Session P29: Optical Spectroscopy on 3D Topological Insulators

Infrared studies of topological insulator systems

The theoretical prediction, and subsequent experimental realization, of topological insulator (TI) systems, has vaulted this new class of materials to the vanguard of condensed matter physics. Since their discovery, we have carried out a number of infrared studies on various TI systems, including Bi$_2$Se$_3$, Bi$_{1-x}$Sb$_x$, and Bi$_{2-x}$Sb$_x$Te$_{3-y}$Se$_y$ crystals as well as Bi$_2$Se$_3$ and (Bi,Sb)$_2$Te$_3$ thin films. A key element of these works is the revelation that the infrared response of Bi$_{1-x}$Sb$_x$ crystals and (Bi,Sb)$_2$Te$_3$ thin films possess a significant, or even dominant, component from the topologically protected surface states. I will review these works and discuss future prospects of measuring the surface state response through optical spectroscopy techniques   

Cyclotron resonance and Faraday rotation in topological insulator $(Bi,Sb)_{2}Te_{3}$

Using magneto-optical spectroscopy, we have explored the complex electronic structure of $(Bi,Sb)_{2}Te_{3}$ (BST) film. From the magneto-optical transmission spectra, we extracted the cyclotron resonance (CR) energy, and subsequently measured the broadband Faraday rotation spectra (FR). From these complementary FR-CR datasets, we were able to identify the conducting channels associated with the topological surface states of the film at the interface with the substrate and with the amorphous capping layer on top of the film. According to the FR data the two surfaces are dominated by carriers of opposite sign, in accord with earlier transport measurements. These results elucidate the origin of the zero-field optical response, observed previously, and give direct evidence of significant SS contribution using a bulk sensitive probe.   

Terahertz Faraday Rotation in the Quantum Anomalous Hall System V-doped (Bi,Sb)2Te3

Time-reversal symmetry breaking in a topological insulator (TI) can be achieved by introducing ferromagnetism, which opens up a gap in the Dirac surface states. When the chemical potential is tuned to lie within the surface gap, the quantum anomalous Hall state emerges, which can be regarded as the quantum Hall state at zero external magnetic field. Recently, this state has been observed by static transport measurements in thin films of magnetically doped TIs. Time-domain terahertz spectroscopy has been demonstrated to be an effective probe of surface states and Hall effects in topological materials. Here, we use polarization modulation terahertz spectroscopy to study the intrinsic properties of massive Dirac electrons in V-doped (Bi,Sb)2Te3 via Faraday rotation measurements.   

Quantized Faraday rotation of surface states in 3D topological insulator thin films

Axion electrodynamics of topological surface states have been predicted a while ago, but the experimental observation has not been realized yet. One of the consequences of axion electrodynamics is a topological magneto-electric effect. In my talk, I will talk about utilizing a charge-transfer-doping method to lower the chemical point near the Dirac point in thin films of the topological insulator Bi$_2$Se$_3$. Using time-domain THz spectroscopy, we observed a crossover from semi-classical cyclotron resonances from topological surface states in the low field regime to a quantum regime at higher fields. A quantized Faraday rotation in the units of the fine structure constant was observed at high fields, which may provide the evidence for the topological magneto-electric effect.   

Nonlinear optical properties of bismuth selenide

Bismuth selenide (Bi2Se3) is a topological insulator with many interesting photonic properties. Much research has been done involving various types of photocurrents in an attempt to highlight the differences between the bulk electronic states and massless conducting surface states. Here, Bi2Se3 films varying in thickness from 6 to 40 quintuple layers have been produced via molecular beam epitaxy as a means to vary the relative contributions of bulk and surface. On these samples, optical measurements were performed at around 1.6 eV, which is enough energy to stimulate transitions from the Fermi level to a region near the second Dirac cone. Z-scan was used to measure saturable absorption, time-resolved two-color pump-probe was used to measure two-photon absorption, and a Fourier transform infrared spectrometer was used to measure linear absorption. Results were examined and analyzed with respect to thickness. Thickness-dependent band structures were produced using a tight-binding model and used to compare with experimental results.   

Fano {\it q} reversal in topological insulator Bi$_2$Se$_3$

We studied magneto-optical response of a canonical topological insulator Bi$_2$Se$_3$ with the goal of addressing a controversial issue of electron-phonon coupling. Magnetic-field induced modifications of reflectance are very pronounced in the infrared part of the spectrum, indicating strong electron-phonon coupling. This coupling causes an asymmetric line-shape of the 60~cm$^{-1}$ phonon mode, and is analyzed within the Fano formalism. The analysis reveals that the Fano asymmetry parameter (q) changes sign when the cyclotron resonance is degenerate with the phonon mode. To the best of our knowledge this is the first example of magnetic field driven q-reversal.   

Evolving optical second-harmonic anisotropy at the cleaved Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ surface.

Bismuth selenide (Bi$_{\mathrm{2}}$Se$_{\mathrm{3}})$ is a centrosymmetric topological insulator with conducting surface states. The surface states have been studied by various electrical and optical techniques in air, but ambience effects and surface aging have not been adequately addressed. Optical second-harmonic generation (SHG) is a suitable probe for the Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ surface because SHG arises from symmetry breaking at the surface and thus should detect surface states preferentially over bulk states. However, a strong time dependence of SHG is often observed, hampering the detection and investigation of the surface states. Here we find a new phenomenon in which the major and minor intensity lobes of a measured rotational-anisotropy SHG pattern from a cleaved Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ (111) surface can significantly change with time and eventually switch their amplitudes. This switching provides a means for tracking the progress of surface oxidation inside a quintuple layer of Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$. We also perform pump-probe SHG experiments, comparatively on freshly cleaved and oxidized Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ surfaces, to study charge dynamics at the oxide/Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ interface and to detect spin polarization of photoexcited surface states in the Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ topological insulator.   

Tight-binding theory of NMR shifts in topological insulators

To date, most experiments in topological insulators have focused on probing the surface states of these materials and suppressing the often inevitable contribution from bulk states. However, the latter are of interest on their own and contain useful information that can be extracted with a local probe like nuclear magnetic resonance (NMR). Recently, 77Se NMR experiments on Bi$_2$Se$_3$ single crystals have reported unusual field-independent linewidths and short spin-echo decays [1]. It is likely that an unexpectedly strong indirect internuclear coupling, characteristic of some inverted band structures, is the cause of these peculiar results. Motivated by this hypothesis, we report on a microscopic theory of NMR shifts and linewidths in Bi$_2$Se$_3$ and Bi$_2$Te$_3$. Our theory provides quantitative estimates for the Knight shift, the orbital shift, the Ruderman-Kittel-Kasuya-Yoshida coupling and the Bloembergen-Rowland coupling. We will compare our findings with the available experimental data. [1] N. Georgieva, D. Rybicki, R. Guhne, G. Williams, S. Chong, I. Garate and J. Haase, arXiv:1511.01727 (2015)   

Gate Tunable Infrared Optical Response of (Bi$_{1-x}$Sb$_{x})_{2}$Te$_{3}$ Topological Insulators

The electronic properties of topological insulators -- narrow band-gap semiconductors that exhibit insulating bulk and semimetallic Dirac surface states -- have been the subject of intense study over the past several years. The optical and optoelectronic behavior of these materials, however, remain widely uncharacterized. It has previously been shown that electrostatic gating can be used to tune the Fermi level in the Dirac semimetal graphene, modifying interband transitions and free carrier absorption. We report here experiments that demonstrate electronic control of the optical properties of 5-20 nm thick (Bi$_{1-x}$Sb$_{x})_{2}$Te$_{3}$ films grown by Van der Waals epitaxy and transferred to silicon dioxide on silicon via an epitaxial lift off process. We find that infrared transmission and reflection from 3 to 10 microns are consistent with modulation of free-carrier absorption and bulk interband transitions in (Bi$_{1-x}$Sb$_{x})_{2}$Te$_{3}$. We discuss transport results as well as the contributions that bulk and topological surface electronic transitions make to the optical response of these materials.   

Optical Second Harmonic Generation Study of Topological Insulator Bi$_{2-x}$Sb$_{x}$Se$_{3}$

Second-order nonlinear optical spectroscopy such as second harmonic generation (SHG) is well-established and versatile technique for surface and interface studies. We apply this technique to study the surface symmetry of topological insulator Bi$_{2-x}$Sb$_{x}$Se$_{3}$ in reflection geometry under four possible polarization configurations. By measuring the azimuthal angular dependence of SHG from the (111) surface of Bi$_{2-x}$Sb$_{x}$Se$_{3}$ single crystals, we identify responses from both in-plane Se-Se bonds and out-of-plane Se-Bi/Sb bonds. This provides us information about the doping effect on the surface crystalline structure, which is critical for understanding the surface properties. The transition from topological to trivial insulator upon Sb doping will be discussed based on SHG data. Future work using sum frequency generation on these crystals will be considered as well.   

Current induced Optical Activity in Topological Insulator Bi2Te2Se1

Current induced polarization rotation of light (provided by a laser with wavelength$=$635nm) was studied from topological insulator (TI), Bi2Te2Se1, grown by Bridgman method. The magnitude of the observed response increases linearly with the applied current and reverses sign upon reversing the current direction. Possible origins of the rotation can include the linear electro-optic Pockels effect (linear birefringence) and spin-Kerr effect due to the current induced spin polarization (e.g, resulting from the spin momentum locking of the surface states) at the sample surface. At room temperature, the rotation was measured as a function of the angle of incidence and laser polarization. Dependence of the rotation angle on the polarization of light (S or P) was used to isolate contributions from these two effects. The contribution from the electro optic effect was found to dominate over that from the current-induced spin- Kerr effect.   

STM studies of topological phase transition in (Bi,In)$_{\mathrm{2}}$Se$_{\mathrm{3}}$

Topological insulators (TI) are a class of materials with insulating bulk and metallic surface state, which is the result of band inversion induced by strong spin-orbit coupling (SOC). The transition from topological phase to non-topological phase is of great significance. In theory, topological phase transition is realized by tuning SOC strength. It is characterized by the process of gap closing and reopening. Experimentally it was observed in two systems: TlBi(S$_{\mathrm{1-x}}$Se$_{\mathrm{x}})_{\mathrm{2}}$ and (Bi$_{\mathrm{1-x}}$In$_{\mathrm{x}})_{\mathrm{2}}$Se$_{\mathrm{3}}$ where the transition is realized by varying isovalent elements doping concentration. However, none of the previous studies addressed the impact of disorder, which is inevitable in doped systems. Here, we present a systematic scanning tunneling microscopy/spectroscopy study on (Bi$_{\mathrm{1-x}}$In$_{\mathrm{x}})_{\mathrm{2}}$Se$_{\mathrm{3}}$ single crystals with different In concentrations across the transition. Our results reveal an electronic inhomogeneity due to the random distribution of In defects which locally suppress the topological surface states. Our study provides a new angle of understanding the topological transition in the presence of strong disorders.   

First-Principle Calculations and Raman Studies of Surface Phonons in the Topological Insulators Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ and Bi$_{\mathrm{2}}$Te$_{\mathrm{3}}$.

Raman [1-2], helium scattering [3] and photoemission experiments [4] on the topological insulators Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ and Bi$_{\mathrm{2}}$Te$_{\mathrm{3}}$ show features in the range \textasciitilde 50-150 cm-1, which have been assigned to Raman-forbidden, infrared modes due to symmetry breaking at the surface [1-2] or surface phonons [3,4], which couple to the topologically protected electronic states [4]. We present first-principle LDA calculations and temperature-dependent Raman studies showing strong evidence of the existence of surface phonons in both Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ and Bi$_{\mathrm{2}}$Te$_{\mathrm{3}}$. The calculations reveal that these modes are quite insensitive to spin-orbit coupling, an indication that their occurrence is unrelated to the topological properties of these materials. [1] K. M. F. Shahil et al., Appl. Phys. Lett. 96, 153103 (2010). [2] V. Gnezdilov et al., Phys. Rev. B 84, 195118 (2011). [3] X. Zhu et al., Phys. Rev. Lett. 107, 186102 (2011). [4] J. A. Sobota et al., Phys. Rev. Lett. 113, (2014).   

Optical helicity control of surface current in SmB$_{\mathrm{6}}$

SmB$_{\mathrm{6}}$ is a promising candidate for topological Kondo insulator. One hallmark signature of topological states is the helical Dirac dispersion with perfect momentum-spin lockage. Here, we report current injection in SmB$_{\mathrm{6}}$ thin film with circularly polarized light at oblique incidence. A polarization-independent photovoltage was also detected. Both signals exhibited strong temperature dependences. While the polarization-independent photovoltage is likely due to thermoelectric effects, the circular photogalvanic effect (CPGE) has two possible origins: topological surface states or regular surface states with strong Rashba type spin-orbit coupling. The drastically different penetration depths of topological and regular surface states in SmB$_{\mathrm{6}}$ provide an opportunity to distinguish them by investigating films with different thicknesses. The strong correlation observed between the film thickness and CPGE photovoltage strongly supports the topological origin of the surface states. This research enhances our knowledge in controlling the spin and orbital degrees of freedom at SmB$_{\mathrm{6}}$ surface, and can also lead to exciting spintronic applications using optical tools.   

Photoinduced Anomalous Hall Effects in Weyl Semimetals

We examine theoretically the interplay between chiral photons and chiral electrons in Weyl semimetals. Owing to its monopole nature, a three-dimensional Weyl node is topologically-robust against a circularly polarized light. A driven Weyl system exhibits node shifts in the momentum space, in sharp contrast to the gap opening in a driven two-dimensional Dirac system. We show that the node shift leads to a change of the Chern vector which gives arise to a net photoinduced anomalous Hall conductivity, in the plane perpendicular to the light propagation. We shall describe the basic idea behind this generic photoinduced Hall effect, illustrate it with a concrete microscope model, and estimate its feasibility based on current optical experimental techniques.