arXiv subjects

A. Donís Vela

Publications and source records attributed to A. Donís Vela.

7 recordsLinked to original sources

arXiv2025

Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice

The massless two-dimensional Dirac equation in a perpendicular magnetic field B supports a B-independent "zeroth Landau level", a dispersionless zero-energy-mode protected by chiral symmetry. On a lattice the zero-mode becomes doubly degenerate with states of opposite chirality, which removes the protection and allows for a broadening when the magnetic field is non-uniform. It is known that this fundamental obstruction can be avoided by spatially separating the doubly degenerate states, adjoining +B and -B regions in a system of twice the size. Here we show that the same objective can be achieved without doubling the system size. The key ingredients are 1) a chirality-preserving "tangent fermion" discretization of the Dirac equation; and 2) a boundary condition that ensures the zero-mode contains only states of a single chirality.

cond-mat.mes-hall↗

arXiv2024

Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions

To apply the powerful many-body techniques of tensor networks to massless Dirac fermions one wants to discretize the $p\cdotσ$ Hamiltonian and construct a matrix-product-operator (MPO) representation. We compare two alternative discretization schemes, one with a sine dispersion, the other with a tangent dispersion, applied to a one-dimensional Luttinger liquid with Hubbard interaction. Both types of lattice fermions allow for an exact MPO representation of low bond dimension, so they are efficiently computable, but only the tangent dispersion gives a power law decay of the propagator in agreement with the continuum limit: The sine dispersion is gapped by the interactions, evidenced by an exponentially decaying propagator. Our construction of a tensor network with an unpaired Dirac cone works around the fermion-doubling obstruction by exploiting the fact that the \textit{nonlocal} Hamiltonian of tangent fermions permits a \textit{local} generalized eigenproblem.

cond-mat.str-el↗

arXiv2023

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 $B$ contains a $B$-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 $B$ 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 $+B$ and $-B$ regions.

cond-mat.mes-hall↗

arXiv2022

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 we introduce an implementation of Dirac fermions on a space-time lattice that removes both obstructions. 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. We show 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.

cond-mat.mes-hall↗

arXiv2022

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.

cond-mat.mes-hall↗

arXiv2021

Chirality inversion of Majorana edge modes in a Fu-Kane heterostructure

Fu and Kane have discovered that a topological insulator with induced s-wave superconductivity (gap $Δ_0$, Fermi velocity $v_{\rm F}$, Fermi energy $μ$) supports chiral Majorana modes propagating on the surface along the edge with a magnetic insulator. We show that the direction of motion of the Majorana fermions can be inverted by the counterflow of supercurrent, when the Cooper pair momentum along the boundary exceeds $Δ_0^2/μv_{\rm F}$. The chirality inversion is signaled by a doubling of the thermal conductance of a channel parallel to the supercurrent. Moreover, the inverted edge can transport a nonzero electrical current, carried by a Dirac mode that appears when the Majorana mode switches chirality. The chirality inversion is a unique signature of Majorana fermions in a spinful topological superconductor: it does not exist for spinless chiral p-wave pairing.

cond-mat.mes-hall↗

arXiv2020

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 $B$. The coupling of Fermi arcs on opposite surfaces broadens the Landau levels with a band width that oscillates periodically in $1/B$. 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 $1/B$-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.

cond-mat.mes-hall↗