An analytical theory for propagation in graphene
An analytical theory for propagation in graphene lead image
Experiments have uncovered many of graphene’s remarkable properties such as low electrical resistance and high thermal conductivity, but to fully model graphene’s properties, one requires propagation models for the hexagonal lattice structure of graphene sheets — a discrete environment that does not have clear correspondence with the smooth classical case.
The new paper by Yukihide Tadano introduces a mathematical model for the discrete structure of graphene using modified wave operators. This approach yields solutions for long-range scattering that could predict the propagation of quantum particles such as electrons and phonons.
Because it is an analytic model, Tadano said the model is a powerful method for exploring graphene’s properties, and can extend its application for the study of topological insulators in general.
“This paper considers the forward scattering problem, but the calculation of the S-matrix is possible using wave operators in this paper,” he said.
Considering forward scattering is useful for deducing electrical and thermal properties, and the construction of the S-matrix allows the inverse scattering problem to be solved, enabling the elucidation of lattice details such as defects.
Tadano built on previous work done on a square lattice, which represented particles in potentials decaying at infinity as a scattering state of a tight-binding Hamiltonian without perturbations, and extended the model to a hexagonal structure. According to him, the long-range nature of the coulomb forces within the lattice are difficult to calculate, so choosing the right method for the approximations is critical.
“It is surprising that we can use microlocal analytic methods for operators on discrete space,” Tadano said. “Strong tools of microlocal analysis developed in the study of Schrödinger operators help us find the properties of tight-binding Hamiltonians.”
Source: “Long-range scattering theory for discrete Schrödinger operators on graphene,” by Yukihide Tadano, Journal of Mathematical Physics (2019). The article can be accessed at https://doi.org/10.1063/1.5087013 .
