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Effects of Interactions and Magnetic Fields on Topological Surface States

 Author / Creator
 Shepherd, Drew

We study the effects of electronelectron interactions and magnetic fields on surface states of threedimensional topological insulators (3D TIs). In this work we use an effective Hamiltonian to describe a slab of the 3D TI Bi$_2$Se$_3$. In the noninteracting limit, and for slab thicknesses greater than approximately 40 \AA, we observe a Dirac cone in the bulk bandgap whose states are highly localized to the surface. Similar behaviour is seen in the spectral function: near the surface it has peaks near the Dirac cone states, and in the bulk, the Dirac cone disappears. In addition, the Dirac cone gap closes at approximately 60 \AA, which agrees well with experimental measurements, and the density of states near the Dirac point is found to be linear. Next, we incorporate shortrange electronelectron interactions through the calculation of the second order selfenergy, and its antiHermitian part, the broadening function. Examining the broadening function allows us to study the qualitative behaviour of the quasiparticle lifetime near the Fermi level. We obtain an infinite lifetime at the Fermi level, and a finite lifetime as we move away from this energy. Returning to the noninteracting regime, but this time adding a finite magnetic field, we observe Landau level (LL) peaks in the density of states. As the thickness of the slabs increases the total number of states increases, but the number of LLs localized to the surface remains constant. The observation of a zeroth LL and the LLs being linear in $\sqrt{nB}$, indicates that the surface states support a relativistic LL dispersion. Finally, electronelectron interactions were added to our topological insulator model for a finite magnetic field. Here, we derived an expression for the second order selfenergy and its accompanying broadening function.

 Graduation date
 201711

 Type of Item
 Thesis

 Degree
 Master of Science

 License
 This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for noncommercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.