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García-Valladares G, Plata CA, Prados A. Buckling in a rotationally invariant spin-elastic model. Phys Rev E 2023; 107:014120. [PMID: 36797953 DOI: 10.1103/physreve.107.014120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2022] [Accepted: 12/22/2022] [Indexed: 06/18/2023]
Abstract
Scanning tunneling microscopy experiments have revealed a spontaneous rippled-to-buckled transition in heated graphene sheets, in absence of any mechanical load. Several models relying on a simplified picture of the interaction between elastic and internal, electronic, degrees of freedom have been proposed to understand this phenomenon. Nevertheless, these models are not fully consistent with the classical theory of elasticity, since they do not preserve rotational invariance. Herein, we develop and analyze an alternative classical spin-elastic model that preserves rotational invariance while giving a qualitative account of the rippled-to-buckled transition. By integrating over the internal degrees of freedom, an effective free energy for the elastic modes is derived, which only depends on the curvature. Minimization of this free energy gives rise to the emergence of different mechanical phases, whose thermodynamic stability is thoroughly analyzed, both analytically and numerically. All phases are characterized by a spatially homogeneous curvature, which plays the role of the order parameter for the rippled-to-buckled transition, in both the one- and two-dimensional cases. In the latter, our focus is put on the honeycomb lattice, which is representative of actual graphene.
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Affiliation(s)
| | - Carlos A Plata
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
| | - Antonio Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
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Mangum JM, Harerimana F, Gikunda MN, Thibado PM. Mechanisms of Spontaneous Curvature Inversion in Compressed Graphene Ripples for Energy Harvesting Applications via Molecular Dynamics Simulations. MEMBRANES 2021; 11:516. [PMID: 34357166 PMCID: PMC8306715 DOI: 10.3390/membranes11070516] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Revised: 06/30/2021] [Accepted: 07/06/2021] [Indexed: 12/03/2022]
Abstract
Electrically conductive, highly flexible graphene membranes hold great promise for harvesting energy from ambient vibrations. For this study, we built numerous three-dimensional graphene ripples, with each featuring a different amount of compression, and performed molecular dynamics simulations at elevated temperatures. These ripples have a convex cosine shape, then spontaneously invert their curvature to concave. The average time between inversion events increases with compression. We use this to determine how the energy barrier height depends on strain. A typical convex-to-concave curvature inversion process begins when the ripple's maximum shifts sideways from the normal central position toward the fixed outer edge. The ripple's maximum does not simply move downward toward its concave position. When the ripple's maximum moves toward the outer edge, the opposite side of the ripple is pulled inward and downward, and it passes through the fixed outer edge first. The ripple's maximum then quickly flips to the opposite side via snap-through buckling. This trajectory, along with local bond flexing, significantly lowers the energy barrier for inversion. The large-scale coherent movement of ripple atoms during curvature inversion is unique to two-dimensional materials. We demonstrate how this motion can induce an electrical current in a nearby circuit.
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Affiliation(s)
| | | | | | - Paul M. Thibado
- Department of Physics, University of Arkansas, Fayetteville, AR 72701, USA; (J.M.M.); (F.H.); (M.N.G.)
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Thibado PM, Kumar P, Singh S, Ruiz-Garcia M, Lasanta A, Bonilla LL. Fluctuation-induced current from freestanding graphene. Phys Rev E 2020; 102:042101. [PMID: 33212603 DOI: 10.1103/physreve.102.042101] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Accepted: 09/09/2020] [Indexed: 06/11/2023]
Abstract
At room temperature, micron-sized sheets of freestanding graphene are in constant motion, even in the presence of an applied bias voltage. We quantify the out-of-plane movement by collecting the displacement current using a nearby small-area metal electrode and present an Ito-Langevin model for the motion coupled to a circuit containing diodes. Numerical simulations show that the system reaches thermal equilibrium and the average rates of heat and work provided by stochastic thermodynamics tend quickly to zero. However, there is power dissipated by the load resistor, and its time average is exactly equal to the power supplied by the thermal bath. The exact power formula is similar to Nyquist's noise power formula, except that the rate of change of diode resistance significantly boosts the output power, and the movement of the graphene shifts the power spectrum to lower frequencies. We have calculated the equilibrium average of the power by asymptotic and numerical methods. Excellent agreement is found between experiment and theory.
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Affiliation(s)
- P M Thibado
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - P Kumar
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Surendra Singh
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - M Ruiz-Garcia
- Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - A Lasanta
- G. Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics and Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Departamento de Álgebra, Facultad de Educación, Economía y Tecnología de Ceuta, Universidad de Granada, E-51001 Ceuta, Spain
| | - L L Bonilla
- G. Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics and Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Courant Institute for Mathematical Sciences, New York University, New York, New York 10012, USA
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Atomic-Site-Specific Analysis on Out-of-Plane Elasticity of Convexly Curved Graphene and Its Relationship to
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Re-Hybridization. CRYSTALS 2018. [DOI: 10.3390/cryst8020102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Ruiz-Garcia M, Bonilla LL, Prados A. Bifurcation analysis and phase diagram of a spin-string model with buckled states. Phys Rev E 2018; 96:062147. [PMID: 29347384 DOI: 10.1103/physreve.96.062147] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2017] [Indexed: 11/07/2022]
Abstract
We analyze a one-dimensional spin-string model, in which string oscillators are linearly coupled to their two nearest neighbors and to Ising spins representing internal degrees of freedom. String-spin coupling induces a long-range ferromagnetic interaction among spins that competes with a spin-spin antiferromagnetic coupling. As a consequence, the complex phase diagram of the system exhibits different flat rippled and buckled states, with first or second order transition lines between states. This complexity translates to the two-dimensional version of the model, whose numerical solution has been recently used to explain qualitatively the rippled to buckled transition observed in scanning tunneling microscopy experiments with suspended graphene sheets. Here we describe in detail the phase diagram of the simpler one-dimensional model and phase stability using bifurcation theory. This gives additional insight into the physical mechanisms underlying the different phases and the behavior observed in experiments.
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Affiliation(s)
- M Ruiz-Garcia
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience, and Industrial Mathematics, and Department of Materials Science and Engineering and Chemical Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain.,Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - L L Bonilla
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience, and Industrial Mathematics, and Department of Materials Science and Engineering and Chemical Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
| | - A Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080, Sevilla, Spain
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Jones GW, Bahamon DA, Castro Neto AH, Pereira VM. Quantized Transport, Strain-Induced Perfectly Conducting Modes, and Valley Filtering on Shape-Optimized Graphene Corbino Devices. NANO LETTERS 2017; 17:5304-5313. [PMID: 28774178 DOI: 10.1021/acs.nanolett.7b01663] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The extreme mechanical resilience of graphene and the peculiar coupling it hosts between lattice and electronic degrees of freedom have spawned a strong impetus toward strain-engineered graphene where, on the one hand, strain augments the richness of its phenomenology and makes possible new concepts for electronic devices, and on the other hand, new and extreme physics might take place. Here, we demonstrate that the shape of substrates supporting graphene sheets can be optimized for approachable experiments where strain-induced pseudomagnetic fields (PMF) can be tailored by pressure for directionally selective electronic transmission and pinching-off of current flow down to the quantum channel limit. The Corbino-type layout explored here furthermore allows filtering of charge carriers according to valley and current direction, which can be used to inject or collect valley-polarized currents, thus realizing one of the basic elements required for valleytronics. Our results are based on a framework developed to realistically determine the combination of strain, external parameters, and geometry optimally compatible with the target spatial profile of a desired physical property-the PMF in this case. Characteristic conductance profiles are analyzed through quantum transport calculations on large graphene devices having the optimal shape.
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Affiliation(s)
- Gareth W Jones
- School of Mathematics, The University of Manchester , Manchester, M13 9PL, England
| | - Dario Andres Bahamon
- MackGraphe-Graphene and Nano-Materials Research Center, Mackenzie Presbyterian University , Rua da Consolação 896, 01302-907, São Paulo, SP, Brazil
| | - Antonio H Castro Neto
- Department of Physics, National University of Singapore , 2 Science Drive 3, Singapore 117542
- Centre for Advanced 2D Materials, National University of Singapore , 6 Science Drive 2, Singapore 117546
| | - Vitor M Pereira
- Department of Physics, National University of Singapore , 2 Science Drive 3, Singapore 117542
- Centre for Advanced 2D Materials, National University of Singapore , 6 Science Drive 2, Singapore 117546
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Attractive force-driven superhardening of graphene membranes as a pin-point breaking of continuum mechanics. Sci Rep 2017; 7:46083. [PMID: 28417957 PMCID: PMC5394694 DOI: 10.1038/srep46083] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2016] [Accepted: 03/10/2017] [Indexed: 11/08/2022] Open
Abstract
Bending at the nanometre scale can substantially modify the mechanical, chemical and electronic properties of graphene membranes. The subsequent response of chemical bonds leads to deviations from plate idealisation in continuum mechanics. However, those phenomena have thus far been investigated exclusively by measuring the electronic properties of graphene deformed by compressing and stretching with local-probe techniques. Here, we report that the interatomic-attractive forces applied on the convexly-curved graphene by the probe tip give rise to a pin-point breaking of the plate idealisation in the continuum mechanics, facilitating atomically-localised enhancements in its chemical reactivity and mechanical strength. Thorough characterisations were conducted by atomic force microscopy and force field spectroscopy on hollow nanotubes, rolled-up graphene, with different diameters. Their topmost parts supplied well-defined curvatures of the convex graphene. We found that a significant enhancement in the out-of-plane Young's modulus from 13 to 163 GPa, "superhardening", was realised with the nonlinear transition of bond configurations. Our findings provide a fundamental understanding of the relationships between the structure of atomistic membranes and the dynamic behaviour of approaching exterior atoms or molecules and their subsequent interplay with chemical and mechanical properties. Thus, these results encourage the application of such membranes in functionally-controllable materials or devices.
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Coquand O, Mouhanna D. Flat phase of quantum polymerized membranes. Phys Rev E 2016; 94:032125. [PMID: 27739861 DOI: 10.1103/physreve.94.032125] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2016] [Indexed: 06/06/2023]
Abstract
We investigate the flat phase of quantum polymerized phantom membranes by means of a nonperturbative renormalization group approach. We first implement this formalism for general quantum polymerized membranes and derive the flow equations that encompass both quantum and thermal fluctuations. We then deduce and analyze the flow equations relevant to study the flat phase and discuss their salient features: quantum to classical crossover and, in each of these regimes, strong to weak coupling crossover. We finally illustrate these features in the context of free-standing graphene physics.
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Affiliation(s)
- O Coquand
- Sorbonne Universités, UPMC Univ Paris 06, LPTMC, CNRS UMR 7600, F-75005 Paris, France
| | - D Mouhanna
- Sorbonne Universités, UPMC Univ Paris 06, LPTMC, CNRS UMR 7600, F-75005 Paris, France
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Measuring the height-to-height correlation function of corrugation in suspended graphene. Ultramicroscopy 2016; 165:1-7. [DOI: 10.1016/j.ultramic.2016.03.010] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2015] [Revised: 03/11/2016] [Accepted: 03/23/2016] [Indexed: 11/22/2022]
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Park Y, Choi JS, Choi T, Lee MJ, Jia Q, Park M, Lee H, Park BH. Configuration of ripple domains and their topological defects formed under local mechanical stress on hexagonal monolayer graphene. Sci Rep 2015; 5:9390. [PMID: 25801337 PMCID: PMC4371081 DOI: 10.1038/srep09390] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2014] [Accepted: 02/27/2015] [Indexed: 11/09/2022] Open
Abstract
Ripples in graphene are extensively investigated because they ensure the mechanical stability of two-dimensional graphene and affect its electronic properties. They arise from spontaneous symmetry breaking and are usually manifested in the form of domains with long-range order. It is expected that topological defects accompany a material exhibiting long-range order, whose functionality depends on characteristics of domains and topological defects. However, there remains a lack of understanding regarding ripple domains and their topological defects formed on monolayer graphene. Here we explore configuration of ripple domains and their topological defects in exfoliated monolayer graphenes on SiO2/Si substrates using transverse shear microscope. We observe three-color domains with three different ripple directions, which meet at a core. Furthermore, the closed domain is surrounded by an even number of cores connected together by domain boundaries, similar to topological vortex and anti-vortex pairs. In addition, we have found that axisymmetric three-color domains can be induced around nanoparticles underneath the graphene. This fascinating configuration of ripple domains may result from the intrinsic hexagonal symmetry of two-dimensional graphene, which is supported by theoretical simulation using molecular dynamics. Our findings are expected to play a key role in understanding of ripple physics in graphene and other two-dimensional materials.
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Affiliation(s)
- Yeonggu Park
- Division of Quantum Phases &devices, Department of Physics, Konkuk University, Seoul, 143-701, Korea
| | - Jin Sik Choi
- Creative Research Center for Graphene Electronics, Electronics and Telecommunications Research Institute (ETRI), Daejeon 305-700, Korea
| | - Taekjib Choi
- Hybrid Materials Research Center, Department of Nanotechnology and Advanced Materials Engineering, Sejong University, Seoul 143-747, Korea
| | - Mi Jung Lee
- Division of Quantum Phases &devices, Department of Physics, Konkuk University, Seoul, 143-701, Korea
| | - Quanxi Jia
- 1] Division of Quantum Phases &devices, Department of Physics, Konkuk University, Seoul, 143-701, Korea [2] Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Minwoo Park
- Division of Quantum Phases &devices, Department of Physics, Konkuk University, Seoul, 143-701, Korea
| | - Hoonkyung Lee
- Division of Quantum Phases &devices, Department of Physics, Konkuk University, Seoul, 143-701, Korea
| | - Bae Ho Park
- Division of Quantum Phases &devices, Department of Physics, Konkuk University, Seoul, 143-701, Korea
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Wei Y, Wang B, Wu J, Yang R, Dunn ML. Bending rigidity and Gaussian bending stiffness of single-layered graphene. NANO LETTERS 2013; 13:26-30. [PMID: 23214980 DOI: 10.1021/nl303168w] [Citation(s) in RCA: 97] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Bending rigidity and Gaussian bending stiffness are the two key parameters that govern the rippling of suspended graphene-an unavoidable phenomenon of two-dimensional materials when subject to a thermal or mechanical field. A reliable determination about these two parameters is of significance for both the design and the manipulation of graphene morphology for engineering applications. By combining the density functional theory calculations of energies of fullerenes and single wall carbon nanotubes with the configurational energy of membranes determined by Helfrich Hamiltonian, we have designed a theoretical approach to accurately determine the bending rigidity and Gaussian bending stiffness of single-layered graphene. The bending rigidity and Gaussian bending stiffness of single-layered graphene are 1.44 eV (2.31 × 10(-19) N m) and -1.52 eV (2.43 × 10(-19) N m), respectively. The bending rigidity is close to the experimental result. Interestingly, the bending stiffness of graphene is close to that of lipid bilayers of cells about 1-2 eV, which might mechanically justify biological applications of graphene.
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Affiliation(s)
- Yujie Wei
- LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China.
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Bonilla LL, Carpio A, Prados A, Rosales RR. Ripples in a string coupled to Glauber spins. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031125. [PMID: 22587056 DOI: 10.1103/physreve.85.031125] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2011] [Revised: 02/17/2012] [Indexed: 05/31/2023]
Abstract
Each oscillator in a linear chain (a string) interacts with a local Ising spin in contact with a thermal bath. These spins evolve according to Glauber dynamics. Below a critical temperature, there appears an equilibrium, time-independent, rippled state in the string that is accompanied by a nonzero spin polarization. On the other hand, the system is shown to form "metastable," nonequilibrium long-lived ripples in the string for slow spin relaxation. The system vibrates rapidly about these quasistationary states, which can be described as snapshots of a coarse-grained stroboscopic map. For moderate observation times, ripples are observed irrespective of the final thermodynamically stable state (rippled or not). Interestingly, the system can be considered as a "minimal" model to understand rippling in clamped graphene sheets.
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Affiliation(s)
- L L Bonilla
- G. Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
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Barnard AS, Snook IK. Ripple induced changes in the wavefunction of graphene: an example of a fundamental symmetry breaking. NANOSCALE 2012; 4:1167-1170. [PMID: 22081215 DOI: 10.1039/c1nr11049g] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Ideally, graphene may be regarded as a strictly 2-D structure. However, as it exists in a 3-D world, perturbations often distort this ideal 2-D structure. Under a variety of conditions graphene has been shown to develop ripples, which may have undesirable consequences for a variety of properties of graphene, such as electron transport. In addition to this, it has been speculated that ripples may be an intrinsic property of graphene, and it has also been suggested that unlocking the secrets of these ripples could be useful in the search for (an understanding of) the elusive Higgs boson. However, ripples in graphene can only be avoided, or utilized, if they can be reproducibly detected. Here we explore the most fundamental aspect of these ripples, that is, the effect of a static ripple structure on various properties of large graphene nanoflakes. We find that the mechanical, thermodynamic and electronic properties are unaltered by this fundamental rippling, but this spontaneous symmetry breaking induces a significant change in the structure of the wavefunction. This profound effect occurs only at the most basic level, but it should be, in principle, experimentally observable.
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Affiliation(s)
- Amanda S Barnard
- CSIRO Materials Science and Engineering, Private Bag 33, Clayton South, VIC 3169, Australia
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O'Hare A, Kusmartsev FV, Kugel KI. A stable "flat" form of two-dimensional crystals: could graphene, silicene, germanene be minigap semiconductors? NANO LETTERS 2012; 12:1045-1052. [PMID: 22236130 DOI: 10.1021/nl204283q] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
The discovery of a flat two-dimensional crystal known as graphene has contradicted Landau-Peierls-Mermin-Wagner arguments that there is no stable flat form of such crystals. Here, we show that the "flat" shape of graphene arises due to a microscopic buckling at the smallest possible interatomic scale. We show that the graphene, silicene, and other two-dimensional crystals are stable due to transverse short-range displacements of appropriate atoms. The distortions are small and form various patterns, which we describe in a framework of Ising model with competing interactions. We show that when temperature decreases, two transitions, disorder into order and order into disorder, arise. The ordered state has a form of stripes where carbon atoms are shifted regularly with respect to the plane. The flat graphene, silicene, or germanene planes look like a microscopic "washboard" with the wavelength of about couple of interatomic spacing of appropriate sublattices, which for graphene is about 1.8-3.6 Å. At lower temperatures, the ordered state transforms into a glass. Because of up-down asymmetry in buckled graphene, silicene and other two-dimensional crystals deposited on substrate, a minibandgap may arise. We derive a criterion for the minigap formation and show how it is related to the buckling and to the graphene-substrate interaction. Because of the bandgap, there may arise new phenomena and in particular a rectification of ac current induced by microwave or infrared radiation. We show that the amplitude of direct current arising at wave mixing of two harmonics of microwave electromagnetic radiation is huge. Moreover, we predict the existence of miniexcitons and a new type of fermionic minipolaritons whose behavior can be controlled by the microwave and terahertz radiation.
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Affiliation(s)
- A O'Hare
- Department of Physics, Loughborough University, Leicestershire, LE11 3TU, United Kingdom
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Guinea F, Vozmediano MAH, López-Sancho MP, González J. Progress in modeling graphene: the novel features of this material. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2011; 23:5324-5326. [PMID: 22299149 DOI: 10.1002/adma.201103354] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
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Upadhyaya N, Vitelli V. Quantum buckling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:040601. [PMID: 22181079 DOI: 10.1103/physreve.84.040601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2011] [Revised: 09/02/2011] [Indexed: 05/31/2023]
Abstract
We study the mechanical buckling of a freestanding superfluid layer. A topological defect in the phase of the quantum order parameter distorts the underlying metric into a surface of negative Gaussian curvature, irrespective of the sign of the defect charge. The resulting instability is in striking contrast with classical buckling, where the in-plane strain induced by positive (negative) disclinations is screened by positive (negative) curvature. We derive the conditions under which the quantum buckling instability occurs in terms of the dimensionless ratio between superfluid stiffness and bending modulus. An ansatz for the resulting shape of the buckled surface is analytically and numerically confirmed.
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Affiliation(s)
- N Upadhyaya
- Instituut-Lorentz, Universiteit Leiden, Postbus 9506, NL-2300 RA Leiden, The Netherlands
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