Modeling Graphene using Holography

Authors: Asad Imam, Matthew Lippert

SUNY Campus: SUNY Old Westbury

Presentation Type: Poster

Location: Old Union Hall

Presentation #: 57

Timeslot: Session C 1:45-2:45 PM

Abstract: Graphene is a single layer of carbon atoms arranged in a honeycomb structure. It has unique electrical, thermal, and mechanical properties, making it a strong candidate for future electronics, which could bring about a new era of technological innovation. The electrons in graphene are strongly coupled, which means traditional methods such as electrodynamics are insufficient to study such a system, requiring a different approach to study this system. Holography is a tool from String Theory that can be used to study such strongly interacting systems. Holography provides a duality between a strongly interacting QFT in d-dimensions (the boundary) to a classical gravitational theory in d+1-dimensions (the bulk). In our research, we study the effects in the bulk by constructing a D3-D5 model which are 3-dimensional and 5-dimensioal D-branes respectively. We do this by using an effective action to describe the D-branes, which essentially minimizes the area of the D-branes. Making use of symmetries we reduce the equations of motion to Ordinary Differential Equations for two variables. We then numerically solved these differential equations using Mathematica and found multiple solutions with the same boundary conditions. For such solutions we are currently investigating the free energy to determine which solution will be thermodynamically stable. The long-term goal is to work out the full phase space of these D-brane embeddings.