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Naumis GG, Herrera SA, Poudel SP, Nakamura H, Barraza-Lopez S. Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 87:016502. [PMID: 37879327 DOI: 10.1088/1361-6633/ad06db] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2023] [Accepted: 10/25/2023] [Indexed: 10/27/2023]
Abstract
This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (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, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré 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 update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. 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 an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.
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Affiliation(s)
- Gerardo G Naumis
- Departamento de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México (UNAM), Apdo. Postal 20-364, CDMX, 01000, Mexico
| | - Saúl A Herrera
- Departamento de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México (UNAM), Apdo. Postal 20-364, CDMX, 01000, Mexico
| | - Shiva P Poudel
- Department of Physics, University of Arkansas, Fayetteville, AR 72701, United States of America
- MonArk NSF Quantum Foundry, University of Arkansas, Fayetteville, AR 72701, United States of America
| | - Hiro Nakamura
- Department of Physics, University of Arkansas, Fayetteville, AR 72701, United States of America
- MonArk NSF Quantum Foundry, University of Arkansas, Fayetteville, AR 72701, United States of America
| | - Salvador Barraza-Lopez
- Department of Physics, University of Arkansas, Fayetteville, AR 72701, United States of America
- MonArk NSF Quantum Foundry, University of Arkansas, Fayetteville, AR 72701, United States of America
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Fillion-Gourdeau F, Lorin E, MacLean S. Numerical quasiconformal transformations for electron dynamics on strained graphene surfaces. Phys Rev E 2021; 103:013312. [PMID: 33601536 DOI: 10.1103/physreve.103.013312] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Accepted: 01/01/2021] [Indexed: 11/07/2022]
Abstract
The dynamics of low-energy electrons in general static strained graphene surface is modelled mathematically by the Dirac equation in curved space-time. In Cartesian coordinates, a parametrization of the surface can be straightforwardly obtained, but the resulting Dirac equation is intricate for general surface deformations. Two different strategies are introduced to simplify this problem: the diagonal metric approximation and the change of variables to isothermal coordinates. These coordinates are obtained from quasiconformal transformations characterized by the Beltrami equation, whose solution gives the mapping between both coordinate systems. To implement this second strategy, a least-squares finite-element numerical scheme is introduced to solve the Beltrami equation. The Dirac equation is then solved via an accurate pseudospectral numerical method in the pseudo-Hermitian representation that is endowed with explicit unitary evolution and conservation of the norm. The two approaches are compared and applied to the scattering of electrons on Gaussian shaped graphene surface deformations. It is demonstrated that electron wave packets can be focused by these local strained regions.
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Affiliation(s)
- François Fillion-Gourdeau
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.,Infinite Potential Laboratories, Waterloo, Ontario, Canada N2L 0A9
| | - Emmanuel Lorin
- School of Mathematics and Statistics, Carleton University, Ottawa, Canada K1S 5B6.,Centre de Recherches Mathématiques, Université de Montréal, Montréal, Canada H3T 1J4
| | - Steve MacLean
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.,Infinite Potential Laboratories, Waterloo, Ontario, Canada N2L 0A9.,Université du Québec, INRS-Énergie, Matériaux et Télécommunications, Varennes, Québec, Canada J3X 1S2
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