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# Effects of Interactions and Magnetic Fields on Topological Surface States

• Author / Creator
Shepherd, Drew
• We study the effects of electron-electron interactions and magnetic fields on surface states of three-dimensional 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 non-interacting 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 short-range electron-electron interactions through the calculation of the second order self-energy, and its anti-Hermitian 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 non-interacting 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 $\sqrt{|n|B}$, indicates that the surface states support a relativistic LL dispersion. Finally, electron-electron interactions were added to our topological insulator model for a finite magnetic field. Here, we derived an expression for the second order self-energy and its accompanying broadening function.

• Subjects / Keywords
Fall 2017
• Type of Item
Thesis
• Degree
Master of Science
• DOI
https://doi.org/10.7939/R3Z892V36