Optical properties of magnetically doped ultrathin topological insulator slabs

Abstract

Starting from a three-dimensional Hamiltonian, we study the optical properties of ultrathin topological insulator slabs for which the coupling between Dirac fermions on opposite surfaces results in two degenerated gapped hyperbolic bands. The gap is a threshold for the optical absorption and translates in a peak in the imaginary part of the optical conductivity. An exchange field applied perpendicular to the slab splits the degenerated hyperbolic bands and a double step structure comes out in the optical absorption, whereas a double peak structure appears in the imaginary part of the longitudinal optical conductivity. The exchange field breaks time-reversal symmetry and for exchange fields larger than the surfaces coupling gap, the zero frequency Hall conductivity is quantized to e 2 /h. This result implies large values of the Kerr rotation angle and a quantization of the Faraday angle. In ultrathin slabs, the absence of light multiple scattering and bulk conductivity makes the Kerr angle remain rather large in a wide range of frequencies.

Resonant magneto-optic Kerr effect in the magnetic topological insulatorCr:(Sbx,Bi1−x)2TePatankar1, Hinton2, Griesmar3 et al. 2015Phys. Rev. B8050View full textAdd to dashboardCite

“…We observe that the frequency dependence of the Kerr resonance remains unchanged even as its amplitude is significantly reduced with decreasing d. The insensitivity of the spectrum to thickness suggests that the width of the resonance is largely determined by the dispersion of energies with respect to the in-plane wavevector, rather than the energies associated with subband splittings. This conclusion is consistent with bandstructure calculations that indicate subband splitting are no larger than 0.2 eV for films as thin as 4 nm 12,27 , which can be compared with the characteristic width of the resonance in Θ K (ω), which is approximately 0.8 eV.…”

Zero-bias photocurrent in ferromagnetic topological insulator

“…In short, the zero-bias photocurrent flows due to the unbalanced transient carrier population ( f ( k ): Fermi-Dirac function) in the deformed Dirac dispersions, that is, f ( k x )− f (− k x ), multiplied by the group velocity, which can be proportional to the local magnetic moment. The optical absorption in the surface Dirac states is supposed to be nearly monotonic as a function of photon energy in our spectral range 19 21 22 23 24 25 54 (see also Supplementary Fig. 2 ).…”

“…In addition to intensive optical spectroscopy 20 21 22 23 24 25 26 27 , a number of photoeffects in TIs have been studied both theoretically and experimentally; photocurrent generation and galvanic effects 28 29 30 31 32 , carrier/spin dynamics elaborated by time-resolved optics 33 34 35 36 37 38 39 40 41 , photoemission 42 43 44 45 46 47 48 49 50 51 and the Floquet state 52 , including the cases of thin films with magnetic dopants 53 54 , to name a few. For the photocurrent generation at the normal incidence, it is predicted that the orbital coupling of light, that is, ħ → ħ − e , provides a predominant contribution to the polarization-independent photocurrent under an in-plane external magnetic field 17 .…”

Optical conductivity of topological insulator thin films in a quantizing magnetic field

“…This has been carried out for graphene which shows good agreement between theory and experiment [24][25][26][27][28]. Recently in [29] optical properties of topological insulator thin films doped with magnetic impurities has been investigated. The authors include hybridization effects and for exchange field that breaks time reversal symmetry show that the value of Kerr and Faraday rotation angles is large for a wide range of frequencies.…”