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:

Bi2Se3, Bi2Te3, Sb2Te3, Bi1-xSbx

• 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

Bi1-xSbx

Bi2Se3, Bi2Te3 and Sb2Te3

Practical realizations of 3D topological insulators

Bi1-xSbx

Bi2Se3, Bi2Te3 and Sb2Te3

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 Bi2Se3 Using Angle-Resolved Photoemission Spectroscopy”

Z.-H. Pan, A. V. Fedorov, D. Gardner, Y. S. Lee, S. Chu, and T. Valla, PRL 108, 187001 (2012)

kx

Crystal structure of Bi2Te3

Alpichshev et al., PRL 104, 016401 (2010).

quintuple unit

quintuple unit

Hechang Lei and C. Petrović, unpublished

Transport properties of Bi2Te3, Sb2Te3 and Bi2Se3

0 50 100 150 200 250 3000.1

1

10

dc (

mc

m)

T (K)

Sb2Te

3

Bi2Se

3

Bi2Te

3

Infrared spectroscopy

IR spectroscopy: • Broadband (0.1mev-6eV)• High resolution (0.1meV)• Connection with theory• Small crystals• Bulk probe (d>1mm)• Non-destructive• Polarized light

Temperature Range:0.3 - 600 K

Energy Range:0.1 meV - 6 eV

Magnetic Field Range:0 - 18 T250 mm

Interferometer Detector

S.V. Dordevic et al., Phys.Rev.B 60, 11321 (1999)

15

0.5

1.0

0.5

1.0

100 10000.0

0.5

1.0

10 K 77 K 200 K 300 K

Sb2Te

3

Ref

lect

ance

Frequency [cm-1]

Bi2Te

3

Bi2Se

3Reflectancespectra of

Bi2Se3

Bi2Te3

Sb2Te3

S.V. Dordević, et al. (2013)

c-axis transport

A.A. Reijnders, et al. (2014)

Fit of reflectance: Bi2Te3

0 500 1000 1500 2000 25000.0

0.2

0.4

0.6

0.8

1.0

Rel

ecta

nce

Frequency (cm-1)0 500 1000 1500 2000 2500

0.0

0.2

0.4

0.6

0.8

1.0

Rel

ecta

nce

Frequency (cm-1)

Charge inhomogeneities might be present!

0.5

1.0

0.5

1.0

100 10000.0

0.5

1.0

10 K DL fit

Sb2Te

3

Ref

lect

ance

Frequency [cm-1]

Bi2Te

3

Bi2Se

3

Drude-Lorentz fits:possible charge inhomogeneities

Josephson Plasmon and Inhomogeneous Superconducting State in La2-xSrxCuO4.S.V. Dordevic et al. Phys.Rev.Lett. 91, 167401 (2003).

20 40 60 800.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

Frequency [cm-1]

Loss function spectra

19

500 1000 15000.00

0.05

0.10

100 200 300 4000.0

0.1

0.2

500 1000 15000.0

0.2

0.4 10 K 77 K 200 K 300 K

Sb2Te

3

Frequency (cm-1)

Bi2Te

3

Im(1

/)

Bi2Se

3

Effective medium theory

ppi

d

0

11

Distribution function

0.998 1.000 1.002

0.0

0.5

1.0

0.997 1.002 1.007

0.0

0.5

1.0

0.97 1.00 1.04 1.08

0.0

0.5

1.0

1.0 1.1 1.2

68.5 69.0 69.5 70.0

112.5 112.8 113.1 113.4

Sb2Te

3

p /

0

Bi2Te

3

(

p)

Bi2Se

3

n [1018 cm-3]

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

Bi2Se3 in 18 Tesla

0.8

1.0

1.2

1.4

1.6

1.80 5 10 15 20 25 30 35 40

0 50 100 150 200 250 300 3500.0

0.2

0.4

0.6

0.8

(b)

Re

flect

an

ce

Frequency (cm-1)

0 Tesla 6 Tesla 12 Tesla 18 Tesla

R(B

) / R

(0

T)

(a)

Energy (meV)

Bi2Se3 in 8 Tesla

LaForge et al. (2010)

Bi2Te3 and Sb2Te3 in 18 Tesla

0 500 1000 1500 2000 25000.0

0.2

0.4

0.6

0.8

1.0

Rel

ecta

nce

Frequency (cm-1)

500 1000 1500 2000 25000.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

Frequency [cm-1]

Bi2Se3 in 18 Tesla

0.8

1.0

1.2

1.4

1.6

1.80 5 10 15 20 25 30 35 40

0 50 100 150 200 250 300 3500.0

0.2

0.4

0.6

0.8

(b)

Re

flect

an

ce

Frequency (cm-1)

0 Tesla 6 Tesla 12 Tesla 18 Tesla

R(B

) / R

(0

T)

(a)

Energy (meV)

Model: free and bound electrons(and/or holes) in magnetic field

i ciii

pi

i

22

0

2

•for wci = 0 we get Drude-Lorentz model •for w0i 0 we get bound carriers in magnetic field

Bi2Se3 in 18 Tesla

0.8

1.0

1.2

1.4

1.6

1.80 5 10 15 20 25 30 35 40

0 50 100 150 200 250 300 3500.0

0.2

0.4

0.6

0.8

(b)

Re

flect

an

ce

Frequency (cm-1)

0 Tesla 6 Tesla 12 Tesla 18 Tesla

R(B

) / R

(0

T)

(a)

Energy (meV)

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

2

0

,

2

22,0

, 1

qFpq

FF

FpF i

i

q

Fq ,0

Fano q

A. Kuzmenko, RefFIT manual

Circular optical conductivity s-(w)

50 100 150 2000

200

400

600

800

1000

1200

1400

- (-1

cm

-1)

Frequency [cm-1]

total conductivity cyclotron resonance

60 cm-1 phonon

130 cm-1phonon

0 5 10 15 20Energy [meV]

Fano q reversal0 2 4 6 8 10 12 14 16 18

0

20

40

60

80

100

120

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18

-10

-5

0

5

10 (b)

q (

cm-1)

B (Tesla)

c

c from Ref.[5]

c from Ref.[14]

(a)

B (Tesla)

Fre

quen

cy (

cm-1)

Energy (m

eV)

S.V. Dordevic et al., to be published soon.

m* = 0.15 me

L. Wu et al., (2015).

M. Orlita et al., (2015).

Circular optical conductivity s-(w)

50 100 150 2000

200

400

600

800

1000

1200

1400

- (-1

cm

-1)

Frequency [cm-1]

total conductivity cyclotron resonance

60 cm-1 phonon

130 cm-1phonon

0 5 10 15 20Energy [meV]

50 100 150 2000

200

400

600

800

1000

1200

1400 cyclotron resonance 60 cm-1 phonon

- (-1

cm

-1)

Frequency [cm-1]

0 5 10 15 20Energy [meV]

Magnetic field driven Fano q reversal

B

Practical realizations of 3D topological insulators

Bi1-xSbx

Bi2Se3, Bi2Te3 and Sb2Te3

Bismuth

Fermi surface

K. Behnia, Science 321, 497 (2008).

holes

electrons

Band structure: semimetal

N. P. Armitage et al, arXiv:1002.4206v1

Reflectance of bismuth

Zero field

“plasmaron”R. Tediosi, et al, PRL 99, 016406 (2007).

100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

Frequency [cm-1]

Zero field fit

100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

fit data

Ref

lect

ance

Frequency [cm-1]

Drude + Lorentzian

Magneto-Reflectance in Voigt geometry

B

Magneto-Reflectance in Voigt geometry

Magneto-Reflectance in Faraday geometry

B

100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

Frequency [cm-1]

100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

Frequency [cm-1]

3 Tesla

100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

Frequency [cm-1]

4 Tesla

100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

Frequency [cm-1]

6 Tesla

100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

Frequency [cm-1]

8 Tesla

100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

Frequency [cm-1]

10 Tesla

100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

Frequency [cm-1]

14 Tesla

100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

Frequency [cm-1]

16 Tesla

100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

Frequency [cm-1]

18 Tesla

Bismuth in high magnetic field

S.V. Dordevic, et al.

Model: free and bound electrons(and holes) in magnetic field

i ciii

pi

i

22

0

2

•for wci = 0 we get Drude-Lorentz model •for w0i 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

100 10000.5

0.6

0.7

0.8

0.9

1.0 300 K 200 K 77 K 10 K

Re

flect

an

ce

Frequency [cm-1]

Magneto-Reflectance in Faraday geometry

B

Magnetic field: Bi1-xSbx

100 200 300 400 5000.5

0.6

0.7

0.8

0.9

1.0

0 T 6 T 12 T 18 T

Re

flect

ance

Frequency [cm-1]

Model: free and bound electrons(and holes) in magnetic field

i ciii

pi

i

22

0

2

• for w0i 0 we get bound carriers in magnetic field • for wci = 0 we get Drude-Lorentz model

Bismuth

Bismuth doped with Sb and As

0.6

0.7

0.8

0.9

1.010 100

100 10000.5

0.6

0.7

0.8

0.9

1.0Bi

1-xSb

x

Ref

lect

ance

Frequency [cm-1]

300 K 200 K 77 K 10 K

Bi1-x

Asx

Energy [meV]

In 18 Tesla

100 200 300 400 5000.5

0.6

0.7

0.8

0.9

1.0

0.6

0.7

0.8

0.9

1.010 20 30 40 50 60

Bi1-x

Sbx

Ref

lect

ance

Frequency [cm-1]

0 Tesla 6 Tesla 12 Tesla 18 Tesla

Bi1-x

Asx

Energy [meV]

Cyclotron resonances0 2 4 6 8 10 12 14 16 18

100

200

300

400

0 2 4 6 8 10 12 14 16 18-50

-40

-30

-20

-10

0(b)

c,2 [c

m-1]

Magnetic Field [Tesla]

Bi1-x

Asx

Bi1-x

Sbx

Magnetic Field [Tesla]

c,

1 [c

m-1]

(a)

dR/dH maps

Thank you!

Questions?

Summary• 3D topological insulators:

Bi2Se3, Bi2Te3, Sb2Te3, Bi1-xSbx

• Infrared and magneto-optical spectroscopy

• What can we learn from these?

Spectroscopic techniques are an important tool in studies of novelmaterials. I will review recent infrared and magneto-opticalstudies of 3D topological insulators Bi2Se3, Bi2Te3, Sb2Te3 andBi_{1-x}Sb_x. A number of issues will be discussed, such as thecyclotron resonance and its field dependence, electronicinhomogeneities, and electron-phonon coupling. We find that inBi2Se3 charge carriers are indeed strongly coupled to an opticalphonon, causing its asymmetric (Fano) lineshape. Moreover, we showthat the asymmetry of the phonon can be switched from negative topositive, with the application of magnetic field. This is theso-called Fano q reversal, which to the best of our knowledge hasnot been observed before in topological insulators.

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http://arxiv.org/abs/1510.01503v1

Crystal structure

http://www.webelements.com/bismuth/crystal_structure.html

http://www.periodni.com/en/bi.html

rhombohedral