Corrigendum to “Single-cone real-space finite difference scheme for the time-dependent Dirac equation” [J. Comput. Phys. 265 (2014) 50–70]

Hammer, René; Pötz, W.; Arnold, Anton

doi:10.1016/j.jcp.2022.111118

Cited by 2 publications

(4 citation statements)

References 2 publications

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“…As shown in the left panel of Figure 6 , although

V_0&gt;\bar{E}

the tangent fermion is fully transmitted through the potential barrier. This is contrasted in the right panel with the partial transmission of the wave packet for a discretization on a staggered space‐time lattice, [ 38 ] which preserves chiral symmetry but has a second Dirac cone in the Brillouin zone. [ 38,39 ]…”

Section: Application: Klein Tunnelingmentioning

confidence: 99%

“…This is contrasted in the right panel with the partial transmission of the wave packet for a discretization on a staggered space‐time lattice, [ 38 ] which preserves chiral symmetry but has a second Dirac cone in the Brillouin zone. [ 38,39 ]…”

Section: Application: Klein Tunnelingmentioning

confidence: 99%

“…The color scale shows

|\Psi |^2

normalized to unit peak height at each of the three times. Full transmission is obtained for the tangent discretization without fermion doubling (left panel), while fermion doubling causes reflections for a staggered space‐time lattice discretization [ 38 ] (right panel). Reproduced with permission.…”

Section: Application: Klein Tunnelingmentioning

confidence: 99%

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Tangent Fermions: Dirac or Majorana Fermions on a Lattice Without Fermion Doubling

et al. 2023

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Methods to discretize the Hamiltonian of a topological insulator or topological superconductor, without giving up on the topological protection of the massless excitations (respectively, Dirac fermions or Majorana fermions) are reviewed. The method of tangent fermions, pioneered by Richard Stacey, is singled out as being uniquely suited for this purpose. Tangent fermions propagate on a 2+1${2\bm {+}1}$ dimensional space‐time lattice with a tangent dispersion: tan2(bold-italicε/2)=tan2(kx/2)+tan2(ky/2)${\text{tan}^2 (\bm {\varepsilon }/2) \bm {=} \text{tan}^2 (k_x/2) \bm {+}\text{tan}^2 (k_y/2)}$ in dimensionless units. They avoid the fermion doubling lattice artefact that will spoil the topological protection, while preserving the fundamental symmetries of the Dirac Hamiltonian. Although the discretized Hamiltonian is nonlocal, as required by the fermion‐doubling no‐go theorem, it is possible to transform the wave equation into a generalized eigenproblem that is local in space and time. Applications that are discussed include Klein tunneling of Dirac fermions through a potential barrier, the absence of localization by disorder, the anomalous quantum Hall effect in a magnetic field, and the thermal metal of Majorana fermions.

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“…As shown in the left panel of Figure 6 , although

V_0&gt;\bar{E}

Section: Application: Klein Tunnelingmentioning

confidence: 99%

Section: Application: Klein Tunnelingmentioning

confidence: 99%

“…The color scale shows

|\Psi |^2

Section: Application: Klein Tunnelingmentioning

confidence: 99%

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Tangent Fermions: Dirac or Majorana Fermions on a Lattice Without Fermion Doubling

et al. 2023

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“…Most of the investigations call for either semi-classical methods [17][18][19] or numerical calculations [20][21][22][23][24][25][26]. In addition to being computationally demanding, commonly used numerical schemes are plagued by unphysical artefacts at the fundamental level [27,28]; thus, there is a need for systematic construction of analytic solutions. RDI fulfils all these needs by providing stationary as well as time- * Electronic address: agontijo@mpi-hd.mpg.de dependent exact solutions in two and three dimensions (see [1] for other solutions).…”

Section: Introductionmentioning

confidence: 99%

Nondispersive analytical solutions to the Dirac equation

Campos

Cabrera

2020

Phys. Rev. Research

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This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first family of solutions describe the shape-preserving translation of a wavepacket along any desired trajectory in the x − y plane. In particular, we show that the dispersionless motion of a Gaussian wavepacket along both elliptical and circular paths can be achieved with rather simple electromagnetic field configurations. A second family of solutions involves a plane electromagnetic wave and a combination of generally inhomogeneous electric and magnetic fields. The novel analytical solutions of the Dirac equation given here provide important insights into the connection between the quantum relativistic dynamics of electrons and the underlying geometry of the Lorentz group.

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Corrigendum to “Single-cone real-space finite difference scheme for the time-dependent Dirac equation” [J. Comput. Phys. 265 (2014) 50–70]

Cited by 2 publications

References 2 publications

Tangent Fermions: Dirac or Majorana Fermions on a Lattice Without Fermion Doubling

Tangent Fermions: Dirac or Majorana Fermions on a Lattice Without Fermion Doubling

Nondispersive analytical solutions to the Dirac equation

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