Mechanical graphene
We present a model of a mechanical system with a vibrational mode spectrum identical to the spectrum of electronic excitations in a tight-binding model of graphene. The model consists of point masses connected by elastic couplings, called ‘tri-bonds’, that implement certain three-body interactions,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2017-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aa57bb |
| _version_ | 1797750801720934400 |
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| author | Joshua E S Socolar Tom C Lubensky Charles L Kane |
| author_facet | Joshua E S Socolar Tom C Lubensky Charles L Kane |
| author_sort | Joshua E S Socolar |
| collection | DOAJ |
| description | We present a model of a mechanical system with a vibrational mode spectrum identical to the spectrum of electronic excitations in a tight-binding model of graphene. The model consists of point masses connected by elastic couplings, called ‘tri-bonds’, that implement certain three-body interactions, which can be tuned by varying parameters that correspond to the relative hopping amplitudes on the different bond directions in graphene. In the mechanical model, this is accomplished by varying the location of a pivot point that determines the allowed rigid rotations of a single tri-bond. The infinite system constitutes a Maxwell lattice, with the number of degrees of freedom equal to the number of constraints imposed by the tri-bonds. We construct the equilibrium and compatibility matrices and analyze the model’s phase diagram, which includes spectra with Weyl points for some placements of the pivot and topologically polarized phases for others. We then discuss the edge modes and associated states of self stress for strips cut from the periodic lattice. Finally, we suggest a physical realization of the tri-bond, which allows access to parameter regimes not available to experiments on (strained) graphene and may be used to create other two-dimensional mechanical metamaterials with different spectral features. |
| first_indexed | 2024-03-12T16:38:06Z |
| format | Article |
| id | doaj.art-05a1a0b50ef34ce8ba8a990843542f11 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:38:06Z |
| publishDate | 2017-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-05a1a0b50ef34ce8ba8a990843542f112023-08-08T14:37:55ZengIOP PublishingNew Journal of Physics1367-26302017-01-0119202500310.1088/1367-2630/aa57bbMechanical grapheneJoshua E S Socolar0Tom C Lubensky1Charles L Kane2Department of Physics, Duke University , Durham, NC, United States of AmericaDepartment of Physics and Astronomy, University of Pennsylvania , Philadelphia, PA, United States of AmericaDepartment of Physics and Astronomy, University of Pennsylvania , Philadelphia, PA, United States of AmericaWe present a model of a mechanical system with a vibrational mode spectrum identical to the spectrum of electronic excitations in a tight-binding model of graphene. The model consists of point masses connected by elastic couplings, called ‘tri-bonds’, that implement certain three-body interactions, which can be tuned by varying parameters that correspond to the relative hopping amplitudes on the different bond directions in graphene. In the mechanical model, this is accomplished by varying the location of a pivot point that determines the allowed rigid rotations of a single tri-bond. The infinite system constitutes a Maxwell lattice, with the number of degrees of freedom equal to the number of constraints imposed by the tri-bonds. We construct the equilibrium and compatibility matrices and analyze the model’s phase diagram, which includes spectra with Weyl points for some placements of the pivot and topologically polarized phases for others. We then discuss the edge modes and associated states of self stress for strips cut from the periodic lattice. Finally, we suggest a physical realization of the tri-bond, which allows access to parameter regimes not available to experiments on (strained) graphene and may be used to create other two-dimensional mechanical metamaterials with different spectral features.https://doi.org/10.1088/1367-2630/aa57bbmetamaterialtopological mechanicsgraphenevibrational modesedge modesWeyl modes |
| spellingShingle | Joshua E S Socolar Tom C Lubensky Charles L Kane Mechanical graphene New Journal of Physics metamaterial topological mechanics graphene vibrational modes edge modes Weyl modes |
| title | Mechanical graphene |
| title_full | Mechanical graphene |
| title_fullStr | Mechanical graphene |
| title_full_unstemmed | Mechanical graphene |
| title_short | Mechanical graphene |
| title_sort | mechanical graphene |
| topic | metamaterial topological mechanics graphene vibrational modes edge modes Weyl modes |
| url | https://doi.org/10.1088/1367-2630/aa57bb |
| work_keys_str_mv | AT joshuaessocolar mechanicalgraphene AT tomclubensky mechanicalgraphene AT charleslkane mechanicalgraphene |