Valley-momentum locking in a graphene superlattice with Y-shaped Kekulé bond texture

Gamayun, Oleksandr; Ostroukh, Viacheslav; Gnezdilov, N. V.; Adagideli, İnanç; Beenakker, C. W. J.

doi:10.1088/1367-2630/aaa7e5

Cited by 75 publications

(155 citation statements)

References 27 publications

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“…We first consider an infinite graphene nanoribbon of width W with zigzag edges and characterized by an uniform Kekulé distortion. Following Gamayun et al 22 , the nearest neighbors tight-binding Hamiltonian describing such system reads,…”

Section: Model and Methodsmentioning

confidence: 99%

“…For pristine graphene the hopping integral between nearest-neighbor sites t l, j = t 0 is around 2.7 eV. The Kekulé distortion of the lattice modifies the bond lengths and it is introduced through a position dependent hopping integral given by 22 ,…”

Section: Model and Methodsmentioning

confidence: 99%

“…surrounding one of the carbon atoms of the new hexagonal a) Electronic mail: ramoncarrillo@uabc.edu.mx unit cell) is called Kek-Y distortion. In contrast with the Kek-O, the Kek-Y shape does not open a gap, but instead, it leads to the locking of valley degree of freedom to the momentum 22 .…”

Section: Introductionmentioning

confidence: 92%

“…Here we analyze the nature and magnitude of the gap for Kek-Y distorted graphene nanoribons in the low energy ap-proximation. In this regime its Hamiltonian has the form 22 ,…”

Section: A Kek-y Zigzag Graphene Nanoribbonsmentioning

confidence: 99%

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Resonant transport in Kekulé-distorted graphene nanoribbons

Andrade

Carrillo-Bastos

Pantaleón

et al. 2020

Journal of Applied Physics

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The formation of a superlattice in graphene can serve as a way to modify its electronic bandstructure and thus to engineer its electronic transport properties. Recent experiments have discovered a Kekulé bond ordering in graphene deposited on top of a Copper substrate, leading to the breaking of the valley degeneracy while preserving the highly desirable feature of linearity and gapless character of its band dispersion. In this paper we study the effects of a Kekulé distortion in zigzag graphene nanoribbons in both, the subband spectrum and on its electronic transport properties. We extend our study to investigate also the electronic conductance in graphene nanoribbons composed of sequentially ordered ν = ±1 Kek-Y superlattice. We find interesting resonances in the conductance response emerging in the otherwise energy gap regions, which scales with the number of Kek-Y interfaces minus one. Such features resembles the physics of resonant tunneling behavior observed in semiconductors heterostructures. Our findings provide a possible way to measure the strenght of Kekulé parameter in graphene nanoribbons.

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Section: Model and Methodsmentioning

confidence: 99%

Section: Model and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 92%

“…Here we analyze the nature and magnitude of the gap for Kek-Y distorted graphene nanoribons in the low energy ap-proximation. In this regime its Hamiltonian has the form 22 ,…”

Section: A Kek-y Zigzag Graphene Nanoribbonsmentioning

confidence: 99%

See 2 more Smart Citations

Resonant transport in Kekulé-distorted graphene nanoribbons

Andrade

Carrillo-Bastos

Pantaleón

et al. 2020

Journal of Applied Physics

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“…A suitable mass term can now open a gap in the band structure. A recent work [49] reported that unlike the Kekule-O distortion [50], the Kekule-Y distortion does not open a gap: instead it preserves a double Dirac cone at the Brillouin zone center. Using our algorithms we identify the symmetries protecting this double Dirac cone.…”

Section: Kekule Distortion In Graphenementioning

confidence: 99%

Qsymm: algorithmic symmetry finding and symmetric Hamiltonian generation

2018

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Symmetry is a guiding principle in physics that allows us to generalize conclusions between many physical systems. In the ongoing search for new topological phases of matter, symmetry plays a crucial role by protecting topological phases. We address two converse questions relevant to the symmetry classification of systems: is it possible to generate all possible single-body Hamiltonians compatible with a given symmetry group? Is it possible to find all the symmetries of a given family of Hamiltonians? We present numerically stable, deterministic polynomial time algorithms to solve both of these problems. Our treatment extends to all continuous or discrete symmetries of non-interacting lattice or continuum Hamiltonians. We implement the algorithms in the Qsymm Python package, and demonstrate their usefulness through applications in active research areas of condensed matter physics, including Majorana wires and Kekule graphene. continuous spatial rotations, space groups, discrete onsite symmetries (such as time reversal, particle-hole and chiral symmetries), and arbitrary combinations of these. Besides static fermionic systems, our methods are also applicable to band structures in photonic crystals [25,26], magnon spectra, classical mechanical [27, 28] and electronic systems [29], and driven Floquet systems [30].The paper is structured as follows: first we review the general symmetry structure of single-particle Hamiltonians. Then we present our algorithm to find Hamiltonians with such symmetries. After that we review the symmetry finding algorithm, which, by factoring out onsite unitary symmetries, makes finding all other symmetries more efficient and guaranteed. We implement our algorithms in the Qsymm Python package [31, 32]. Finally we provide a set of examples where our method was used on problems in active areas of research. We show that Majorana wire devices may be protected against band-tilting by a magnetic symmetry, and double Dirac cones in Kekule distorted graphene are protected by point group and sublattice symmetry. We also construct model Hamiltonians for transition metal dichalcogenides and distorted spin-orbit coupled SnTe. Hamiltonian families and symmetries 2.1. Continuum and tight-binding HamiltoniansWe focus on non-interacting Hamiltonians. The quadratic Hamilton operator of a finite (zero-dimensional) system can be written as New J. Phys. 20 (2018) 093026 D Varjas et al

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Chiral Symmetry Breaking in Kekulé-Ordered Graphene

Bao

2023

Springer Theses

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Valley-momentum locking in a graphene superlattice with Y-shaped Kekulé bond texture

Cited by 75 publications

References 27 publications

Resonant transport in Kekulé-distorted graphene nanoribbons

Resonant transport in Kekulé-distorted graphene nanoribbons

Qsymm: algorithmic symmetry finding and symmetric Hamiltonian generation

Chiral Symmetry Breaking in Kekulé-Ordered Graphene

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