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

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.