of unidirectional snake trajectories, these states have no classical equivalence. The existence of such quantum states has been predicted more than a decade ago by theoretical considerations of Reijniers and coworkers [1]. We further show how their properties depend on the amplitude of the magnetic field profile as well as on the Fermi energy.
We derive semiclassical quantization equations for graphene mono- and bilayer systems where the excitations are confined by the applied inhomogeneous magnetic field. The importance of a semiclassical phase, a consequence of the spinor nature of the excitations, is pointed out. The semiclassical eigenenergies show good agreement with the results of quantum mechanical calculations based on the Dirac equation of graphene and with numerical tight binding calculations.
While the dynamics for three-dimensional axially symmetric two-electron quantum dots with parabolic confinement potentials is in general non-separable we have found an exact separability with three quantum numbers for specific values of the magnetic field. Furthermore, it is shown that the magnetic properties such as the magnetic moment and the susceptibility are sensitive to the presence and strength of a vertical confinement. Using a semiclassical approach the calculation of the eigenvalues reduces to simple quadratures providing a transparent and almost analytical quantization of the quantum dot energy levels which differ from the exact energies only by a few percent.
We consider a three-dimensional topological insulator (TI) wire with a non-uniform chemical potential induced by gating across the cross-section. This inhomogeneity in chemical potential lifts the degeneracy between two one-dimensional surface state subbands. A magnetic field applied along the wire, due to orbital effects, breaks time-reversal symmetry and lifts the Kramers degeneracy at zero-momentum. If placed in proximity to an $s$-wave superconductor, the system can be brought into a topological phase at relatively weak magnetic fields. Majorana bound states (MBSs), localized at the ends of the TI wire, emerge and are present for an exceptionally large region of parameter space in realistic systems. Unlike in previous proposals, these MBSs occur without the requirement of a vortex in the superconducting pairing potential, which represents a significant simplification for experiments. Our results open a pathway to the realisation of MBSs in present day TI wire devices.
When magnetic field $B$ is applied to a metal, nearly all observable quantities exhibit oscillations periodic in $1/B$. Such quantum oscillations reflect the fundamental reorganization of electron states into Landau levels as a canonical response of the metal to the applied magnetic field. We predict here that, remarkably, in the recently discovered Dirac and Weyl semimetals quantum oscillations can occur in the complete absence of magnetic field. These zero-field quantum oscillations are driven by elastic strain which, in the space of the low-energy Dirac fermions, acts as a chiral gauge potential. We propose an experimental setup in which the strain in a thin film (or nanowire) can generate pseudomagnetic field $b$ as large as 15T and demonstrate the resulting de Haas-van Alphen and Shubnikov-de Haas oscillations periodic in $1/b$.
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.
B. Schuler
,M. Cerchez
,Hengyi Xu
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(2014)
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"Observation of quantum states without a semiclassical equivalence bound by a magnetic field gradient"
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Bernd Sch\\\"uler
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