We theoretically investigate tunneling magnetoresistance (TMR) devices, which are probing the spin-momentum coupled nature of surface states of the three-dimensional topological insulator Bi$_{2}$Se$_{3}$. Theoretical calculations are performed based
on a realistic tight-binding model for Bi$_{2}$Se$_{3}$. We study both three dimensional devices, which exploit the surface states of Bi$_{2}$Se$_{3}$, as well as two-dimensional devices, which exploit the edge states of thin Bi$_{2}$Se$_{3}$ strips. We demonstrate that the material properties of Bi$_{2}$Se$_{3}$ allow a TMR ratio at room temperature of the order of 1000%. Analytical formulas are derived that allow a quick estimate of the achievable TMR ratio in these devices. The devices can be used to measure the spin polarization of the topological surface states as an alternative to spin-ARPES. Unlike TMR devices based on magnetic tunnel junctions the present devices avoid the use of a second ferromagnetic electrode whose magnetization needs to be pinned.
We study the properties of the surface states in three-dimensional topological insulators in the presence of a ferromagnetic exchange field. We demonstrate that for layered materials like Bi$_2$Se$_3$ the surface states on the top surface behave qual
itatively different than the surface states at the side surfaces. We show that the group velocity of the surface states can be tuned by the direction and strength of the exchange field. If the exchange field becomes larger than the bulk gap of the material, a phase transition into a topologically nontrivial semimetallic state occurs. In particular, the material becomes a Weyl semimetal, if the exchange field possesses a non-zero component perpendicular to the layers. Associated with the Weyl semimetallic state we show that Fermi arcs appear at the surface. Under certain circumstances either one-dimensional or even two-dimensional surface flat bands can appear. We show that the appearence of these flat bands is related to chiral symmetries of the system and can be understood in terms of topological winding numbers. In contrast to previous systems that have been suggested to possess surface flat bands, the present system has a much larger energy scale, allowing the observation of surface flat bands at room temperature. The flat bands are tunable in the sense that they can be turned on or off by rotation of the ferromagnetic exchange field. Our findings are supported by both numerical results on a finite system as well as approximate analytical results.
