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We report on a study of an ultrathin topological insulator film with hybridization between the top and bottom surfaces, placed in a quantizing perpendicular magnetic field. We calculate the full Landau level spectrum of the film as a function of the applied magnetic field and the magnitude of the hybridization matrix element, taking into account both the orbital and the Zeeman spin splitting effects of the field. For an undoped film, we find a quantum phase transition between a state with a zero Hall conductivity and a state with a quantized Hall conductivity equal to $e^2/h$, as a function of the magnitude of the applied field. The transition is driven by the competition between the Zeeman and the hybridization energies.
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It is well-known that helical surface states of a three-dimensional topological insulator (TI) do not respond to a static in-plane magnetic field. Formally this occurs because the in-plane magnetic field appears as a vector potential in the Dirac Hamiltonian of the surface states and can thus be removed by a gauge transformation of the surface electron wavefunctions. Here we show that when the top and bottom surfaces of a thin film of TI are hybridized and the Fermi level is in the hybridization gap, a nonzero diamagnetic response appears. Moreover, a quantum phase transition occurs at a finite critical value of the parallel field from an insulator with a diamagnetic response to a semimetal with a vanishing response to the parallel field.
Ferromagnetism in topological insulators (TIs) opens a topologically non-trivial exchange band gap, providing an exciting platform to manipulate the topological order through an external magnetic field. Here, we experimentally show that the surface of an antiferromagnetic thin film can independently control the topological order of the top and the bottom surface states of a TI thin film through proximity couplings. During the magnetization reversal in a field scan, two intermediate spin configurations stem from unsynchronized magnetic switchings of the top and the bottom AFM/TI interfaces. These magnetic configurations are shown to result in new topological phases with non-zero Chern numbers for each surface, introducing two counter-propagating chiral edge modes inside the exchange gap. This change in the number of transport channels, as the result of the topological transitions, induces antisymmetric magneto-resistance spikes during the magnetization reversal. With the high Neel ordering temperature provided by the antiferromagnetic layers, the signature of the induced topological transition persists in transport measurements up to a temperature of around 90 K, a factor of three over the Curie temperature in a typical magnetically doped TI thin film.
We report that the finite thickness of three-dimensional topological insulator (TI) thin films produces an observable magnetoresistance (MR) in phase coherent transport in parallel magnetic fields. The MR data of Bi2Se3 and (Bi,Sb)2Te3 thin films are compared with existing theoretical models of parallel field magnetotransport. We conclude that the TI thin films bring parallel field transport into a unique regime in which the coupling of surface states to bulk and to opposite surfaces is indispensable for understanding the observed MR. The {beta} parameter extracted from parallel field MR can in principle provide a figure of merit for searching TI compounds with more insulating bulk than existing materials.
The response of thin films of Bi$_2$Se$_3$ to a strong perpendicular magnetic field is investigated by performing magnetic bandstructure calculations for a realistic multi-band tight-binding model. Several crucial features of Landau quantization in a realistic three-dimensional topological insulator are revealed. The $n=0$ Landau level is absent in ultra-thin films, in agreement with experiment. In films with a crossover thickness of five quintuple layers, there is a signature of the $n=0$ level, whose overall trend as a function of magnetic field matches the established low-energy effective-model result. Importantly, we find a field-dependent splitting and a strong spin-polarization of the $n=0$ level which can be measured experimentally at reasonable field strengths. Our calculations show mixing between the surface and bulk Landau levels which causes the character of levels to evolve with magnetic field.
We propose a method that can consecutively modulate the topological orders or the number of helical edge states in ultrathin film semiconductors without a magnetic field. By applying a staggered periodic potential, the system undergoes a transition from a topological trivial insulating state into a non-trivial one with helical edge states emerging in the band gap. Further study demonstrates that the number of helical edge state can be modulated by the amplitude and the geometry of the electric potential in a step-wise fashion, which is analogous to tuning the integer quantum Hall conductance by a megntic field. We address the feasibility of experimental measurement of this topological transition.
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