Infrared and magneto- optical studies of topological insulators Saša V. Ðorđević Department of Physics

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Acknowledgments M.Wolf and G. Foster (UA) N. Stojilovic (UWO) H. Lei and C.Petrovic (BNL) M. V. Nikolic, Z. Z. Djuric, S. S. Vujatovic and P. M. Nikolic (SANU) Z. Chen, Z.Q.Li and R. Tung (NHMFL)

Outline 3D topological insulators: Bi 2 Se 3, Bi 2 Te 3, Sb 2 Te 3, Bi 1-x Sb x Infrared and magneto-optical spectroscopy What can we learn from these?

Band theory: insulators vs. metals C. Kittel, “Introduction to Solid State Physics”

2D metal Topological insulators 3D insulator 2D metal 2D metallic states on the surface are Dirac fermions, characterized by linear dispersion.

Practical realizations of 3D topological insulators  Bi 1-x Sb x  Bi 2 Se 3, Bi 2 Te 3 and Sb 2 Te 3

Practical realizations of 3D topological insulators  Bi 1-x Sb x  Bi 2 Se 3, Bi 2 Te 3 and Sb 2 Te 3

Predicted topological insulators Zhang et al. (2009)

Dirac cones on the surface Y. Xia et al., Nature Physics 5, 398 (2010)

“Measurement of an Exceptionally Weak Electron-Phonon Coupling on the Surface of the Topological Insulator Bi 2 Se 3 Using Angle-Resolved Photoemission Spectroscopy” Z.-H. Pan, A. V. Fedorov, D. Gardner, Y. S. Lee, S. Chu, and T. Valla, PRL 108, (2012) kxkx

Crystal structure of Bi 2 Te 3 Alpichshev et al., PRL 104, (2010). quintuple unit

Hechang Lei and C. Petrović, unpublished Transport properties of Bi 2 Te 3, Sb 2 Te 3 and Bi 2 Se 3

Infrared spectroscopy IR spectroscopy: Broadband (0.1mev-6eV) High resolution (0.1meV) Connection with theory Small crystals Bulk probe (  >1  m) Non-destructive Polarized light Temperature Range: K Energy Range: 0.1 meV - 6 eV Magnetic Field Range: T 250  m InterferometerDetector S.V. Dordevic et al., Phys.Rev.B 60, (1999)

15 Reflectance spectra of Bi 2 Se 3 Bi 2 Te 3 Sb 2 Te 3 S.V. Dordević, et al. (2013)

c-axis transport A.A. Reijnders, et al. (2014)

Fit of reflectance: Bi 2 Te 3 Charge inhomogeneities might be present!

Drude-Lorentz fits: possible charge inhomogeneities Josephson Plasmon and Inhomogeneous Superconducting State in La 2-x Sr x CuO 4. S.V. Dordevic et al. Phys.Rev.Lett. 91, (2003).

Loss function spectra 19 Effective medium theory

Distribution function S.V. Dordević, et al. (2013)

Tallahassee, Florida National High Magnetic Field Lab

Magneto-Reflectance spectroscopy in Faraday geometry 2D metal 3D insulator 2D metal B

Bi 2 Se 3 in 18 Tesla

Bi 2 Se 3 in 8 Tesla LaForge et al. (2010)

Bi 2 Te 3 and Sb 2 Te 3 in 18 Tesla

Bi 2 Se 3 in 18 Tesla

Model: free and bound electrons (and/or holes) in magnetic field for  ci = 0 we get Drude-Lorentz model for  0i  0 we get bound carriers in magnetic field

Bi 2 Se 3 in 18 Tesla

60 cm -1 phonon has been know to be asymmetric LaForge et al. (2010)

Ugo Fano (1912 – 2001) Examples of Fano resonances can be found in atomic physics, nuclear physics, condensed matter physics, circuits, microwave engineering, nonlinear optics, nanophotonics, etc.

Fano model Fano q A. Kuzmenko, RefFIT manual

Circular optical conductivity  - (  )

Fano q reversal S.V. Dordevic et al., to be published soon. m * = 0.15 m e L. Wu et al., (2015). M. Orlita et al., (2015).

Circular optical conductivity  - (  )

Magnetic field driven Fano q reversal B

Practical realizations of 3D topological insulators  Bi 1-x Sb x  Bi 2 Se 3, Bi 2 Te 3 and Sb 2 Te 3

Bismuth

Fermi surface K. Behnia, Science 321, 497 (2008). holes electrons

Band structure: semimetal N. P. Armitage et al, arXiv: v1

Reflectance of bismuth

Zero field “plasmaron” R. Tediosi, et al, PRL 99, (2007).

Zero field fit Drude + Lorentzian

Magneto-Reflectance in Voigt geometry B

Magneto-Reflectance in Faraday geometry B

Bismuth in high magnetic field S.V. Dordevic, et al.

Model: free and bound electrons (and holes) in magnetic field for  ci = 0 we get Drude-Lorentz model for  0i  0 we get bound carriers in magnetic field

Bismuth in magnetic field J.Levallois, et al. (2014)

Magneto-plasmons in bismuth

dR/dH maps A.A. Schafgans, et al. (2012)

Bismuth

Bismuth - Antimony B. Lenoir, M. Cassart, J.-P. Michenaud, H. Scherrer, and S. Scherrer, J. Phys. Chem. Solids 57, 89 (1996).

Zero field + Fits

Magneto-Reflectance in Faraday geometry B

Magnetic field: Bi 1-x Sb x

Model: free and bound electrons (and holes) in magnetic field for  0i  0 we get bound carriers in magnetic field for  ci = 0 we get Drude-Lorentz model

Bismuth

Bismuth doped with Sb and As

In 18 Tesla

Cyclotron resonances

dR/dH maps

Thank you! Questions?

Summary 3D topological insulators: Bi 2 Se 3, Bi 2 Te 3, Sb 2 Te 3, Bi 1-x Sb x Infrared and magneto-optical spectroscopy What can we learn from these?

Spectroscopic techniques are an important tool in studies of novel materials. I will review recent infrared and magneto-optical studies of 3D topological insulators Bi2Se3, Bi2Te3, Sb2Te3 and Bi_{1-x}Sb_x. A number of issues will be discussed, such as the cyclotron resonance and its field dependence, electronic inhomogeneities, and electron-phonon coupling. We find that in Bi2Se3 charge carriers are indeed strongly coupled to an optical phonon, causing its asymmetric (Fano) lineshape. Moreover, we show that the asymmetry of the phonon can be switched from negative to positive, with the application of magnetic field. This is the so-called Fano q reversal, which to the best of our knowledge has not been observed before in topological insulators.

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Crystal structure bismuth/crystal_structure.html rhombohedral