6 research outputs found
Method to preserve the chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice
The spectrum of massless Dirac fermions on the surface of a topological
insulator in a perpendicular magnetic field contains a -independent
"zeroth Landau level", protected by chiral symmetry. If the Dirac equation is
discretized on a lattice by the method of "Wilson fermions", the chiral
symmetry is broken and the zeroth Landau level is broadened when has
spatial fluctuations. We show how this lattice artefact can be avoided starting
from an alternative nonlocal discretization scheme introduced by Stacey. A key
step is to spatially separate the states of opposite chirality in the zeroth
Landau level, by adjoining and regions.Comment: Contribution to a special issue of Annals of Physics in memory of
Kostya Efeto
Magnetic breakdown spectrum of a Kramers-Weyl semimetal
We calculate the Landau levels of a Kramers-Weyl semimetal thin slab in a
perpendicular magnetic field . The coupling of Fermi arcs on opposite
surfaces broadens the Landau levels with a band width that oscillates
periodically in . We interpret the spectrum in terms of a one-dimensional
superlattice induced by magnetic breakdown at Weyl points. The band width
oscillations may be observed as -periodic magnetoconductance oscillations,
at weaker fields and higher temperatures than the Shubnikov-de Haas
oscillations due to Landau level quantization. No such spectrum appears in a
generic Weyl semimetal, the Kramers degeneracy at time-reversally invariant
momenta is essential.Comment: 13 pages, 18 figure
Massless dirac fermions on a space‐time lattice with a topologically protected dirac cone
The symmetries that protect massless Dirac fermions from a gap opening may become ineffective if the Dirac equation is discretized in space and time, either because of scattering between multiple Dirac cones in the Brillouin zone (fermion doubling) or because of singularities at zone boundaries. Here an implementation of Dirac fermions on a space-time lattice that removes both obstructions is introduced. The quasi-energy band structure has a tangent dispersion with a single Dirac cone that cannot be gapped without breaking both time-reversal and chiral symmetries. It is shown that this topological protection is absent in the familiar single-cone discretization with a linear sawtooth dispersion, as a consequence of the fact that there the time-evolution operator is discontinuous at Brillouin zone boundaries.Theoretical Physic
Dynamical simulation of the injection of vortices into a Majorana edge mode
Theoretical Physic
Reflectionless Klein tunneling of Dirac fermions: Comparison of split-operator and staggered-lattice discretization of the Dirac equation
Massless Dirac fermions in an electric field propagate along the field lines
without backscattering, due to the combination of spin-momentum locking and
spin conservation. This phenomenon, known as "Klein tunneling", may be lost if
the Dirac equation is discretized in space and time, because of scattering
between multiple Dirac cones in the Brillouin zone. To avoid this, a staggered
space-time lattice discretization has been developed in the literature, with
one single Dirac cone in the Brillouin zone of the original square lattice.
Here we show that the staggering doubles the size of the Brillouin zone, which
actually contains two Dirac cones. We find that this fermion doubling causes a
spurious breakdown of Klein tunneling, which can be avoided by an alternative
single-cone discretization scheme based on a split-operator approach.Comment: v1: first submission; v2: added appendix with gap opening
calculation; v3: added appendix that compares staggered fermions with naive
fermions; revised title, the original title was "Brillouin zone doubling
causes fermion doubling for a staggered lattice discretization of the Dirac
equation"; to appear in the JPCM special Issue on "Electron quantum optics in
Dirac materials