Numerical Simulation of Quantum Critical Behaviour in Graphene and Related Systems

Prof. Simon Hands, Department of Physics, Swansea University
Prof. Allan MacDonald (Center for Complex Quantum Systems, University of Texas at Austin)

Objective: It is proposed to study 2+1d relativistic quantum field theories of fermions by numerical lattice field theory simulations employing the recently proposed “domain wall fermions” (Hands, JHEP09(2015)047), which unlike earlier formulations faithfully capture the crucial global symmetries. The goal is to characterise the Quantum Critical Point where, for sufficiently strong coupling, the properties of the system alter abruptly, eg. changing from metallic to insulating behaviour as a consequence of the condensation of bound pairs of positive and negative charge carriers in the ground state. The scaling of physical observables near the QCP is universal, independent of the fine details of the lattice discretisation, effectively defining a strongly-interacting quantum field theory at this point.

Significance: the theory in question is an effective description for low energy excitations in graphene, a 2-dimensional allotrope of carbon with remarkable electronic properties. The strength of the interaction between charge carriers in graphene sheets depends on the mounting substrate, but can be strong enough to lie in the vicinity of the QCP. Gap formation leading to a Mott insulating phase has profound implications for the feasibility of graphene-based electronic devices. The generalisation to two-layer graphene systems, where carrier density can be controlled with a bias voltage is straightforward. Theory can compare with the rich phenomenology of monolayer, bilayer, trilayer, and tetralayer systems now being explored experimentally.

The project student will be based in Swansea’s Particle Theory group and receive a thorough grounding in relativistic quantum field theory and associated topics. High performance computing resources will be made available both locally and via HPC Wales, and familiarity with a high-level programming language such as Fortran is desirable. The student will develop skills and knowledge in condensed matter physics both through both regular video meetings with Prof. MacDonald and hopefully at least 2 extended visits to Austin.