Landau levels and snake states of pseudo-spin-1 Dirac-like electrons in gapped Lieb lattices

Jakubský, Vít; Zelaya, Kevin

doi:10.1088/1361-648x/ac9e84

Cited by 4 publications

(8 citation statements)

References 51 publications

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“…2b for illustration. A similar analysis holds for higher values of t 3 , where the Dirac points are displaced with respect to K. For a detailed discussion, see [13].…”

Section: Lieb Lattice and Pseudospin-1 Dirac Equationmentioning

confidence: 54%

“…Their geometries can extend beyond the honeycomb lattice. For instance, there are Kagome [10], Dice or α − T 3 [11,12], and Lieb lattices [13,14], which lead to effective pseudospin-1 Dirac equations. It was recently showed that the Kagome lattice can be obtained from a geometrical deformation of the Lieb lattice [15].…”

Section: Introductionmentioning

confidence: 99%

“…Gap-opening can be induced by on-site energy that differs on three sublattices or by the phase acquired by the electron when jumping between the neighboring sites [24], see also [27]. In this article, we adopt the second approach where a purely imaginary next nearest-neighbor interaction, attributed to spin-orbital coupling [13], is taken into account.…”

Section: Introductionmentioning

confidence: 99%

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Lieb lattices and pseudospin-1 dynamics under barrier- and well-like electrostatic interactions

Jakubský¹,

Zelaya²

2023

Preprint

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This work considers the confining and scattering phenomena of electrons in a Lieb lattice subjected to the influence of a rectangular electrostatic barrier. In this setup, hopping amplitudes between nearest neighbors in orthogonal directions are considered different, and the next-nearest neighbor interaction describes spin-orbit coupling. This makes it possible to confine electrons and generate bound states, the exact number of which is exactly determined for null momentum parallel to the barrier. In such a case, it is proved that one even and one odd bound state is always generated, and the number of bound states increases for nonnull and increasing values of the parallel momentum. That is, current-carrying states are generated. In the scattering regime, the energies are determined so that resonant tunneling occurs. The existence of perfect tunneling energy in the form of super-Klein tunneling is proved to exist regardless of the bang gap opening. Finally, it is shown that perfect reflection appears when solutions are coupled to the intermediate flat-band solution.

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“…2b for illustration. A similar analysis holds for higher values of t 3 , where the Dirac points are displaced with respect to K. For a detailed discussion, see [13].…”

Section: Lieb Lattice and Pseudospin-1 Dirac Equationmentioning

confidence: 54%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Lieb lattices and pseudospin-1 dynamics under barrier- and well-like electrostatic interactions

Jakubský¹,

Zelaya²

2023

Preprint

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“…This set, shown in figure 2, consists of the two intersecting planes A and B, which are defined by equations ( 14) and (16). The energy of the upper and lower dispersion bands on these planes are described by solutions (19) and (21). The corresponding eigenfunctions are given through the general formula (10).…”

Section: Discussionmentioning

confidence: 99%

“…In particular, the existence of infinite series of bound states near the flat band appears to be of great interest [18]. Very recently, the transport properties and snake states of pseudospin-1 Diraclike electrons have been analyzed by Jakubský and Zelaya [20,21] in Lieb lattice under barrierand well-like electrostatic interactions.…”

Section: Introductionmentioning

confidence: 99%

Bound states and point interactions of the one-dimensional pseudospin-one Hamiltonian

Zolotaryuk,

Gusynin

2023

J. Phys. A: Math. Theor.

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The spectrum of a one-dimensional pseudospin-one Hamiltonian with a three-component potential is studied for two conﬁgurations: (i) all the potential components are constants over the whole coordinate space and (ii) the proﬁle of some components is of a rectangular form. In case (i), it is illustrated how the structure of three (lower, middle and upper) bands depends on the conﬁguration of potential strengths including the appearance of ﬂat bands at some special values of these strengths. In case (ii), the set of two equations for ﬁnding bound states is derived. The spectrum of bound-state energies is shown to depend crucially on the conﬁguration of potential strengths. Each of these conﬁgurations is speciﬁed by a single strength parameter V . The bound-state energies are calculated as functions of the strength V and a one-point approach is developed realizing correspondent point interactions. For diﬀerent potential conﬁgurations, the energy dependence on the strength V is described in detail, including its one-point approximation. From a whole variety of bound-state spectra, four characteristic types are singled out.

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Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions

Jakubský,

Zelaya

2024

Phys. Scr.

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This manuscript explores the Darboux transformation employed in the construction of exactly solvable models for pseudospin-one particles described by the Dirac-type equation. We focus on the settings where a flat band of zero energy is present in the spectrum of the initial system. Using the flat band state as one of the seed solutions substantially improves the applicability of the Darboux transformation, for it becomes necessary to ensure the Hermiticy of the new Hamiltonians. This is illustrated explicitly in four examples, where we show that the new Hamiltonians can describe quasi-particles in Lieb lattice with inhomogeneous hopping amplitudes.

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Landau levels and snake states of pseudo-spin-1 Dirac-like electrons in gapped Lieb lattices

Cited by 4 publications

References 51 publications

Lieb lattices and pseudospin-1 dynamics under barrier- and well-like electrostatic interactions

Lieb lattices and pseudospin-1 dynamics under barrier- and well-like electrostatic interactions

Bound states and point interactions of the one-dimensional pseudospin-one Hamiltonian

Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions

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