Generalized eigenproblem without fermion doubling for Dirac fermions on  a lattice

Pacholski, M. J.; Lemut, G.; Tworzydło, J.; Beenakker, C. W. J.

doi:10.21468/scipostphys.11.6.105

Cited by 9 publications

(12 citation statements)

References 37 publications

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“…TMDCs are semiconducting 2D crystals, such as WSe 2 or MoS 2 , with strong spin-orbit. The possibility of inducing a strong SOC on graphene monolayers by placing it in contact to a TMDC was demonstrated using a variety of theoretical [66][67][68] and experimental techniques [55][56][57][57][58][59][60]. Two main types of SOC are generated on the low-energy sector of monolayer graphene close to the neutrality point: Ising and Rashba [59,60,67].…”

Section: Introductionmentioning

confidence: 99%

Majorana bound states in encapsulated bilayer graphene

et al. 2023

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The search for robust topological superconductivity and Majorana bound states continues, exploring both one-dimensional (1D) systems such as semiconducting nanowires and two-dimensional (2D) platforms. In this work we study a 2D approach based on graphene bilayers encapsulated in transition metal dichalcogenides that, unlike previous proposals involving the Quantum Hall regime in graphene, requires weaker magnetic fields and does not rely on interactions. The encapsulation induces strong spin-orbit coupling on the graphene bilayer, which opens a sizeable gap and stabilizes fragile pairs of helical edge states. We show that, when subject to an in-plane Zeeman field, armchair edges can be transformed into p-wave one-dimensional topological superconductors by contacting them laterally with conventional superconductors. We demonstrate the emergence of Majorana bound states (MBSs) at the sample corners of crystallographically perfect flakes, belonging either to the D or the BDI symmetry classes depending on parameters. We compute the phase diagram, the resilience of MBSs against imperfections, and their manifestation as a 4\piπ-periodic effect in Josephson junction geometries, all suggesting the existence of a topological phase within experimental reach.

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Section: Introductionmentioning

confidence: 99%

Majorana bound states in encapsulated bilayer graphene

et al. 2023

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“…Over the years, various remedies have been put forward that can be clustered into two general categories according to the dimensionality of the underlying model. The first category contains true two-dimensional models, such as Wilson fermions [2,3] or staggered fermions [4][5][6]. These are computationally efficient but complicate the description and bandstructure of the system.…”

Section: Introductionmentioning

confidence: 99%

Geometry-independent tight-binding method for massless Dirac fermions in two dimensions

Ziesen¹,

Fulga²,

Hassler³

2023

Preprint

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The Nielsen-Ninomiya theorem, dubbed 'fermion-doubling', poses a problem for the naive discretization of a single (massless) Dirac cone on a two-dimensional surface. The inevitable appearance of an additional, unphysical fermionic mode can, for example, be circumvented by introducing an extra dimension to spatially separate Dirac cones. In this work, we propose a geometry-independent protocol based on a tight-binding model for a three-dimensional topological insulator on a cubic lattice. The low-energy theory, below the bulk gap, corresponds to a Dirac cone on its two-dimensional surface which can have an arbitrary geometry. We introduce a method where only a thin shell of the topological insulator needs to be simulated. Depending on the setup, we propose to gap out the states on the undesired surfaces either by breaking the time-reversal symmetry or by introducing a superconducting pairing. We show that it is enough to have a thickness of the topological-insulator shell of three to nine lattice constants. This leads to an effectively two-dimensional scaling with minimal and fixed shell thickness. We test the idea by comparing the spectrum and probability distribution to analytical results for both a proximitized Dirac mode and a Dirac mode on a sphere which exhibits a nontrivial spin-connection. The protocol yields a tight-binding model on a cubic lattice simulating Dirac cones on arbitrary surfaces with only a small overhead due to the finite thickness of the shell.

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“…[13] (at the level of the scattering matrix) and in ref. [14] (at the level of the Hamiltonian). It was shown that the eigenvalue equation

H\Psi =E\Psi

can be discretized into a generalized eigenvalue problem

{\cal H}\Psi =E{\cal P}\Psi

with local Hermitian tight‐binding operators on both sides of the equation.…”

Section: Introductionmentioning

confidence: 99%

“…In what follows we turn to the dynamical problem, by generalizing the approach of refs. [12–14] to the discretization of space and time. In the next Section 2 we show that the time discretization removes the pole in the tangent dispersion, which becomes a smooth function of momentum

\bm {k}

and quasi‐energy ε (yellow bands in Figure 1).…”

Section: Introductionmentioning

confidence: 99%

Massless Dirac Fermions on a Space‐Time Lattice with a Topologically Protected Dirac Cone

et al. 2022

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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.

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Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice

Cited by 9 publications

References 37 publications

Majorana bound states in encapsulated bilayer graphene

Majorana bound states in encapsulated bilayer graphene

Geometry-independent tight-binding method for massless Dirac fermions in two dimensions

Massless Dirac Fermions on a Space‐Time Lattice with a Topologically Protected Dirac Cone

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