Zero‐Energy Vortices in Dirac Materials

Downing, C. A.; Portnoi, M. E.

doi:10.1002/pssb.201800584

Cited by 18 publications

(17 citation statements)

References 127 publications

(211 reference statements)

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“…Thus, the pair interaction we consider here is attractive on a small scale and repulsive on the large distance. The bound electron pairs (BEPs) formed as a result of this interaction [4][5][6] are drastically different from other composite particles, which are currently widely studied in bulk materials, [7,8] low-dimensional systems, [9][10][11][12][13] and even for cold atoms in optical lattice. [14] Another feature of the PSOI is that it depends on the configuration of the Coulomb field which acts between electrons and can be controlled by a gate in low-dimensional systems.…”

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confidence: 99%

Bound Electron Pairs Formed by the Spin–Orbit Interaction in 2D Gated Structures

Gindikin

Vigdorchik

Sablikov

2020

Physica Rapid Research Ltrs

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The bound electron pairs (BEPs) arising due to the pair spin–orbit interaction (PSOI) in 2D structures are explored with a gate that allows the BEPs to be manipulated. The gate breaks the in‐plane reflection symmetry of the pair Coulomb field and creates a one‐particle Rashba spin–orbit interaction. It is found that the normal component of the electric field substantially affects the BEPs but the key role in forming the BEPs belongs to the in‐plane component. The ground state of a BEP with zero total momentum, which is doubly degenerate in the absence of the gate, splits into two states. One of them is tunable by varying the gate voltage, whereas the other is on the contrary robust. The tunable BEP has a higher binding energy which grows as the gate voltage increases, with its orbital and spin structure changing continuously. At large negative voltage, the tunable BEP decays. The orbital and spin structure of the robust BEP does not depend on the gate voltage. Its energy level crosses the conduction band bottom at high gate voltage of any polarity, but the robust BEP remains bound and localized even when in continuum.

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confidence: 99%

Bound Electron Pairs Formed by the Spin–Orbit Interaction in 2D Gated Structures

Gindikin

Vigdorchik

Sablikov

2020

Physica Rapid Research Ltrs

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“…This way, they can provide insight into a wider class of settings where analytical treatment is not possible. Remark that analytical solutions for bound states with non-zero energy are quite unusual in the literature where mainly zero-modes confined by electrostatic potentials are considered [5][6][7][19][20][21].…”

Section: Discussionmentioning

confidence: 99%

Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots

Jakubsky,

Kuru,

Negro

2021

Preprint

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We study the confinement of Dirac fermions in armchair graphene nanoribbons by means of a quantum-dot-type electrostatic potential. With the use of specific projection operators, we find exact solutions for some bound states that satisfy appropriate boundary conditions. We show that the energies of these bound states belong either to the gap of valence and conducting bands or they represent BIC's (bound states in the continuum) whose energies are embedded in the continuous spectrum.

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“…The problems related to the solution of such an equation are avoided when bound states with zero energy are of interest, see e.g. [33], [34], [35] [36]. The zero modes in presence of ihnomogeneous electric potential and an effective mass were discussed recently in [37].…”

Section: Confinement By the Inter-layer Interactionmentioning

confidence: 99%

Confinement in bilayer graphene via intra- and inter-layer interactions

Castillo-Celeita,

Jakubský,

Zelaya

2021

Preprint

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We consider confinement of Dirac fermions in AB-stacked bilayer graphene by inhomogeneous on-site interactions, (pseudo-)magnetic field or inter-layer interaction. Working within the framework of four-band approximation, we focus on the systems where the stationary equation is reducible into two stationary equations with 2 × 2 Dirac-type Hamiltonians and auxiliary interactions. We show that it is possible to find localized states by solving an effective Schrödinger equation with energy-dependent potential. We consider several scenarios where bilayer graphene is subject to inhomogneous (pseudo-)magnetic field, on-site interactions or inter-layer coupling. In explicit examples, we provide analytical solutions for the states localized by local fluctuations or periodicity defects of the interactions.

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Zero‐Energy Vortices in Dirac Materials

Cited by 18 publications

References 127 publications

Bound Electron Pairs Formed by the Spin–Orbit Interaction in 2D Gated Structures

Bound Electron Pairs Formed by the Spin–Orbit Interaction in 2D Gated Structures

Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots

Confinement in bilayer graphene via intra- and inter-layer interactions

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