The origin and nature of Boson Peak: the normal mode analysis of disordered granular crystals

TL;DR

This study investigates the Boson peak in disordered granular crystals, revealing its origin as an interplay of mesoscopic screening and microscopic elasticity disorder, providing new insights into vibrational states in amorphous materials.

Contribution

It demonstrates the presence of Boson peak in 2D granular packings and proposes a novel mechanism explaining its origin beyond traditional theories.

Findings

Boson peak observed in 2D granular packing.

DOS structures resemble those in glasses and gels.

Boson peak arises from mesoscopic screening and elasticity disorder.

Abstract

Despite extensive theoretical \cite{GanterPRL1998, ElliotPRL2001,SchirmacherPRL2007, TanakaNatureM2008, MonacoPNAS2009, MarruzzoSCIRP2013} and experimental studies \cite{ChumakovPRL2011, ChumakovPRL2014, KayaScience2010,KChenPRL2010, LXuPRL2012, BonnPreprint2014}, a longstanding puzzle in condensed matter physics remains regarding the origin and nature of "Boson peak" (BP), where the vibrational density of states (DOS) in glasses possesses an excess of states compared with the crystalline counterpart. Here we show that BP is successfully observed in 2D hexagonal granular packing, where the disorder is due to the force network, i.e. the spatial heterogeneity of elasticity \cite{MarruzzoSCIRP2013}. Using photo-elastic techniques \cite{TrushNature2005}, the disordered particle interaction can be precisely measured to resolve the origin and nature of BP for the first time in a real scenario. We discover the structures of DOS of disordered crystals reminiscent of the corresponding perfect crystals, which is consistent with the recent studies in $SiO_2$\cite{ChumakovPRL2014} and in disordered gels\cite{LorenzoGelPaper2011}, notwithstanding the drastically different systems. Moreover, we propose a mechanism to clarify that BP is not merely a broadened and shifted van Hove singularity \cite{ElliotPRL2001, ChumakovPRL2011} but instead it is due to an interplay of the mesoscopic screening effect and the microscopic elasticity disorder -- causing, respectively, the broadening and the attenuation of the first and the second van Hove singularity. This may lead to an in-depth understanding of BP in structure glasses.