We have developed a semiclassical, tight-binding model for the transfer of an electron or hole between ions in a layered silicate which is also an insulator without free states in the conduction and valence bands a large band gap. The transfer probability increases exponentially when ions became closer allowing the coupling of vibrations and electron transfer. We have solved the problem of the large different time scales between electron and ions movement using powerful algorithms that are symmetric, symplectic and conserve the charge probability at each integration step [1], reproducing the physical properties of the system and the analytical properties of the model. We have been able to obtain breathers, that is, localized vibrations that when coupled to a charge are called polarobreathers. They can be stationary with long-life and they can also travel long distances. We obtain approximate ones using specific but simple initial conditions and using them as a seed obtain exact polarobreathers that reproduce their profile after an integer number of sites called the step, extending the theory developed for exact breathers without charge [2,3].The frequency-momentum spectrum of the lattice, the charge probability and the charge amplitude are related but show different frequencies. For the exact polarobreathers there is a fundamental period which is multiple of both the fundamental periods of the three quantities. These quantities have also different steps, that is, the number of sites when a function is repeated. We developed methods to deal with the invariance of the charge amplitude under multiplication by exp(-i mu t), one of them based on the density matrix theory. The results allow for a precise description of exact polarobreathers and advance the possibility for identification in real systems. They can also explain the phenomenon of hyperconductivity observed experimentally in layered silicates, which consists of the transport of charge in absence of an electric field when the crystal is bombarded with alpha particles [4-7].
The authors acknowledge the following projects and grants:
JFRA: MICINN PID2019-109175GB-C22, Junta de Andalucía US-1380977, USVIIPPITUS 2023.
JB: Latvia Post-doctoral Research Aid No. 1.1.1.2/VIAA/4/20/617.
YD: JSPS Kahenhi (C) No. 19K03654.
MK: JSPS Kakenhi (C) No. 21K03935..
References:
[1] J Bajārs; JFR Archilla; Mathematics 10 3460 (2022)
[2] JFR Archilla, Y Doi; M. Kimura; Phys. Rev E 100 022206 (2019)
[3] J Bajārs; JFR Archilla; Physica D 441 133497 (2022)
[4] FM Russell; JFR Archilla; F Frutos; S Medina-Carrasco; EPL 120 46001 (2017)
[5] FM Russell; MW Russell; JFR Archilla; EPL 127 16001 (2019)
[6] FM Russell; JFR Archilla; Phys. Status Solidi RRL 19 2100420 (2022)
[7] FM Russell; JFR Archilla; Low Temp. Phys 48 1009 (2022)
