Flat-lens focusing of electrons on the surface of a topological insulator

Hassler, Fabian; Akhmerov, A. R.; Beenakker, C. W. J.

doi:10.1103/physrevb.82.125423

Cited by 22 publications

(27 citation statements)

References 38 publications

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“…Unlike SLG and BLG where s = −1 states are always hole-like in the sense that the motion of electron is antiparallel to its wavevector, the s = −1 branch states of R2DEG are electron-like in the outer circle α = +1 and hole-like in the inner circle α = −1. The existence of hole-like states in the s = −1 branch suggests that negative electron refraction and electron focusing effect1617, previously reported in SLG11, BLG18 and topological insulator1920, can also be realized in R2DEG via transmission of electrons to α = −1 circle of the s = −1 branch.…”

Section: Resultssupporting

confidence: 54%

Chiral-like tunneling of electrons in two-dimensional semiconductors with Rashba spin-orbit coupling

Ang

Zhang

2014

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The unusual tunneling effects of massless chiral fermions (mCF) and massive chiral fermions (MCF) in a single layer graphene and bilayer graphene represent some of the most bizarre quantum transport phenomena in condensed matter system. Here we show that in a two-dimensional semiconductor with Rashba spin-orbit coupling (R2DEG), the real-spin chiral-like tunneling of electrons at normal incidence simultaneously exhibits features of mCF and MCF. The parabolic branch of opposite spin in R2DEG crosses at a Dirac-like point and has a band turning point. These features generate transport properties not found in usual two-dimensional electron gas. Albeit its π Berry phase, electron backscattering is present in R2DEG. An electron mimics mCF if its energy is in the vicinity of the subband crossing point or it mimics MCF if its energy is near the subband minima.

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Section: Resultssupporting

confidence: 54%

Chiral-like tunneling of electrons in two-dimensional semiconductors with Rashba spin-orbit coupling

Ang

Zhang

2014

Sci Rep

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“…For example, we conclude that implementation of the phase gate using charging energy, as described in Ref. 18, does not suffer from temperature being larger than the minigap since it relies on fermion parity, not on the wave-function structure.…”

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confidence: 96%

“…The signal strength however is reduced significantly when the temperature is comparable with the minigap due to dephasing of the internal degrees of freedom of vortices. Using interferometry of Josephson vortices, 18 which do not trap low-energy excitations allows to avoid this problem.…”

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confidence: 99%

Topological quantum computation away from the ground state using Majorana fermions

Akhmerov

2010

Phys. Rev. B

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We relax one of the requirements for topological quantum computation with Majorana fermions. Topological quantum computation was discussed so far as manipulation of the wave function within degenerate many-body ground state. The simplest particles providing degenerate ground state, Majorana fermions, often coexist with extremely low-energy excitations so keeping the system in the ground state may be hard. We show that the topological protection extends to the excited states, as long as the Majorana fermions do not interact neither directly nor via the excited states. This protection relies on the fermion parity conservation and so it is generic to any implementation of Majorana fermions.Topological quantum computation is manipulation of the wave function within a degenerate many-body ground state of many nonabelian anyons. Interchanging the anyons applies a unitary transformation to the ground-state wave function. The simplest of the nonabelian anyons useful for topological quantum computation are Majorana fermions. These are expected to exist in 5/2 fractional quantum Hall effect 1 and in certain exotic superconductors. [2][3][4][5] In 5/2 fractional quantum Hall effect, the Majorana fermions are charge e / 4 quasiholes, and in superconductors Majorana fermions are zero-energy single-particle states either trapped in vortex cores or other inhomogeneities. 2,[6][7][8] Superconducting implementations of Majorana fermions potentially allow for a larger bulk gap of a few kelvin as compared with 500 mK for fractional quantum Hall effect. One significant difference between the superconductors and the fractional quantum Hall effect is that Majorana fermions in superconductors appear where the superconducting gap in excitation spectrum closes. This means that Majorana fermions would not be isolated from other excitations by the bulk gap but coexisting with a lot of bound fermionic states with level spacing on the order of the minigap ⌬ 2 / E F , where ⌬ ϳ 1 K is the superconducting gap and E F the fermi energy. 9 If E F ϳ 1 eV, minigap is at least a thousand times smaller than the bulk gap so coupling between Majorana states and excited states is unavoidable with existing experimental methods. Already detection of Majorana fermions becomes problematic in this regime and requires ballistic samples and spatial resolution of density of states on the scale of Fermi wavelength. 10 This is why there is research aimed at increasing the minigap. 11 We adopt a different strategy and show that coupling to excited states does not remove the topological protection as long as different Majorana fermions stay decoupled. The topological protection persists because coupling to excited states has to preserve the global fermion parity. Using only the conservation of the global fermion parity and the fact that different Majorana fermions are well separated, we identify new Majorana operators, which are protected even if the original Majorana fermions coexist with many excited states. We also check that the braiding rules for the new Major...

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“…12 With the theoretically predicted existence of topologically protected surface states confirmed in experiment, one of the next steps is to learn to manipulate them by structural design and to utilize their properties in chiral fermion devices. On the theoretical side, numerous papers have been published on related topics, such as magneto-transport on TI surfaces in presence of ferromagnetic layers, [13][14][15][16][17][18] spinpolarized magnetic impurities on TI surfaces and Landau levels, [19][20][21][22][23] the interaction of magnetic domain walls with Dirac fermions, [24][25][26] lensing effects and transport perpendicular to domain walls, 27,28 crossover from weak antilocalization to weak localization, 29 and gate control of TI channel states. 30 An interferometer for chiral fermions has been proposed recently.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of domain-wall Dirac fermions on a topological insulator: A chiral fermion beam splitter

Hammer

Pötz

2013

Phys. Rev. B

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The intersection of two ferromagnetic domain walls placed on the surface of topological insulators provides a one-way beam splitter for domain-wall Dirac fermions. Based on an analytic expression for a static two-soliton magnetic texture we perform a systematic numerical study of the propagation of Dirac wave packets along such intersections. A single-cone staggered-grid finite difference lattice scheme is employed in the numerical analysis. It is shown that the angle of intersection plays a decisive role in determining the splitting ratio of the fermion beam. For a non-rectangular intersection, the width and, to a lesser extent, the type of domain walls, e.g. Bloch or Néel, determine the properties of the splitter. As the ratio between domain-wall width and transverse localization length of the Dirac fermion is increased its propagation behavior changes from quantum-mechanical (wave-like) to classical ballistic (particle-like). An electric gate placed near the intersection offers a dynamic external control knob for adjusting the splitting ratio.

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Flat-lens focusing of electrons on the surface of a topological insulator

Cited by 22 publications

References 38 publications

Chiral-like tunneling of electrons in two-dimensional semiconductors with Rashba spin-orbit coupling

Chiral-like tunneling of electrons in two-dimensional semiconductors with Rashba spin-orbit coupling

Topological quantum computation away from the ground state using Majorana fermions

Dynamics of domain-wall Dirac fermions on a topological insulator: A chiral fermion beam splitter

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