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
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)
Fabian Craes University of Cologne Capri Spring School 2011
STS
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
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
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
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
Fabian Craes University of Cologne Capri Spring School 2011
Bi2Te3 – scattering of topological surface states
real space reciprocal space
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
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
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
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
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
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
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surface step E=100meV
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
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surface step E=100meV
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!
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
Fabian Craes University of Cologne Capri Spring School 2011
(10x10)nm², U=33mV, I=0.24nA
Bi2Te3 - scattering at magnetic defects
K M
FT
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
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
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
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)
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
Fabian Craes University of Cologne Capri Spring School 2011
Fabian Craes University of Cologne Capri Spring School 2011
S1: theory
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
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
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
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