stm and sts investigations of the topological insulator...
TRANSCRIPT
![Page 1: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/1.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
STM and STS investigations of the topological insulator Bi2Te3
F. Craes, E. Sela, T. Michely, A. Rosch, C. Busse
![Page 2: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/2.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
STM and STS
• Metallic tip scanning the surface in 1nm distance. 5 main parameters determine scanning tunneling microscopy (STM): I, U, x, y, z
• STM mode constant current: fix I and U, vary z(x,y) à topography (constant density of states)
• Scanning tunneling spectroscopy (STS): measure variable density of states, e.g. I(V)
![Page 3: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/3.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
STS
![Page 4: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/4.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
STS
• measure dI/dU directly by Lock-In detection: best signal-to-noise ratio
• Ubias + AC modulation f • detect current harmonic with modulation frequency f • amplitude directly proportional to dI/dU, thus density
of states à real space picture of LDOS
![Page 5: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/5.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Clean surfaces
stick method
view into the UHV chamber
Generating a clean surface by in-situ crystal cleaving in UHV
![Page 6: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/6.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Clean surfaces
stick method
view into the UHV chamber
Generating a clean surface by in-situ crystal cleaving in UHV
![Page 7: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/7.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Topological insulator Bi2Te3
(2.5x2.5)nm², U=-0.5V
(20x20)nm², I=0.7nA, U= -0.6V
![Page 8: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/8.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Bi2Te3 – scattering of topological surface states
real space reciprocal space
![Page 9: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/9.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
• How to measure LDOS with an STM? • solution: reflection of electronic statesà formation of standing waves à modulation of density of states:
Measure standing wave patterns of LDOS at point defects and steps (energy resolved Friedel oscillations)
• method: measure dI/dU by Lock-in detection
Surface states and STM
![Page 10: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/10.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
• How to measure LDOS with an STM? • solution: reflection of electronic statesà formation of standing waves à modulation of density of states:
Measure standing wave patterns of LDOS at point defects and steps (energy resolved Friedel oscillations)
• method: measure dI/dU by Lock-in detection
Surface states and STM
kSW kin
kout
![Page 11: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/11.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Bi2Te3 – scattering of topological surface states
• direct backscattering (q1) forbidden by TRI • scattering solely enabled by nesting vectors
Zhang, T. et al., PRL 103, 2009
Fu et al., PRL 103, 2009
![Page 12: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/12.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Bi2Te3 scattering at a step
-20mV
50mV 80mV
100mV
124mV
141mV 181mV
dI/dU map of standing waves on Bi2Te3(111)
U x=26nm, I=0.1nA,T=7.5K
surface step
![Page 13: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/13.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Bi2Te3 scattering at a step
-20mV
50mV 80mV
100mV
124mV
141mV 181mV
U x=26nm, I=0.1nA,T=7.5K
surface step
![Page 14: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/14.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Bi2Te3 scattering at a step determine E(k) by fitting y-averaged linescans of dI/dU for each energy with sinc-function
! " #! #" $! $" %!
!
$!
&!
'!
(!
#!!
)
)
*)+,-
. )+/0-
surface step E=100meV
![Page 15: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/15.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Bi2Te3 scattering at a step determine E(k) by fitting y-averaged linescans of dI/dU for each energy with sinc-function
! " #! #" $! $" %!
!
$!
&!
'!
(!
#!!
)
)
*)+,-
. )+/0-
surface step E=100meV
![Page 16: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/16.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Bi2Te3 scattering at a step determine E(k) by fitting y-averaged linescans of dI/dU for each energy with sinc-function
ED
Linear dispersion verified!
![Page 17: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/17.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Bi2Te3 scattering at magnetic defects (40x40)nm², U=0.7V, I=0.1nA, T=7.5K
• idea: breaking TRI à use magnetic defects
• evaporate 0.02ML Eu on Bi2Te3(111) surface at T=20K
• Eu: huge magnetic moment
![Page 18: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/18.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
(10x10)nm², U=33mV, I=0.24nA
Bi2Te3 - scattering at magnetic defects
K M
FT
![Page 19: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/19.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Bi2Te3 - scattering at magnetic defects (40x29)nm², U=700mV, I=0.1nA, T=7.5K
dI/dU map
(40x40)1/nm², U=700mV, I= 0.1nA
FFT of dI/dU map
K M
FT
![Page 20: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/20.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Bi2Te3 - scattering at magnetic defects (40x29)nm², U=700mV, I=0.1nA, T=7.5K
dI/dU map
(40x40)1/nm², U=700mV, I= 0.1nA
FFT of dI/dU map
à direct backscattering?
K M
![Page 21: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/21.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
Bi2Te3 - breaking TRI? calculated intensity from magnetic point scattering
intensity from magnetic scattering vanishes, only potential scattering left
see also Guo and Franz, PRB 81, 2010
![Page 22: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/22.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
summary
• scattering at step: linear dispersion relation of Dirac fermions could be observed on samples
• scattering at magnetic point defects does not show direct backscattering (consistent with our theory: presence of time-reversed process)
![Page 23: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/23.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
outlook • measure scattering at strong local magnetic moments
(magnetic clusters) in order to suppress temporal fluctuations
• use magnetic tip in order to suppress time reversed processes
• Consistency with measurements of Okada et al.: new scattering channels on Bi2-xFexTe3+d? Scattering into other states?
Okada et al., arXiv:1011.4913, 2010
![Page 24: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/24.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
![Page 25: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/25.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
S1: theory
![Page 26: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/26.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
S2: STS
• STS difficulties: – tip not featureless – really a free electron gas as
assumed in many calculations? – tunneling transmission probability: impossible to
measure states that do not overlap with states of tip
– lacks chemical sensitivity
![Page 27: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/27.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
S3: LTSTM system AG Michely
• UHV 10-13mbar – 1bar àsample clean for several
weeks • temperature range 6K – 300K • 2 chambers: STM + preparation • sample preparation at 20K – 1500K
![Page 28: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/28.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
S4: Bi2Te3 - scattering of topological surface states literature
Alpichshev et al. ARPES Zhang et al. STS Alpichshev et al. STS AG Michely STS
ED
![Page 29: STM and STS investigations of the topological insulator …tfp1.physik.uni-freiburg.de/Capri11/lectures/ShortSeminars/Craes... · Fabian Craes University of Cologne Capri Spring School](https://reader030.vdocuments.us/reader030/viewer/2022020214/5a7a219a7f8b9a71348cc0bd/html5/thumbnails/29.jpg)
Fabian Craes University of Cologne Capri Spring School 2011
S5: Clean surfaces
• STM essentially needs clean surfaces • Possible ways to obtain:
– Ion bombardment and high temperuture treatment (mainly one component systems)
– in-situ growth (e.g. molecular beam epitaxy (MBE), not too many components)
– in-situ cleaving: method of choice for complex materials, especially layered ones