Nonlinear Optical Probe of Tunable Surface Electrons on a Topological Insulator

D. Hsieh, J. W. McIver, D. H. Torchinsky, D. R. Gardner, Y. S. Lee, and N. Gedik

Phys. Rev. Lett. 106, 057401 – Published 1 February 2011

Abstract

We use ultrafast laser pulses to experimentally demonstrate that the second-order optical response of bulk single crystals of the topological insulator ${Bi}_{2} {Se}_{3}$ is sensitive to its surface electrons. By performing surface doping dependence measurements as a function of photon polarization and sample orientation we show that second harmonic generation can simultaneously probe both the surface crystalline structure and the surface charge of ${Bi}_{2} {Se}_{3}$ . Furthermore, we find that second harmonic generation using circularly polarized photons reveals the time-reversal symmetry properties of the system and is surprisingly robust against surface charging, which makes it a promising tool for spectroscopic studies of topological surfaces and buried interfaces.

Received 4 December 2010

DOI:https://doi.org/10.1103/PhysRevLett.106.057401

Authors & Affiliations

D. Hsieh¹, J. W. McIver^1,2, D. H. Torchinsky¹, D. R. Gardner¹, Y. S. Lee¹, and N. Gedik^1,*

¹Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

^*gedik@mit.edu

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Vol. 106, Iss. 5 — 4 February 2011

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Images

Figure 1
(a) Schematic of the SHG experimental geometry. Surface and bulk regions are colored white and gray, respectively. (b) Crystal structure of the ${Bi}_{2} {Se}_{3} (111)$ surface showing the topmost Se layer and underlying Bi layer. (c)-(j) Normalized SHG intensity $I (2 ω)$ from the ${Bi}_{2} {Se}_{3} (111)$ surface measured as a function of azimuthal angle $ϕ$ between the bisectrix ( $11 \bar{2}$ ) and the scattering plane. Measurements taken immediately after cleavage in (c) $P_{in} − P_{out}$ , (d) $S_{in} − P_{out}$ , (e) $P_{in} − S_{out}$ , and (f) $S_{in} − S_{out}$ incident and outgoing photon polarization geometries. Panels (g)–(j) show analogous scans measured 200 minutes after cleavage. All data sets are normalized to the maximum intensity measured at $t = 200 mins$ in the $P_{in} − P_{out}$ geometry. The fewer data points in (g)–(j) is due to the need for faster data collection. Solid red lines are theoretical fits to Eq. (2) [21].Reuse & Permissions
Figure 2
Normalized SHG intensity along high symmetry directions of the ${Bi}_{2} {Se}_{3} (111)$ surface Brillouin zone measured as a function of time after cleavage in air with (a) $P_{in} − P_{out}$ , (b) $S_{in} − P_{out}$ , (c) $P_{in} − S_{out}$ , and (d) $S_{in} − S_{out}$ photon polarization geometries. Insets in (c) and (d) show the time evolution of peak intensities starting at 100 minutes after cleavage in air, prior to which the sample was not exposed to laser light.Reuse & Permissions
Figure 3
(a) Time-dependent peak intensity curves measured in the $P_{in} − S_{out}$ polarization geometry after cleaving in $O_{2}$ . Similar behaviors were also observed in other polarization geometries. (b) Schematic of the energy evolution of the bulk conduction band minimum ( $E_{C}$ ) and bulk valence band maximum ( $E_{V}$ ) relative to the Fermi level ( $E_{F}$ ) as a function of distance to the $O_{2}$ or (c) air covered surface. Typical ${Bi}_{2} {Se}_{3}$ samples show bulk conducting character ( $E_{F} > E_{C}$ ) owing to Se vacancies [9, 22]. The gray, white, and yellow regions correspond to the bulk, accumulation layer, and surface of ${Bi}_{2} {Se}_{3}$ . Schematic of the bulk (black) and surface (red) band structure is drawn near the surface region.Reuse & Permissions
Figure 4
Normalized $ϕ$ -dependent SHG intensity patterns measured 200 minutes after cleavage in air under (a) left-circular in ( $L_{in}$ ) $S_{out}$ and right-circular in ( $R_{in}$ ) $S_{out}$ , and (b) $L_{in} − P_{out}$ and $R_{in} − P_{out}$ photon polarization geometries. Solid lines are theoretical fits (see text). (c) Circular dichroism ( $I_{R} − I_{L}$ ) corresponding to data in panels (a) and (b). (d) Difference between circular dichroism measured at 200 minutes after cleavage and immediately after cleavage.Reuse & Permissions

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