Informal Physics Seminar: Pseudospins and Time-Reversal Invariance in the Trigonal Band Structure of Graphene

CFM Seminars

Speaker

Roland Winkler, Argonne National Laboratory and Northern Illinois University, USA. Currently Ikerbasque sabbatical fellow at UPV, Bilbao

When

2011/11/29
13:00

Place

Auditorium of the Centro de Fisica de Materiales, Paseo Manuel de Lardizabal 5, Donostia

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Pseudospins and Time-Reversal Invariance in the Trigonal Band Structure of Graphene R. Winkler 1,2,3,4 currently 1The University of the Basque Country, Bilbao 2IKERBASQUE, Basque Foundation for Science 3Argonne National Laboratory, Argonne, IL 60439, USA 4Northern Illinois University, DeKalb, IL 60115, USA In recent years the unusual band structure of graphene (a single layer of graphite) has raised significant interest. While for most materials the band dispersion E(k) near a band extremum is a quadratic function of the wave vector k, the band dispersion of graphene is linear, thus resembling the spectrum of massless Dirac fermions. We will present a systematic symmetry analysis of the band structure in graphene near the Fermi edge. We will show that the k-linear dispersion arises as an unusual consequence of the interplay of time-reversal invariance and the trigonal symmetry of the electron states. The symmetry analysis allows us to incorporate perturbations such as external electric and magnetic fields, strain, and spin- orbit coupling in a systematic way, so that our findings are directly relevant for comparison with experiments. (Pseudo) spin degrees of freedom which occur in the Dirac-like Hamiltonian of graphene have raised significant interest due to possible applications in spintronics and quantum com- puting. In general we need to distinguish between systems incorporating the electrons’ proper spin degree of freedom and systems utilizing pseudospin degrees of freedom showing spin-like properties. Here we compare in detail the properties of spin and pseudospin degrees of freedom. We show that time reversal θ allows one to distinguish the proper spin degree of freedom from common examples of pseudospin degrees of freedom. We demonstrate that half-integer pseudospin degrees of freedom can be either fermionic (characterized by theta^2 = −1) or bosonic (theta^2 = +1). Spin- dependent transport provides a means to distinguish these two cases. If the system is fermionic, it can show weak antilocalization whereas a bosonic pseudospin degree of freedom gives rise to weak localization. Work done in collaboration with Ulrich Zulicke (Victoria University, New Zealand).