Curvature-induced quantum spin-Hall effect on a Möbius strip

Flouris, Kyriakos; Jimenez, Miller Mendoza; Herrmann, Hans J.

doi:10.1103/physrevb.105.235122

Cited by 16 publications

(10 citation statements)

References 36 publications

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“…Other studies relying on low-energy approximations dwell on the optical and electronic properties of graphene [51,52], on curvature-induced quantum spin-Hall effects in Möbius strips [53], on the topological Hall effect in strained twisted graphene bilayers with enhanced interactions [54], and on the valley-dependent time evolution of coherent electron states in tilted anisotropic Dirac materials [55]. In addition, the optical properties of massive anisotropic tilted Dirac materials [56], valley polarisers and filters [57], the creation of complex magnetic fields [58] or of Landau levels in curved spaces [59], the propagation of pseudo-electromagnetic waves [60], and comparisons between twistronics and straintronics in twisted bilayers of graphene and TMDCs [61] have also appeared in the literature.…”

Section: Low-energy Effective Models: Dirac Equation Withmentioning

confidence: 99%

“…A closely related phenomena is the curvature-induced spin-Hall effect in a graphene Möbius strip. The solution of the Dirac equation shows that despite the absence of a Hall current, a spin-Hall current is a natural consequence for such a topology [53]. Other works have studied topological phases arising from strain and its interplay with interactions in graphene [100,116,136,[150][151][152].…”

Section: Flat Electronic Bands and Electron-electron Correlations In ...mentioning

confidence: 99%

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Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

Naumis,

Herrera,

Poudel

et al. 2023

Rep. Prog. Phys.

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This is an update of a previous review on the subject \cite{Naumis_2017}. Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials have been considered. Specific topics of discussion include: (i) methods to induce valley and sublattice polarisation ($\mathbf{P}$) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, inducing polarisation $\mathbf{P}$ on hexagonal boron nitride monolayers {\it via} strain, (iv) measuring strain, and modifying through strain the optoelectronic properties of transition metal dichalcogenides, (v) ferroic 2D materials with intrinsic elastic ($\sigma$), electric ($\mathbf{P}$) and magnetic ($\mathbf{M}$) polarisation under strain, as well as incipient 2D multiferroics and (vi) moir'e bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The review features the extremely recent experimental realizations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of monoelemental 2D ferroelectric bismuth, and 2D multiferroic NiI$_2$. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents a fresh and up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

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Section: Low-energy Effective Models: Dirac Equation Withmentioning

confidence: 99%

Section: Flat Electronic Bands and Electron-electron Correlations In ...mentioning

confidence: 99%

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

Naumis,

Herrera,

Poudel

et al. 2023

Rep. Prog. Phys.

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“…This new field, named curvatronics, explores new features driven by the curvature of low-dimensional samples. In fact, by deforming the graphene layer, strong pseudo-magnetic fields due to the strain and edge states are found [8][9][10] Among the two-dimensional geometries proposed, a graphene Möbius strip has been studied both theoretically and experimentally [11][12][13][14][15][16]. The graphene Möbius strip is a single-sided surface built by gluing the two ends of graphene ribbons, after rotating one end by 180 o [17].…”

Section: Introductionmentioning

confidence: 99%

Electronic states in quantum wires on a Möbius strip

Pinto,

Silva,

Almeida

2024

Phys. Scr.

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We study the properties of an electron constrained on wires along an M"{o}bius strip. We considered wires around the strip and along the transverse direction, across the width of the strip. We considered wires around the strip and along the transverse direction, across the width of the strip. For each direction, we investigate how the curvature modifies the electronic states and their corresponding energy spectrum. At the center of the strip, the wires around the surface form quantum rings whose spectrum depends on the strip radius $a$. For wires at the edge of the strip, the inner edge turns into the outer edge. Accordingly, the curvature yields localized states in the middle of the wire. Along the strip width, the effective potential exhibits a parity symmetry breaking leading to the localization of the bound state on one side of the strip.

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“…The discrete Dirac operator on networks is a direct extension of the Dirac operator used in the continuum and its numerical implementations [21,22]. The Dirac operator plays an important role for example in supersymmetric theories [23] and in non-commutative geometry [24][25][26][27][28][29] where to our knowledge it has been first formulated [14] [Note however that that this topological definition of the Dirac operator is distinct from the one used in quantum graphs literature where links are considered linear one dimensional spaces on which a d + 1 = 1 + 1 Dirac equation is defined [30][31][32][33][34].]…”

Section: Introductionmentioning

confidence: 99%

Dirac gauge theory for topological spinors in 3+1 dimensional networks

Bianconi

2023

J. Phys. A: Math. Theor.

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Gauge theories on graphs and networks are attracting increasing attention not only as approaches to quantum gravity but also as models for performing quantum computation.Here we propose a Dirac gauge theory for topological spinors in $3+1$ dimensional networks associated to an arbitrary metric. Topological spinors are the direct sum of $0$-cochains and $1$-cochains defined on a network and describe a matter field defined on both nodes and links of a network. Recently in Ref. \cite{bianconi2021topological} it has been shown that topological spinors obey the topological Dirac equation driven by the discrete Dirac operator. In this work we extend these results by formulating the Dirac equation on weighted and directed $3+1$ dimensional networks which allow for the treatment of a local theory. The commutators and anti-commutators of the Dirac operators are non vanishing an they define the curvature tensor and magnetic field of our theory respectively. This interpretation is confirmed by the non-relativistic limit of the proposed Dirac equation. In the non-relativistic limit of the proposed Dirac equation the sector of the spinor defined on links follows the Schr\"odinger equation with the correct giromagnetic moment, while the sector of the spinor defined on nodes follows the Klein-Gordon equation and is not negligible. The action associated to the proposed field theory comprises of a Dirac action and a metric action. We describe the gauge invariance of the action under both Abelian and non-Abelian transformations and we propose the equation of motion of the field theory of both Dirac and metric fields. This theory can be interpreted as a limiting case of a more general gauge theory valid on any arbitrary network in the limit of almost flat spaces.

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Curvature-induced quantum spin-Hall effect on a Möbius strip

Cited by 16 publications

References 36 publications

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

Electronic states in quantum wires on a Möbius strip

Dirac gauge theory for topological spinors in 3+1 dimensional networks

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