(Poster) Dynamical phase transition in vibrational surface modes

HERNAN L. CALVO; HORACIO M. PASTAWSKI

Angra dos Reis

Congreso; XII Latin American Congress of Surface Science and its applications; 2005

Sociedade Brasileira de Fisica

We consider the dynamical properties of a standard model of vibrational surface modes: an oscillator of mass m0 and natural frequency w0 which is coupled to an semi-infinite harmonic chain (bulk) of masses m with an excitation spectrum in the range 0 < w < 2*wx. Here, wx relates the interactions between bulk masses. By evaluating the Green´s function to infinite order in perturbation theory we obtain the exact spectrum of surface excitations J0(w) for the whole range of w0. We use this result to discuss the dynamics of the surface mass. One can identify the effective frequency wR of the surface resonance as the real part in the pole of Green´s function. For small values at the bulk masses, i.e. a = m/m0 < 1, the effective frecuency is centered at wR = w0/sqrt(1-a/2) and has a width a*wx. There are two regimes standardly discussed in theliterature: the localized regime that appears when the effective frequency takes values near the bandwidth, i.e., w0 > wx*(1+sqrt(1-a)). In this regime, bulk displacements decrease exponentially when the distance from the surface mass increases and the excitation survives undamped. For the other hand we have the oscillatory regime where the surface mode decays in bulk excitations with a rate h´ associated to the imaginary part of the pole. However, we also find a second phase transition when wR width is affected by the left band edge. This phase transition occurs when the natural frequency is w0 = wx*(1-sqrt(1-a)) . Hence, a third regime appears for these small w0´s values where the mode frequency becomes purely imaginary and describes an overdamped regime. Notably, this transition, which to our knowledge has not been previously described, has an exact correspondence to the oscillating-overdamped transition obtained for the standard phenomenological model of an oscillator with a frictional force proportional to the speed -h*v*m0. In the extreme case where a tends to 0, wx tends to infinity with a*wx = const. we observe the same behavior in both models for h = a*wx. Therefore, we obtain with such simple model an analytical description of the dissipation process in harmonic systems. This phase transitions between the described regimes can become of great importance to describe the vibrational properties of systems like cantilevers and molecular nanostructures.