Lattice relaxation,mirror symmetry and magnetic field effects on ultraflat bands in twisted trilayer graphene

Twisted graphene multilayers exhibit strongly correlated insulating states and superconductivity due to the presence of ultraflat bands near the charge neutral point.In this paper,the response of ultraflat bands to lattice relaxation and a magnetic field in twisted trilayer graphene(tTLG)with different stacking arrangements is investigated by using a full tight-binding model.We show that lattice relaxations are indispensable for understanding the electronic properties of tTLG,in particular,of tTLG in the presence of mirror symmetry.Lattice relaxations renormalize the quasiparticle spectrum near the Fermi energy and change the localization of higher energy flat bands.Furthermore,different from the twisted bilayer graphene,the Hofstadter butterfly spectrum can be realized at laboratory accessible strengths of magnetic field.Our work verifies tTLG as a more tunable platform than the twisted bilayer graphene in strongly correlated phenomena.

Phonon dispersion on Ag(100)surface:A modified analytic embedded atom method study

Within the harmonic approximation, the analytic expression of the dynamical matrix is derived based on the modified analytic embedded atom method （MAEAM） and the dynamics theory of surface lattice. The surface phonon dispersions along three major symmetry directionsX,M, and X（v） are calculated for the clean Ag （100） surface by using our derived formulas. We then discuss the polarization and localization of surface modes at points X and by plotting the squared polarization vectors as a function of the layer index. The phonon frequencies of the surface modes calculated by MAEAM are compared with the available experimental and other theoretical data. It is found that the present results are generally in agreement with the referenced experimental or theoretical results, with a maximum deviation of 10.4%. The agreement shows that the modified analytic embedded atom method is a reasonable many-body potential model to quickly describe the surface lattice vibration. It also lays a significant foundation for studying the surface lattice vibration in other metals.

A Theoretical Interpretation of Free Volume at Glass Transition

We device a relaxed lattice model （RLM） to study the mechanism of glass transition, which unifies the cage- effects from particle-particle interaction and entropy. By analyzing entropy in RLM with considering the influence of interactions on equilibrium, we demonstrate that glass transition is a second-order phase transition. For a perfect one- dimensional linked particle system like linear polymer under normal pressure, the free volume at glass transition is rigorously deduced out to be 2.6%, which provides a theoretical basis for the iso-free volume of 2.5% given by Willian, Landel and Ferry （WLF） equation. Extending to system with dead particles linked with higher dimensions like branched or cross-linked chains under positive or negative pressure, free volume at glass transition is varied, based on which we construct a phase diagram of glass transition in the space of free volume-dead particle-pressure. This demonstrates that free volume is not the single parameter determining glass transition, while either dead particles like cross-linked points or external force fields like pressure can vary free volume at the glass transition.