Soft Report - Dipartimento di Fisica - Sapienza

The low-energy excess of vibrational states inv-SiO2: the role of transverse dynamicsInsulating disordered solids exhibit some commonpeculiarities in their low-temperature and low-energydynamics, including an excess of modes in thevibrational density of states, known as the bosonpeak (BP). An unambiguous understanding of theseextra modes, and of their possible relation with otheranomalies, is still lacking, In the case of v-SiO2, themost widely accepted explanation is that the BPoriginates from the piling up of modes near the firstvan Hove singularity of the transverse acousticvibrational branch. In addition to the ambientpressure data, useful information is available for v-SiO2 at higher densities: densification results in ashift of the BP towards higher energies and in asimultaneous decrease of its intensity.a weak shoulder in the transverse spectra only at Q> 10 nm −1 . We assign this feature to the longitudinalsound-like branch. The behaviour of the low energyexcitation is complementary: it is always present inthe transverse spectra, while it appears in thelongitudinal currents only at Q > 8 nm−1. At smallQ, the low energy peak disperses linearly with asound velocity of ≈3800 ms −1 (appropriate for thetransverse sound modes), and becomes almost nondispersingat Q > 8 nm−1. This feature —which isthe main one in the transverse spectra— is thetransverse acoustic mode. The presence of thesignature of transverse dynamics in the longitudinalcurrent spectra, and vice versa, is due to the factthat the polarization character of the modes becomesill defined at short wavelengths. Spectra for thesample at the highest density studied (ρ=4.0 gcm −3 ), are reported in the right panels of the figure.One can observe that no evidence of wronglypolarized modes is present; moreover, the T branchno longer shows a flattening.The conclusion that can be drawn is that the excessof states in the normal sample accumulates in aregion, which is almost coincident with the energyrange where the transverse branch flattens,indicating that the BP arises from the high Q portionof the transverse branch. This assignment isconfirmed by the behaviour of the high-energytransverse dynamics upon densification.Fig. 1 - Longitudinal (full) and transverse (dashed)current spectra at selected Q values (nm −1 ) for ρ =2.2 (left) and 4.0 rigt) g cm −3 .We present here simulation results on v- SiO 2 atdifferent densities which help in clarifying the originand the nature of the excess modes, as well as theintensity and shift effects on the BP as a function ofdensity.The systems investigated consist of 680 SiO 2 units(N=2040 ions), enclosed in cubic boxes of differentlengths (from L=3.1359 nm, ρ=2.2 g*cm −3 for theglass at room pressure, down to L=2.5693 nm,density ρ=4.0 g*cm −3 ), with periodic boundaryconditions. The ions interact through the BKS [31]two-body potential.We have computed the dynamic structure factorS(Q,ω) and the longitudinal (L) and transverse (T)current spectra C L,T(Q,ω). In figure 1, left panel, wereport longitudinal and transverse current spectra atselected Q values for the uncompressed sample (ρ =2.2 g cm−3). For Q larger than about 8 nm −1 , bothCL(Q,ω) and CT(Q,ω) show two distinct maxima, andthis structure becomes more and more evident withincreasing Q. The excitation at higher energydisperses with Q and is observed at all Q values inthe longitudinal current spectra, while it shows up asExperimentally, it is observed that upon densification(i) the BP shifts to higher energy and (ii) its intensitystrongly decreases. From our simulations we observethat, by increasing the density, the T branch flattensat a higher energy and, upon further densification,no flattening is observed at all. A similar behaviour isobserved for the calculated density of states as afunction of density [1]: the low-energy part of theDOS shifts to higher energies and decreases inintensity. As a consequence, the BP stronglydecreases in intensity and shifts to high energies [1].References[1] O. Pilla et al., J. Phys. Cond. Mat. 16, 8519(2004).Authors:O. Pilla (1), S. Caponi (1,2), A. Fontana (1,2), J.R.Goncalves (1,3), M. Montagna (1), F. Rossi (1), G.Viliani (1,2), L. Angelani (4,5), G. Ruocco (2,4), G.Monaco (6), F. Sette (6) - (1) Dipartimento di Fisica,Università di Trento, Italy; (2) INFM-CRS SOFT,Università di Roma La Sapienza, Italy; (3)Departamento de Fısica, Universidade do Cearà,Brazil; (4) Dipartimento di Fisica, Universit`a diRoma La Sapienza, Italy(5) INFM-CRS SMC,Universit`a di Roma La Sapienza, Italy; (6) EuropeanSynchrotron Radiation Facility, Grenoble, France75SOFT Scientific Report 2004-06