Upon ultrafast high-energy-density deposition into matter, e.g. with femtosecond lasers or swift heavy ions (SHI), an electronic system of a solid is heated to temperatures significantly above the atomic one. This transient state then relaxes leading to equilibration of the electronic and atomic temperatures. This process of equilibration takes place via so-called electron-phonon (or, more generally, electron-ion) coupling. It has been predicted with various theoretical approaches that electron-ion coupling is a relatively slow process, leading to typically picosecond timescales of equilibration between the electronic and the atomic temperatures at typical irradiation conditions: dynamic structure factor calculations 1,2, a coupled modes approach 3, tight-binding molecular dynamics 4, all show similar results. They are supported by state-of-the-art experimental observations of electron-ion coupling in solids, suggesting that it may be even slower than most theories predict 5,6.
In a stark contrast to those results, it has been known for over decades that SHI irradiation of solids leads to creation of ion tracks at extremely short timescales. SHIs primarily deposit energy into the electronic system, similarly to laser pulse irradiation 7. The difference from the laser spot is that excited electrons appear within a sub-nanometer vicinity around the ion trajectory 7. Such extremely localized energy deposition leads to fast energy transport and cooling of the electronic system in an ion track within hundred-femtosecond timescales – much shorter than those required for electron-phonon coupling to heat the atomic system 1. Yet, SHI tracks are detected experimentally 8, implying that much faster atomic heating takes place there.
A necessity of significant heating of materials in SHI impacts to form observable tracks during times of cooling of the electronic system suggests extremely fast coupling of the electron system to the atomic one, see Fig. 1 extracted from the data from Ref. 9. Those estimates imply that the atomic heating must be orders of magnitude faster than that measured in laser-irradiation experiments and consistently calculated with various models. A contradiction ensued, puzzling the respective communities for over two decades.
In this work, we point out that the electron-phonon coupling is not the only mechanism of atomic heating. Ultrafast energy deposition into the electronic system also affects an atomic potential energy surface because electrons form an interatomic potential. Excitation of electrons changes the electronic distribution, which in turn modifies the interatomic potential 10,11. This converts into increase of the kinetic energy of atoms because altered interatomic forces push atoms towards their new equilibrium positions 10,12.
At high deposited doses, or correspondingly high electronic temperatures, it may lead to phase transitions even without significant atomic heating. The most famous example of this effect is the so-called nonthermal melting 13,14. It is known since 1990s to take place in covalently bonded semiconductors 10,12,15. Recently, it has been theoretically shown that the same effect also takes place in ionic crystals 16, oxides 17 and polymers 18. Thus, nonthermal phase transitions may be regarded as a universal effect taking place in non-metallic targets upon energy deposition faster than the electron-ion (electron-phonon) coupling (while an even more complex picture of various nonthermal effects may take place in metals 19). Such nonthermal phase transitions are accompanied by increase of the atomic temperature as a consequence of atomic acceleration as a reaction to interatomic potential changes18,20.
At doses below a nonthermal phase transition threshold, excited electrons also trigger some “nonthermal” atomic heating via modification of the potential energy surface. This effect is known as displacive excitation of coherent phonons 21, or squeezed phonons as a precursor to nonthermal melting 22.
Atomic heating due to modification of the interatomic potential after excitation of the electronic system forms a distinct mechanism from the electron-phonon coupling. The latter one relies on the electron transitions between electronic energy levels triggered by atomic displacements, i.e. it is a nonadiabatic effect 4,23,24. In contrast, nonthermal atomic heating via modification of the interatomic potential is an adiabatic effect, occurring within Born-Oppenheimer approximation 20,22, without nonadiabatic electron-ion coupling involved.
Below we will consider the nonthermal atomic heating in various materials, its rate and timescales at various doses. We will also analyze a synergy between nonthermal heating and electron-ion coupling, considering the dependence of the coupling parameter on the atomic temperature.