infrared and magneto- optical studies of topological insulators saša v. Ðorđević department of...
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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Hechang Lei and C. Petrović, unpublished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