Method to preserve the chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice

Vela, A. Donís; Lemut, G.; Tworzydło, J.; Beenakker, C. W. J.

doi:10.1016/j.aop.2022.169208

Cited by 1 publication

(5 citation statements)

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“…[52] Indeed, the Landau level spectrum for tangent fermions has a zeroth Landau level in both the C = +1 and C = −1 manifold. [48] One way to understand this obstruction, is to consider the process by which a uniform magnetic field is concentrated into an array of h∕e flux tubes, each of which is fully contained within a unit cell. The winding number cannot change by such a smooth deformation, but the resulting magnetic field distribution may be gauged away on the lattice, hence the net value of C must be equal to zero.…”

Section: Topologically Protected Zeroth Landau Levelmentioning

confidence: 99%

“…[ 52 ] Indeed, the Landau level spectrum for tangent fermions has a zeroth Landau level in both the

C=+1

and

C=-1

manifold. [ 48 ]…”

Section: Application: Anomalous Quantum Hall Effectmentioning

confidence: 99%

“…Fortunately, there is a work‐around: [ 48 ] One may spatially separate the opposite chirality manifolds by adjoining a

+B

and

-B

region next to each other in the 2D plane. Each of the two regions then has a chirality polarized zeroth Landau level.…”

Section: Application: Anomalous Quantum Hall Effectmentioning

confidence: 99%

“…The density of states (DOS) of the zeroth Landau level is not broadened by a spatially fluctuating B, provided that the slab thickness d is sufficiently large that the two surfaces are decoupled. Reproduced under the terms of the CC-BY 4.0 license [48]. Published 2023, Elsevier.…”

mentioning

confidence: 99%

“…The plot is for m 0 = ℏv∕a. Reproduced under the terms of the CC-BY 4.0 license [48]. Published 2023, Elsevier.…”

mentioning

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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Section: Topologically Protected Zeroth Landau Levelmentioning

confidence: 99%

“…[ 52 ] Indeed, the Landau level spectrum for tangent fermions has a zeroth Landau level in both the

C=+1

and

C=-1

manifold. [ 48 ]…”

Section: Application: Anomalous Quantum Hall Effectmentioning

confidence: 99%

“…Fortunately, there is a work‐around: [ 48 ] One may spatially separate the opposite chirality manifolds by adjoining a

+B

and

-B

region next to each other in the 2D plane. Each of the two regions then has a chirality polarized zeroth Landau level.…”

Section: Application: Anomalous Quantum Hall Effectmentioning

confidence: 99%

mentioning

confidence: 99%

“…The plot is for m 0 = ℏv∕a. Reproduced under the terms of the CC-BY 4.0 license [48]. Published 2023, Elsevier.…”

mentioning

confidence: 99%

See 3 more Smart Citations

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

et al. 2023

Self Cite

View full text Add to dashboard Cite

show abstract

Method to preserve the chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice

Cited by 1 publication

References 20 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

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