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