Quantum anomalous Hall effect in magnetic topological insulators
Transcript of Quantum anomalous Hall effect in magnetic topological insulators
Ke He
Quantum Anomalous Hall Effect in Magnetic Topological Insulators
Harvard, Sept 2014
Department of Physics, Tsinghua University
Acknowledgement
Cui-Zu Chang, Xiao Feng, Kang Li, Yun-bo Ou, Li-Guo Zhang, Li-Li Wang, Shuai-Hua Ji, Xi Chen, Xu-Cun Ma, Qi-Kun Xue
Tsinghua - IOP, CAS
MBE, STM, and ARPES
Jinsong Zhang, Minhao Liu, Zuocheng Zhang, Minghua Guo, Yang Feng, Yayu Wang Tsinghua Jie Shen, Zhong-Qing Ji, Li Lu, Yongqing Li IOP, CAS
Transport
Xi Dai, Zhong Fang IOP, CAS
Theory & Calc.
Peizhe Tang, W. Duan Tsinghua C.-X. Liu Penn. State
Jing Wang, X.-L. Qi, S.-C. Zhang Stanford
Outline
• From quantum Hall effect (QHE) to quantum anomalous Hall effect (QAHE)
• Experimental realization of the QAHE in thin films of magnetic topological insulators
• Thickness dependence of the QAHE
Edwin H. Hall
I
Vxy B
Rxy = Vxy / I
Hall Effect
Vxx
Rxx = Vxx / I
Ordinary and Anomalous Hall Effect
B
RH
in a ferromagnetic material
B
RH
Ordinary Hall Effect (OHE) 1879
Anomalous Hall Effect (AHE) 1881
in a non-magnetic material
(with ⊥ easy axis)
Quantum Hall Effect GaAs
AlGaAs
Klaus Von
Klitzing ρyx = h / ie2
ρxx = 0
B
Two dimensional electron gas
Ω: Berry curvature C : Chern number
CkdBZ
=Ω∫
π21
Gauss-Bonnet Theorem
K: Gauss curvature χ : Euler characteristic
χπ
=∫S
KdA21
E E
χ = 2 χ = 0
C = 0 C = 1
Topological origin of QHE
Haldane PRL 61, 2015 (1988)
Can we obtain QHE without Landau levels?
Graphene with periodic magnetic field but without net flux
Quantized AHE
B
ρyx AHE
Hall effect at zero field
h/e2
B
QAHE ρyx
QHE at zero field
Karplus & Luttinger, Phys. Rev. 1954 Intrinsic: induced by energy band
Smit, Physica 1958 Skew scattering
Berger, PRB 1970 Side jump
Extrinsic: induced by impurities
∑ ∫Ω=occupied BZ
xy kdhe
πσ
212
Onoda & Nagaosa, PRL 2003 Onoda, Sugimoto & Nagaosa, PRL 2006
can be quantized in a ferromagnetic insulator with C ≠ 0 (Chern insulator)
Chang & Niu PRB 1996, Sundaram & Niu PRB 1999, Fang et al., Science 2003
kx ky
E
2D TI (Quantum Spin Hall effect) 3D TI
Empty Band
Occupied Band
edge state surface state
Fu, Kane & Mele, PRL 2007 Moore & Balents, PRB 2007
Roy, PRB 2009
Mele & Kane, PRL 2005 Bernevig & Zhang, PRL 2006
TR-Invariant Topological Insulators
⊙ ⊗
3D TI: Bi1-xSbx 2D TI: HgTe Quantum Well
Real TI Materials
3D TI: Bi2Se3 Family (Bi2Se3, Bi2Te3,
Sb2Te3, )
Bernevig, Hughes & Zhang, Science 2006 Konig et al., Science 2007
Fu & Kane Phys. Rev. B 2007 Hsieh et al., Nature 2008
H. Zhang et al., Nature Phys. 2009
Y. Xia et al., Nature Phys. 2009
Y. –L. Chen et al., Science 2009
QAHE in magnetic TIs
C. -X. Liu et al., PRL 2008 R. Yu et al., Science 2010
2D TI 3D TI
FMI
FMI TI
X. -L. Q & S. -C. Zhang, PRL 2008 K. Nomra & N. Nagaosa, PRL 2011
X. -L. Qi, Y. S. Wu & S. -C. Zhang, PRB 2006
To observe QAHE in a TI
• Thin film with appropriate thickness MBE growth • FM insulator phase with perpendicular
magnetic anisotropy Magnetic doping • Tunable chemical potential (carriers) Chemical doping Field effect
Molecular Beam Epitaxy (MBE)
• high sample quality • well-controlled thickness (single atomic layer) • homogeneous doping
Alfred Y. Cho
Scanning Tunneling Microscope (STM)
atomic resolution
Tunneling
Rohrer and Binnig
Angle-Resolved PhotoEmission Spectroscopy (ARPES)
A. Einstein
Photoelectric Effect Ek = hυ – W – E (k//) Ek : kinetic energy hυ : photon energy W : work function E (k//) : band dispersion
K. M. Siegbahn
Direct band structure mapping
MBE-STM-ARPES combo system
ARPES: Band structure MBE: Sample preparation
STM: Atomic arrangement
@ Qi-Kun Xue’s group (Tsinghua & IOP, CAS)
Facility for Transport Experiments
250 mK, 15 Tesla @ Yayu Wang’s Group
(Tsinghua)
30 mK, 18 Tesla @ Li Lu’s Group
@ Yongqing Li’s Group (IOP, CAS)
Figure 2
k// (Å-1)
3QL 5QL 6QL Bind
ing
Ener
gy (e
V)
MBE-Grown Bi2Se3 Thin Films
Yi Zhang et al., Nature Phys. 6, 584 (2010).
1QL 2QL
k// (Å-1) k// (Å-1)
1QL Top ↑
Bottom ↑
Bottom ↓
Top ↓
Thin Thick
For QAHE,
∆ < Eexchange ∆
2QL 1QL
EF
Sb2Te3 and Bi2Te3 Thin Films
Y. –Y, Li et al., Adv. Mater. 22, 4002 (2010).
G. Wang et al., Nano Res. 3, 874 (2010).
R. Yu et al., Science 329, 61 (2010).
Magnetically doped Bi2Se3 family TIs: FM of van Vleck mechanism
EF
Cr-doped Sb2Te3
Chien et al.
Cr-doped Bi2Se3 group TIs
Long range FM order M. Liu et al., PRL 108, 036805 (2012)
J. Zhang et al., Science 339, 1582 (2013) C. -Z. Chang et al., PRL 112,056801 (2014)
No long range FM order
C. –Z. Chang et al., Adv. Mater. 25, 1065 (2013)
(Bi1-xSbx)2Te3: from p- to n-type
n2Dmin.~
1.4x1012 /cm2
Jinsong Zhang et al., Nat.Commun. 2, 574 (2011)
-1 0 1-1 0 1-1 0 1-1 0 1-1 0 1-1 0 1
-3
-2
-1
0
1
2
3
0 25 50 75 100
R xx (k
Ω)
ρ yx (k
Ω)
T(K)T(K)T(K)T(K)T(K)T(K)
µ0H (T)µ0H (T)µ0H (T)µ0H (T)µ0H (T)µ0H (T)
0 25 50 75
0 25 50 75
0 25 50 75
0 25 50 75
0 25 50 750
10
20
30
x2x10
x5
1.5 K 3 K 5 K 10 K 15 K 20 K 30 K 40 K 60 K
x = 0.15 x = 0.2 x = 0.25 x = 0.35
Carrier Independent Ferromagnetism
x = 0 x = 0.5
p type n type
-1.0 -0.5 0.0 0.5 1.0-8
-4
0
4
8 35 V 20 V 100 V 0 V -20 V -210 V
ρ yx(k
Ω)
µ0H (T)
SrTiO3
TI film C. –Z. Chang et al., Adv. Mater. 25,
1065 (2013)
Realization of the QAHE in 5 QL Cr-doped (Bi,Sb)2Te3 (ρyx(B))
-55 V 220 V 0 V
-55 V 220 V 0 V
ρxx-B at different gate voltages
Vg dependent zero field ρxx and ρyx
ρxx dip
Quantum plateau observed
1 (h/e2) 0.99 (e2/h)
Dissipationless transport in
magnetic field (@ 30 mK)
-15 -10 -5 0 5 10 15-1.0
-0.5
0.0
0.5
1.0ρ yx
(h/e
2 )
µ0H (T)
-15 -10 -5 0 5 10 150.0
0.5
1.0
1.5
2.0
ρ xx (h
/e2 )
µ0H (T)
Temperature dependence
QAHE at higher temperature?
• Larger gap Two energy scales: Curie temperature Spin-orbit coupling Why the effective gap size now is so small? • More disorder, lower dimension Promote localization of dissipative channels
Both can reach room temperature
Summary
• MBE-grown TI thin films
• Magnetically doped TI thin films
• QAHE
• Chemical potential tuning
Summary Thickness dependence of QAHE
ordinary insulator
Thickness
chemical potential difference
Chern insulator
localization
ferromagnetism
Thank you for your attention !
STM of Cr doped Sb2Te3
Te
Sb1 Te Sb2 Te
Cr atoms • No Clustering • Occupying Sb sites!
Sb site
Te site
Cr-doped (Bi0.5Sb0.5)2Te3 Tc ~ 40K
LT-ARPES in Xingjiang Zhou’s Lab (IOP)
Scaling relation between δσxy and σxx
Nagaosa et al., Rev. Mod. Phys. 2011