If the displacements from the equilibrium positions of some atoms in a crystal are large enough, the linear description is no longer valid. Stationary and travelling solutions are no longer phonons and very often can remain localized a long time. They can be of different types as kinks, solitons, breathers and others. If they transport electric  charge they are known as polarobreathers, solectrons and other terms. 

Figure 1: A breather in germanium

Figure 2: Left. Fourier of the breather in GE. Right. theoretical (lines) and experimental (circles) phonon spectrum of GE.

The reason for localization is that the frequencies and momenta  of a localized excitation do not overlap with the phonon frequencies and momenta. As an example, Figure 1 shows a stationary breather in Ge that involves the out of phase vibration of two atoms and their six neighbours. Figure 2 plots its  Fourier spectrum.  The single fundamental frequency and its harmonics reveal the periodicity and the nonlinear character of the vibration. The frequencies are well above germanium phonon bands.   

Mathematically, the proof of existence of stationary breathers is well established [1].  Moving breathers, typically have a single frequency in the moving frame, where solitons and kinks do not vibrate [2]. Breathers have been obtained using molecular dynamics [3] and ab initio molecular dynamics [4]. They can experience elastic scattering in simulations [5]. Experimentally, moving localized excitations can be stimulated by ion bombardment [6] and if they transport charge, the current can be measured [7]. Their signature appears in neutron spectroscopy [8].  

We need more theory to predict properties that can be measured and more measurements where nonlinear localization appears. Among them: spectroscopy, interaction with defects and phase transitions, electric currents, carrier density, production by plasmas and ions. This is the objective of the minicolloquium.  

References 

[1] R.S. Mackay, S. Aubry, Nonlinearity 7:1623 (1994). 

[2]  J.F.R. Archilla, Y. Doi, M. Kimura, Phys. Rev E 100:022206 (2019). 

[3] M. Haas, V. Hizhnyakov, A. Shelkan et al., Phys. Rev, B 84:144303 (2011). 

[4] I. Lobzenko, J. Baimova, K. Krylova, Chem. Phys. 530:110608 (2020). 

[5] J. Bajars, J.C. Eilbeck, B. Leimkuhler, Phys. Rev.  E 103, 022212 (2021).  

[6] F.M. Russell, J.C. Eilbeck, EPL  78:10004 (2007). 

[7] F. M. Russell, M. Russell, J.F.R. Archilla, EPL 127:16001 (2019)].  

[8] M.E. Manley, O. Hellman, N. Shulumba et al., Nat. Commun. 10:1928 (2019).