Transcript Real-space Imaging of Dirac-Laudau Orbits in Topological Surface State Yingshuang Fu 付英双 Huazhong University of Science and Technology RIKEN Center for Emergent Matter Science.

Real-space Imaging of Dirac-Laudau Orbits in
Topological Surface State
Yingshuang Fu
付英双
Huazhong University of Science and Technology
RIKEN Center for Emergent Matter Science
Acknowledgement

Collaborators
M. Kawamura

T. Hanaguri
Funding
K. Igarashi
T. Sasagawa
H. Takagi
Dirac fermions in 2 dimensional electron systems
Graphene (GRP)
Topological surface state (TSS)
sublattice pseudospin-momentum coupled
spin-momentum coupled
Spin and valley degenerated
Spin nondegenerated
Topological Insulators
Band insulator + gapless edge/surface state
Quantum
Spin Hall Effect
Quantum
B
SOC
B
B
Bulk
insulator
Gapless edge state (2D TI)
Gapless surface state (3D TI)
Energy
Conduction Band
Valence Band
momentum
Helical Dirac fermions
3D topological insulator Bi2Se3
Bi2Se3
Verified by ARPES
Y. Xia et al., Nat. Phys. 5, 398 (2009).
Se
Se
Se
Band calculation
H. Zhang et al., Nat. Phys. 5, 438 (2009).
Spectroscopic imaging STM
E
E
EF
EF
eV
DOS
Tunneling current:
aspects
STM
eV
 (r ) z )  LDOS sample (r , E )dE
I t sensitivity
exp(2
Surface
0
Spatial resolution
Momentum resolution
Differential
conductance:
Magnetic
dI t filed
compatibility
 LDOS sample (r , E )
dV
ARPES
LDOS
Landau quantization of Dirac fermions
• Eigen energies
Conventional electrons
Dirac electrons
DOS
DOS
E
Half-integer QHE
• Eigen functions
Conventional electrons
E
QHE at RT
Dirac electrons
n=0
n≠0
K. S. Novoselov
et al.,
Where is the 2-component
feature?
Science 315, 1379 (2007).
K. S. Novoselov et al., Nature 438, 197 (2005).
Y. Zhang et al., Nature 438, 201 (2005).
How to image the Landau level wave functions?
conventional Landau Levels
on InSb(110)
V(r)
LDOS
Localize Landau level states
with potential variations
N nodes!
V(r)
LDOS
r
r
K. Hashimoto,
etPRL
al., 101,
PRL 109,
116805
(2012).
K. Hashimoto,
et al.,
256802
(2008).
STM based Landau level spectroscopy of Bi2Se3
Topography
STS of Landau levels
Se
Top view
Se
Se
30 nm×30 nm, -100 mV/0.1 nA
T. Hanaguri et al., PRB 82, 081305(R) (2010).
See also P. Cheng et al., PRL 105, 076801 (2010).
Spectroscopic Imaging of Landau orbits
Conductance map of Bi2Se3
Potential
map at Vmin
Point
spectroscopy
11T, 1.5K
1
2
3 4 …
n=0
120 nm×83 nm, +50 mV/50 pA
Drifting Landau orbits along equipotential line
n=0
n=1
n=2
Radial dependence of dI/dV intensity
n=0
1
2
3
4
LDOS across drifting Landau orbits
n=4
n=3
n=2
Two peaks
for ALL n ≠ 0 states.
LL splitting
Different from conventional LLs!
cf. InSb(110)
n nodes for LLn
n=1
n=0
K. Hashimoto, et al.,
PRL 109, 116805 (2012).
n=0
1
2
3
4
…
Model calculation
V(r)
r
Sub-surface charge
Y
r0
Good quantum number :
Eigen energies :
x
Calculated LDOS
Calculation
n=0
Experiment
1
2
3
n=0
1
2
3
4
2-component feature
n=0
n≠0
n=0
1
2
3
4
…
Calculated LDOS
Calculation
n=0
Experiment
1
2
3
n=0
1
2
3
4
n=4
2-component kills the nodes
n=3
n=0
n=2
n=1
n≠0
n=0
Non-trivial spin texture
LDOS
n=0
LSDOS
1
2
3
up
sz
down
𝑠𝑥
,
𝑠𝑦
spin density
Non-trivial spin texture to be detected with SPSTM…
Spin-polarized STM
R. Wiesendanger, Rev. Mod. Phys. 81, 1459 (2009)
I SP (V0 )  I 0  [1  Ptip  Psample  cos(mtip  m sample )]
dI SP (V0 )
 nt  ns  [1  Ptip  Psample  cos(mtip  m sample )]
dV
Summary
Dirac Landau levels under potential variation
No nodes in drifting Landau orbits
Landau level splitting at Vmin
2-component Landau level wave function
Real-space nontrivial spin textures
Ying-Shuang Fu, et al.， “Imaging the two-component nature of
Dirac-Landau levels in the topological surface state of Bi2Se3”，
Nature Physics (2014), doi:10.1038/nphys3084
See also: arXiv:1408.0873