Classification of topological phonons in linear mechanical metamaterials

Topological phononic crystals, alike their electronic counterparts, are characterized by a bulk–edge correspondence where the interior of a material dictates the existence of stable surface or boundary modes. In the mechanical setup, such surface modes can be used for various applications such as wave guiding, vibration isolation, or the design of static properties such as stable floppy modes where parts of a system move freely. Here, we provide a classification scheme of topological phonons based on local symmetries. We import and adapt the classification of noninteracting electron systems and embed it into the mechanical setup. Moreover, we provide an extensive set of examples that illustrate our scheme and can be used to generate models in unexplored symmetry classes. Our work unifies the vast recent literature on topological phonons and paves the way to future applications of topological surface modes in mechanical metamaterials.

EFFECTS OF SAMPLE-SPECIFIC VARIATIONS AND FLUCTUATIONS OF THERMAL OCCUPANCY ON FLUCTUATIONS OF THERMODYNAMIC QUANTITIES

Standard results for the fluctuations of thermodynamic quantities are derived under the assumption of sampling identical systems that are in different, not fully equilibrated states. These results apply to fluctuations with time in a particular macroscopic body and can be traced to the fluctuations of thermal occupancy. When many identically prepared — but not identical — systems are studied, mesoscopic fluctuations due to variations from sample-to-sample contribute to the fluctuations of thermodynamic quantities. We study the combined effect of mesoscopic fluctuations and fluctuations of thermal occupancy. In particular, we evaluate the total particle number and specific heat fluctuations in a two-dimensional, noninteracting electron gas in classically integrable and chaotic circumstances.

ELECTRONIC TRANSPORT IN RANDOM DIMER/TRIMER GaAs/AlxGa1-xAs SUPERLATTICES

By using a transfer matrix model, we examined in this paper the extended states of a noninteracting electron in one-dimensional dimer/trimer randomly placed in superlattices (SLs). We study numerically the effects of short-range correlated disorder on the electronic transport properties and intentionally disordered GaAs/Al x Ga 1-x As SLs. We consider layers having identical thickness where the Al concentration x takes at random two different values with the constraint that one of them appears only in pairs or triply i.e., the random dimer/trimer barrier.