# NUSOD Blog

Connecting Theory and Practice in Optoelectronics

## NUSOD 2017 Preview: Strain tuning of absorption spectrum in a topological insulator

Topological insulators have attracted a huge amount of attention in the field of condensed matter physics. This new state of matter is characterized by a bulk band gap and conducting surface states. The surface states have linear dispersion resembling relativistic Dirac fermions, in analogy with graphene. In contrast to graphene the 2D fermions on the surface are non-degenerate, whereas electrons in graphene are spin and valley degenerate. The linear dispersion and 2D nature of the electrons in graphene leads to the universal optical absorbance απ≈2.3% given by the fine structure constant , independent on the material parameters and the photon energy. Due to this relatively large absorption for a single atomic layer, graphene is a promising material for optoelectronic applications e.g. photodetectors, which has been demonstrated [1]. Similarly a topological insulator has an absorbance of απ/2≈1.1% for photon energies below the bulk band gap, due to the surface states at the top and bottom surface. It has been shown that the signal-to-noise ratio of photodetector based on a thin slab of the topological insulator Bi_{2}Se_{3 }can be significantly larger than for a graphene based device[2]. For a slab thickness below 6 nm the surface states on opposing sides interact leading to a band gap, which can be tuned by varying the thickness. However, this way of manipulating the optical properties is not very flexible since Bi_{2}Se_{3} has a layered structure with five atomic layers strongly bound in a quintuple layer, limiting the possible thicknesses to only integer numbers of quintuple layers (QL). If instead strain is used to tune the optical properties, this can be done continuously and dynamically.

Using a k.p model for the electrons in a Bi_{2}Se_{3} slab to second order in the wave vector and first order in strain we calculate the optical absorbance of the surface state electrons. The absorbance, defined as the ratio of absorbed intensity to the incident light intensity, is shown in the figure for a 2 QL slab. The band gap and the band edge absorbance are significantly increased with increasing tensile strain, and for ε_{zz}=6% the band gap occurs at a finite wave vector giving a divergent band edge absorbance and a discontinuous decrease at the larger gap at zero wave vector.

At the NUSOD 2017 conference further details on the model will be presented as well as results for shear strain, which breaks the isotropy of the Dirac cone leading to a polarization dependent change in the absorbance (talk TuA2).

[1] Xia et al, Nat. Nanotech. 4, 839 – 843 (2009)

[2] Zhang et al, Phys. Rev. B 82, 245107 (2010)