Bound-states and polarized charged zero modes in three-dimensional topological insulators induced by a magnetic vortex

Fonseca, Jakson M.; Moura-Melo, W. A.; Pereira, A. R.

doi:10.1140/epjb/e2013-40812-9

Cited by 6 publications

(9 citation statements)

References 57 publications

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“…For ξ = −1 the antiparticle energy as a function of β is equal to zero at β = 1/2, and the wave function of antiparticle state with E a = 0 is F a (r) = σ 3 F * (r), where F (r) is determined by (28). Therefore, the AB vector potential can yield bound states and localized spinpolarized charged zero modes (see, also [39,40]). Since F a (r) does not coincide with F (r) the fermionic charge keeps integer.…”

Section: Relativistic Bound Fermion States In 2+1 Dimensionsmentioning

confidence: 99%

Bound states of massive fermions in Aharonov–Bohm-like fields

Khalilov

2014

Eur. Phys. J. C

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Bound states of massive fermions in AharonovBohm (AB)-like fields have analytically been studied. The Hamiltonians with the (AB)-like potentials are essentially singular and therefore require specification of a one-parameter self-adjoint extension. We construct selfadjoint Dirac Hamiltonians with the AB potential in 2+1 dimensions that are specified by boundary conditions at the origin. It is of interest that for some range of the extension parameter the AB potential can bind relativistic charged massive fermions. The bound-state energy is determined by the AB magnetic flux and depends upon the fermion spin and extension parameter; it is a periodical function of the magnetic flux. We also construct self-adjoint Hamiltonians for the so-called Aharonov-Casher (AC) problem, show that nonrelativistic neutral massive fermions can be bound by the (AC) background, determine the range of the extension parameter in which fermion bound states exist, and find their energies as well as wave functions.

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Section: Relativistic Bound Fermion States In 2+1 Dimensionsmentioning

confidence: 99%

Bound states of massive fermions in Aharonov–Bohm-like fields

Khalilov

2014

Eur. Phys. J. C

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“…More recently, the work of Ref. [34] suggests an interesting possibility to experimentally realize a 2D hydrogen atom in connection with magnetic vortices in topological insulators.…”

Section: Introductionmentioning

confidence: 99%

Effects on the non-relativistic dynamics of a charged particle interacting with a Chern-Simons potential

et al. 2013

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The hydrogen atom in two dimensions, described by a Schrödinger equation with a Chern-Simons potential, is numerically solved. Both its wave functions and eigenvalues were determined for small values of the principal quantum number n. The only possible states correspond to l = 0. How the result depends on the topological mass of the photon is also discussed. In the case n = 1, the energy of the fundamental state, corresponding to different choice for the photon mass scale, are found to be comprehended in the interval −3.5 × 10 −3 eV ≤ E ≤ −9.0 × 10 −2 eV, corresponding to a mean radius of the electron in the range (5.637 ± 0.005) × 10 −8 cm ≤ r ≤ (48.87 ± 0.03) × 10 −8 cm. In any case, the planar atom is found to be very weekly bounded showing some features similar to the Rydberg atoms in three dimensions with a Coulombian interaction.PACS. 03.65.-w Quantum mechanics -03.65.Ge Solutions of wave equations: bound states

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“…Charged zero-modes can be also found in a topological insulator when its surface is coated with a ferromagnetic film supporting an in-plane magnetic vortex. In this case, they have the additional property of being fully polarized modes located near the vortex center [37].…”

Section: Physical Spectrum: Bound-states and Zero-modesmentioning

confidence: 99%

Berry phases and zero-modes in toroidal topological insulator

et al. 2016

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An effective Hamiltonian describing the surface states of a toroidal topological insulator is obtained, and it is shown to support both bound-states and charged zero-modes. Actually, the spin connection induced by the toroidal curvature can be viewed as an position-dependent effective vector potential, which ultimately yields the zero-modes whose wave-functions harmonically oscillate around the toroidal surface. In addition, two distinct Berry phases are predicted to take place by the virtue of the toroidal topology.

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Bound-states and polarized charged zero modes in three-dimensional topological insulators induced by a magnetic vortex

Cited by 6 publications

References 57 publications

Bound states of massive fermions in Aharonov–Bohm-like fields

Bound states of massive fermions in Aharonov–Bohm-like fields

Effects on the non-relativistic dynamics of a charged particle interacting with a Chern-Simons potential

Berry phases and zero-modes in toroidal topological insulator

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