Abstract

As the search for new compounds of a topological insulator (TI) becomes more extensive, it is increasingly important to develop an experimental technique that can identify TIs. In this work, we theoretically propose a simple optical method for distinguishing between topological and conventional insulator thin films. An electromagnetic interference wave consisting of waves transmitted through and reflected by the TI thin film is sensitive to the circular polarization direction of the incident electromagnetic wave. Based on this fact, we can identify a TI by observing the interference wave. This method is straightforward, and thus should propel TI research.

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  1. M. Z. Hasan and C. L. Kane, “Topological insulators,” Rev. Mod. Phys.82, 3045–3067 (2010).
    [CrossRef]
  2. X. L. Qi and S. C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys.83, 1057–1110 (2011).
    [CrossRef]
  3. M. Z. Hasan and J. E. Moore, “Three-dimensional topological insulators,” Ann. Rev. Condens. Matter Phys.2, 55–78 (2011).
    [CrossRef]
  4. X. L. Qi, T. L. Hughes, and S. C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B78, 195424-1 (2008).
    [CrossRef]
  5. W. K. Tse and A. H. MacDonald, “Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators,” Phys. Rev. Lett.105, 057401 (2010).
    [CrossRef] [PubMed]
  6. M. C. Chang and M. F. Yang, “Optical signature of topological insulators,” Phys. Rev. B80, 113304 (2009).
    [CrossRef]
  7. J. Maciejko, X. L. Qi, H. D. Drew, and S. C. Zhang, “Topological quantization in units of the fine structure constant,” Phys. Rev. Lett.105, 166803-1–166803-4 (2010).
    [CrossRef]
  8. F. Wilczek, “Two applications of axion electrodynamics,” Phys. Rev. Lett.58, 1799–1802 (1987).
    [CrossRef] [PubMed]
  9. W. Dittrich and M. Reuter, Selected Topics in Gauge Theories (Springer, 1986).
  10. X. L. Qi, J. Zang, and S. C. Zhang, “Inducing a magnetic monopole with topological surface states,” Science323, 1184–1187 (2009).
    [CrossRef] [PubMed]
  11. M. Fiebig, “Revival of the magnetoelectric effect,” J. Phys. D: Appl. Phys.38, R123–R152 (2005).
    [CrossRef]
  12. A. M. Essin, J. E. Moore, and D. Vanderbilt, “Magnetoelectric polarizability and axion electrodynamics in crystalline insulators,” Phys. Rev. Lett.102, 146805 (2009).
    [CrossRef] [PubMed]
  13. E. Sakai, A. Chikamatsu, Y. Hirose, T. Shimada, and T. Hasegawa, “Magnetic and transport properties of anatase TiO2 codoped with Fe and Nb,” Appl. Phys. Express3, 043001 (2010).
    [CrossRef]
  14. C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron.16, 367–375 (2010).
    [CrossRef]

2011

X. L. Qi and S. C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys.83, 1057–1110 (2011).
[CrossRef]

M. Z. Hasan and J. E. Moore, “Three-dimensional topological insulators,” Ann. Rev. Condens. Matter Phys.2, 55–78 (2011).
[CrossRef]

2010

W. K. Tse and A. H. MacDonald, “Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators,” Phys. Rev. Lett.105, 057401 (2010).
[CrossRef] [PubMed]

J. Maciejko, X. L. Qi, H. D. Drew, and S. C. Zhang, “Topological quantization in units of the fine structure constant,” Phys. Rev. Lett.105, 166803-1–166803-4 (2010).
[CrossRef]

M. Z. Hasan and C. L. Kane, “Topological insulators,” Rev. Mod. Phys.82, 3045–3067 (2010).
[CrossRef]

E. Sakai, A. Chikamatsu, Y. Hirose, T. Shimada, and T. Hasegawa, “Magnetic and transport properties of anatase TiO2 codoped with Fe and Nb,” Appl. Phys. Express3, 043001 (2010).
[CrossRef]

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron.16, 367–375 (2010).
[CrossRef]

2009

A. M. Essin, J. E. Moore, and D. Vanderbilt, “Magnetoelectric polarizability and axion electrodynamics in crystalline insulators,” Phys. Rev. Lett.102, 146805 (2009).
[CrossRef] [PubMed]

X. L. Qi, J. Zang, and S. C. Zhang, “Inducing a magnetic monopole with topological surface states,” Science323, 1184–1187 (2009).
[CrossRef] [PubMed]

M. C. Chang and M. F. Yang, “Optical signature of topological insulators,” Phys. Rev. B80, 113304 (2009).
[CrossRef]

2008

X. L. Qi, T. L. Hughes, and S. C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B78, 195424-1 (2008).
[CrossRef]

2005

M. Fiebig, “Revival of the magnetoelectric effect,” J. Phys. D: Appl. Phys.38, R123–R152 (2005).
[CrossRef]

1987

F. Wilczek, “Two applications of axion electrodynamics,” Phys. Rev. Lett.58, 1799–1802 (1987).
[CrossRef] [PubMed]

Chang, M. C.

M. C. Chang and M. F. Yang, “Optical signature of topological insulators,” Phys. Rev. B80, 113304 (2009).
[CrossRef]

Chikamatsu, A.

E. Sakai, A. Chikamatsu, Y. Hirose, T. Shimada, and T. Hasegawa, “Magnetic and transport properties of anatase TiO2 codoped with Fe and Nb,” Appl. Phys. Express3, 043001 (2010).
[CrossRef]

Dittrich, W.

W. Dittrich and M. Reuter, Selected Topics in Gauge Theories (Springer, 1986).

Drew, H. D.

J. Maciejko, X. L. Qi, H. D. Drew, and S. C. Zhang, “Topological quantization in units of the fine structure constant,” Phys. Rev. Lett.105, 166803-1–166803-4 (2010).
[CrossRef]

Essin, A. M.

A. M. Essin, J. E. Moore, and D. Vanderbilt, “Magnetoelectric polarizability and axion electrodynamics in crystalline insulators,” Phys. Rev. Lett.102, 146805 (2009).
[CrossRef] [PubMed]

Fiebig, M.

M. Fiebig, “Revival of the magnetoelectric effect,” J. Phys. D: Appl. Phys.38, R123–R152 (2005).
[CrossRef]

Hasan, M. Z.

M. Z. Hasan and J. E. Moore, “Three-dimensional topological insulators,” Ann. Rev. Condens. Matter Phys.2, 55–78 (2011).
[CrossRef]

M. Z. Hasan and C. L. Kane, “Topological insulators,” Rev. Mod. Phys.82, 3045–3067 (2010).
[CrossRef]

Hasegawa, T.

E. Sakai, A. Chikamatsu, Y. Hirose, T. Shimada, and T. Hasegawa, “Magnetic and transport properties of anatase TiO2 codoped with Fe and Nb,” Appl. Phys. Express3, 043001 (2010).
[CrossRef]

Hirose, Y.

E. Sakai, A. Chikamatsu, Y. Hirose, T. Shimada, and T. Hasegawa, “Magnetic and transport properties of anatase TiO2 codoped with Fe and Nb,” Appl. Phys. Express3, 043001 (2010).
[CrossRef]

Hughes, T. L.

X. L. Qi, T. L. Hughes, and S. C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B78, 195424-1 (2008).
[CrossRef]

Kane, C. L.

M. Z. Hasan and C. L. Kane, “Topological insulators,” Rev. Mod. Phys.82, 3045–3067 (2010).
[CrossRef]

Kriegler, C. E.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron.16, 367–375 (2010).
[CrossRef]

Linden, S.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron.16, 367–375 (2010).
[CrossRef]

MacDonald, A. H.

W. K. Tse and A. H. MacDonald, “Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators,” Phys. Rev. Lett.105, 057401 (2010).
[CrossRef] [PubMed]

Maciejko, J.

J. Maciejko, X. L. Qi, H. D. Drew, and S. C. Zhang, “Topological quantization in units of the fine structure constant,” Phys. Rev. Lett.105, 166803-1–166803-4 (2010).
[CrossRef]

Moore, J. E.

M. Z. Hasan and J. E. Moore, “Three-dimensional topological insulators,” Ann. Rev. Condens. Matter Phys.2, 55–78 (2011).
[CrossRef]

A. M. Essin, J. E. Moore, and D. Vanderbilt, “Magnetoelectric polarizability and axion electrodynamics in crystalline insulators,” Phys. Rev. Lett.102, 146805 (2009).
[CrossRef] [PubMed]

Qi, X. L.

X. L. Qi and S. C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys.83, 1057–1110 (2011).
[CrossRef]

J. Maciejko, X. L. Qi, H. D. Drew, and S. C. Zhang, “Topological quantization in units of the fine structure constant,” Phys. Rev. Lett.105, 166803-1–166803-4 (2010).
[CrossRef]

X. L. Qi, J. Zang, and S. C. Zhang, “Inducing a magnetic monopole with topological surface states,” Science323, 1184–1187 (2009).
[CrossRef] [PubMed]

X. L. Qi, T. L. Hughes, and S. C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B78, 195424-1 (2008).
[CrossRef]

Reuter, M.

W. Dittrich and M. Reuter, Selected Topics in Gauge Theories (Springer, 1986).

Rill, M. S.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron.16, 367–375 (2010).
[CrossRef]

Sakai, E.

E. Sakai, A. Chikamatsu, Y. Hirose, T. Shimada, and T. Hasegawa, “Magnetic and transport properties of anatase TiO2 codoped with Fe and Nb,” Appl. Phys. Express3, 043001 (2010).
[CrossRef]

Shimada, T.

E. Sakai, A. Chikamatsu, Y. Hirose, T. Shimada, and T. Hasegawa, “Magnetic and transport properties of anatase TiO2 codoped with Fe and Nb,” Appl. Phys. Express3, 043001 (2010).
[CrossRef]

Tse, W. K.

W. K. Tse and A. H. MacDonald, “Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators,” Phys. Rev. Lett.105, 057401 (2010).
[CrossRef] [PubMed]

Vanderbilt, D.

A. M. Essin, J. E. Moore, and D. Vanderbilt, “Magnetoelectric polarizability and axion electrodynamics in crystalline insulators,” Phys. Rev. Lett.102, 146805 (2009).
[CrossRef] [PubMed]

Wegener, M.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron.16, 367–375 (2010).
[CrossRef]

Wilczek, F.

F. Wilczek, “Two applications of axion electrodynamics,” Phys. Rev. Lett.58, 1799–1802 (1987).
[CrossRef] [PubMed]

Yang, M. F.

M. C. Chang and M. F. Yang, “Optical signature of topological insulators,” Phys. Rev. B80, 113304 (2009).
[CrossRef]

Zang, J.

X. L. Qi, J. Zang, and S. C. Zhang, “Inducing a magnetic monopole with topological surface states,” Science323, 1184–1187 (2009).
[CrossRef] [PubMed]

Zhang, S. C.

X. L. Qi and S. C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys.83, 1057–1110 (2011).
[CrossRef]

J. Maciejko, X. L. Qi, H. D. Drew, and S. C. Zhang, “Topological quantization in units of the fine structure constant,” Phys. Rev. Lett.105, 166803-1–166803-4 (2010).
[CrossRef]

X. L. Qi, J. Zang, and S. C. Zhang, “Inducing a magnetic monopole with topological surface states,” Science323, 1184–1187 (2009).
[CrossRef] [PubMed]

X. L. Qi, T. L. Hughes, and S. C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B78, 195424-1 (2008).
[CrossRef]

Ann. Rev. Condens. Matter Phys.

M. Z. Hasan and J. E. Moore, “Three-dimensional topological insulators,” Ann. Rev. Condens. Matter Phys.2, 55–78 (2011).
[CrossRef]

Appl. Phys. Express

E. Sakai, A. Chikamatsu, Y. Hirose, T. Shimada, and T. Hasegawa, “Magnetic and transport properties of anatase TiO2 codoped with Fe and Nb,” Appl. Phys. Express3, 043001 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

C. E. Kriegler, M. S. Rill, S. Linden, and M. Wegener, “Bianisotropic photonic metamaterials,” IEEE J. Sel. Top. Quantum Electron.16, 367–375 (2010).
[CrossRef]

J. Phys. D: Appl. Phys.

M. Fiebig, “Revival of the magnetoelectric effect,” J. Phys. D: Appl. Phys.38, R123–R152 (2005).
[CrossRef]

Phys. Rev. B

X. L. Qi, T. L. Hughes, and S. C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B78, 195424-1 (2008).
[CrossRef]

M. C. Chang and M. F. Yang, “Optical signature of topological insulators,” Phys. Rev. B80, 113304 (2009).
[CrossRef]

Phys. Rev. Lett.

J. Maciejko, X. L. Qi, H. D. Drew, and S. C. Zhang, “Topological quantization in units of the fine structure constant,” Phys. Rev. Lett.105, 166803-1–166803-4 (2010).
[CrossRef]

F. Wilczek, “Two applications of axion electrodynamics,” Phys. Rev. Lett.58, 1799–1802 (1987).
[CrossRef] [PubMed]

W. K. Tse and A. H. MacDonald, “Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators,” Phys. Rev. Lett.105, 057401 (2010).
[CrossRef] [PubMed]

A. M. Essin, J. E. Moore, and D. Vanderbilt, “Magnetoelectric polarizability and axion electrodynamics in crystalline insulators,” Phys. Rev. Lett.102, 146805 (2009).
[CrossRef] [PubMed]

Rev. Mod. Phys.

M. Z. Hasan and C. L. Kane, “Topological insulators,” Rev. Mod. Phys.82, 3045–3067 (2010).
[CrossRef]

X. L. Qi and S. C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys.83, 1057–1110 (2011).
[CrossRef]

Science

X. L. Qi, J. Zang, and S. C. Zhang, “Inducing a magnetic monopole with topological surface states,” Science323, 1184–1187 (2009).
[CrossRef] [PubMed]

Other

W. Dittrich and M. Reuter, Selected Topics in Gauge Theories (Springer, 1986).

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Figures (2)

Fig. 1
Fig. 1

Typical results of the TI test for a conventional insulator ((a), (c), (e)) and for a topological insulator thin film ((b), (d), (f)). The horizontal axes in all the plots is 2(n2/c)ωd and the vertical axes in the top, middle, and bottom rows are ΔI(+ : ±), |E(+ : +)|2, and |E(+ : −)|2, respectively.

Fig. 2
Fig. 2

(a) Schematics of the geometry used to obtain the numerical results of TI test in Fig. 1. An insulator thin film (width d) being studied (topological or conventional one) is represented by the dark gray rectangle. (b) An interface of a conventional (z < 0) and topological insulator (z ≥ 0). (c) Free-standing geometry of a topological/conventional insulator.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

axion = θ d r E B .
D = ε ( z ) E a t Θ ( z ) B ,
H = 1 μ 0 B + b t Θ ( z ) E ,
ε ( z ) = ε 1 Θ ( z ) + ε 2 Θ ( z ) .
1 μ 0 z ( B y B x ) = i ε 2 ω ( E x E y ) + b t δ ( z ) ( E y E x ) ,
σ ( z ) = [ δ ( z ) δ ( z d ) ] ( 0 σ x y σ x y 0 ) .
t + z < 0 ( ω ) = 4 n 0 n 2 ( n 0 + n 2 ) 2 + σ ˜ H 2 1 ( n 2 n 0 ) 2 + σ ˜ H 2 ( n 2 + n 0 ) 2 + σ ˜ H 2 exp ( i 2 k 2 d ) exp ( i ( n 0 n 2 ) d ω / c ) ,
r + z < 0 ( ω ) = n 0 n 2 i σ ˜ H n 0 + n 2 + i σ ˜ H ( 1 exp ( 2 i k 2 d ) ) 1 ( n 2 n 0 ) 2 + σ ˜ H 2 ( n 2 + n 0 ) 2 + σ ˜ H 2 exp ( 2 i k 2 d ) ,
t z < 0 ( σ ˜ H ) = t + z > d ( σ ˜ H ) = t + z > d ( σ ˜ H ) = t + z < 0 ( σ ˜ H ) ,
r z < 0 ( σ ˜ H ) = r + z > d ( σ ˜ H ) = r z > d ( σ ˜ H ) = r + z < 0 ( σ ˜ H ) ,
Δ I | t + z < 0 + r + z > d | 2 | t + z < 0 + r z > d | 2 ,

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