Nonlinear propagating localized modes in a 2D hexagonal crystal lattice

Bajars, Janis; Eilbeck, J. C.; Leimkuhler, Benedict

doi:10.1016/j.physd.2015.02.007

Cited by 48 publications

(45 citation statements)

References 29 publications

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“…Related studies of trapping of charge by mobile anharmonic excitations in 2D arrays added credence to this suggestion [8][9][10]. Numerical modelling and analogue studies of simplified muscovite lattices showed that quodons could be longitudinal breathers [11][12][13][14]. The propagation of breathers in other 2D lattices has also been described [15][16][17].…”

Section: Introductionmentioning

confidence: 92%

Infinite charge mobility in muscovite at 300 K

Russell¹,

Archilla²,

Frutos³

et al. 2017

EPL

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Evidence is presented for infinite charge mobility in natural crystals of muscovite mica at room temperature. Muscovite has a basic layered structure containing a flat monatomic sheet of potassium sandwiched between mirror silicate layers. It is an excellent electrical insulator. Studies of defects in muscovite crystals indicated that positive charge could propagate over great distances along atomic chains in the potassium sheets in absence of an applied electric potential. The charge moved in association with anharmonic lattice excitations that moved at about sonic speed and created by nuclear recoil of the radioactive isotope 40 K. This was verified by measuring currents passing through crystals when irradiated with energetic alpha particles at room temperature. The charge propagated more than 1000 times the range of the alpha particles of average energy and 250 times the range of channelling particles of maximum energy. The range is limited only by size of the crystal.

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Section: Introductionmentioning

confidence: 92%

Infinite charge mobility in muscovite at 300 K

Russell¹,

Archilla²,

Frutos³

et al. 2017

EPL

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“…There is also interest in the study of the possibility of excitation and propagation of solitons, discrete breathers and kinks in two-dimensional lattices. Different interatomic potentials, including discrete sine-Gordon and Lennard-Jones 27,28,45,46 and Morse 29,47 potentials, were used in these studies which confirm the existence and long lifetime of the kink solutions in two-dimensional lattices, including a two-dimensional model proposed for mica muscovite 27,28 . In the present work, we consider a one-dimensional lattice model which allows us to perform more rigorous study of the existence and stability of nonlinear excitations in a system with realistic interatomic potentials.…”

Section: Nonlinear Waves In Two-dimensional Latticesmentioning

confidence: 74%

“…Discreteness of the media seriously obstructs existence of exact moving topological solitons 18 . However, it has been shown in numerous cases both analytically [19][20][21][22] and numerically [23][24][25][26] that these solutions exist, also in two-dimensional lattices [27][28][29] ,despite the obvious resonance with the plane waves of the system. Therefore they fall into the family of the embedded solitons, that are literally embedded in the linear spectrum of the system as defined in Ref.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear waves in a model for silicate layers

Archilla

Zolotaryuk

Kosevich

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Some layered silicates are composed of positive ions, surrounded by layers of ions with opposite sign. Mica muscovite is a particularly interesting material, because there exist fossil and experimental evidence for nonlinear excitations transporting localized energy and charge along the cation rows within the potassium layers. This evidence suggests that there are different kinds of excitations with different energies and properties. Some of the authors proposed recently a one-dimensional model based on physical principles and the silicate structure. The main characteristic of the model is that it has a hard substrate potential and two different repulsion terms, between ions and nuclei. In a previous work with this model, it was found the propagation of crowdions, i.e., lattice kinks in a lattice with substrate potential that transport mass and charge. They have a single specific velocity and energy coherent with the experimental data. In the present work, we perform a much more thorough search for nonlinear excitations in the same model using the pseudospectral method to obtain exact nanopteron solutions, which are single kinks with tails, crowdions, and bi-crowdions. We analyze their velocities, energies, and stability or instability and the possible reasons for the latter. We relate the different excitations with their possible origin from recoils from different beta decays and with the fossil tracks. We explore the consequences of some variation of the physical parameters because their values are not perfectly known. Through a different method, we also have found stationary and moving breathers, that is, localized nonlinear excitations with an internal vibration. Moving breathers have small amplitude and energy, which is also coherent with the fossil evidence.

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“…They can be produced by K + recoil, leaving behind a vacancy or anti-kink. Simulations have been done for 1D models, and at least in some models the kinks do not spread for a long distance [14,15]. Supersonic lattice kinks have only a discrete set of velocities and energies for which they do not radiate energy.…”

Section: A Lattice Kink or Crowdionmentioning

confidence: 99%

On the charge of quodons

Archilla¹,

Russell²

2016

LoM

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Muscovite mica is a mineral in which the tracks of charged swift particles, from radioactivity or cosmic rays, can be recorded and made visible by decoration with the mineral magnetite. Also, the tracks of quasi-one-dimensional lattice excitations, called quodons, moving along close-packed directions can be recorded. Most quodon tracks evolve from nuclear recoils following decay of the radioactive isotope . We analyze the possible results taking into account charge, energy and momentum conservation and considering the possible ionization states of the K atoms, which can be intrinsic localized modes, solitons, kinks or crowdions, travelling charge states and combinations of them.

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Nonlinear propagating localized modes in a 2D hexagonal crystal lattice

Cited by 48 publications

References 29 publications

Infinite charge mobility in muscovite at 300 K

Infinite charge mobility in muscovite at 300 K

Nonlinear waves in a model for silicate layers

On the charge of quodons

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