**Title:** A study of vibrational properties of twisted bilayer graphene system

**Presenter:** Mahesh R. Neupane

**Affiliation:** University of California, Riverside

**Co-authors:** Darshana Wickramaratne, Supeng Ge, K. M. Masum Habib, and Roger K. Lake

**Abstract:** Graphene, a two-dimensional (2D) allotrope of carbon, has become a material of choice for theoretical and experimental studies because of its distinctive electronic, thermal and optical properties.
Both the electrical and thermal properties of graphene qualitatively change between the three-dimensional (3D) form (graphite) and two-dimensional (2D) form (graphene). Real applications of 2D graphene require
a finite cross section to transport a useful amount of heat or current. One possible approach to achieving this is using a stack of misaligned layers of graphene in which the layer-to-layer orientation is random.
The experimental and theoretical evidence is clear that for twist angles greater than ~10o, the electronic states of the individual layers in twisted, bilayer graphene are decoupled **1,2,3**. The effect of twist
angle on the phonon dispersion is still an open question, and the effect of twist angle on the in-plane thermal transport has yet to be studied. Motivated by this, we investigate the twist angle dependent vibrational
properties of the twisted bilayer graphene system, using Fix-Phonon module **4**, as implemented in the LAMMPS, a classical molecular dynamics code **5**. The adaptive intermolecular reactive empirical bond order (AIREBO)
potential **6, 7** is used to describe the carbon–carbon interactions, carbon-hydrogen interactions and non-bonding atomic interactions. The phonon spectra are computed by evaluating the eigenvalues of the dynamical
matrix constructed by observing the displacement fluctuations of atoms during molecular dynamic simulations, based on the fluctuation–dissipation theorem. In order to validate the model and method used, vibrational
properties of single and unroated bilayer systems are verified against the results from the first principle calculation. The observed vibrational properties for the twisted bilayer system such as phonon modes, group
velocities, and phonon density of states, are compared against the published experimental data.

This work was supported in part by FAME, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.

**1** S. Shallcross, S. Sharma, and O.A. Pankratov, Phys. Rev. Lett. 101 (056803), 2008

**2** A. Luican, G. Li, A. Reina, J. Kong, R.R. Nair, K.S. Novoselov, A.K. Geim, and E.Y. Andrei, Phys. Rev. Lett. 106 (126802), 2011

**3** P. Poncharal, A. Ayari, T. Michel, and J.-L. Sauvajol, Phys. Rev. B 78 (113407), 2008

**4** L.T. Kong, Comput Phys Commun, 182 (2201), 2011

**5** S.J. Plimpton , J Comp Phys, 117 (1), 1995

**6** S.J. Stuart, A.B. Tutein, J.A. Harrison , J Chem Phys, 112 (14), 2000

**7** D.W. Brenner , Phys Status Solidi B, 217 (1), 2000