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Quantum topological Hall effect in noncoplanar antiferromagnetic oxides
The integer quantum Hall
(IQH)
effect, first
discovered in 1980 by von Klitzing [1] (a 1985 Nobel Laureate)
,
is one of the most
fascinating
discoveries in physics.
When a strong perpendicular magnetic field is applied to a two-dimensional
(2D) electron gas
(EG)
at low temperatures, the Hall conductance is precisely quantized
due to Landau-level quantization
, and its values are an integer (
N
C
) multiple of
the fundamental conductance quantum (e
2
/h).
In 1982, Thouless (a 2016 Nobel Laureate) demonstrated that
this quantization is directly connected to
the topological property of the 2D
bulk
insulating states,
characterized by a topological invariant called the Chern number
(
N
C
) [2]
.
Intriguingly, the conductance quantum number (
N
C
) is exactly equal to the number (
N
C
) of dissipationless chiral edge states in the 2DEG plane [Figure 1(a)].
Th
e
topological interpretation of the IQH
effect
implies that the
effect
can also occur
in other time-reversal symmetry broken systems with a topological
ly
non-trivial band structure
in the absence of the external magnetic field,
such as ferromagnetic topological insulators,
leading to the so-called quantum anomalous Hall
(QAH)
effect
[Figure 1(b)], as
first proposed
for
a honeycomb lattice model
in 1988
by Haldane
[3] (2016 Nobel Laureate).
Due to its intriguing nontrivial topological properties and the potential application of its dissipationless edge states for designing low-power consumption electronics and spintronics, extensive studies have been performed to search for real materials to host the QAH effect. Indeed, this extensive effort culminated in the experimental observation of the QAH effect in Cr-doped (Bi,Sb)
2
Te
3
ferromagnetic topological insulator films in 2013 by Xue and coworkers [4]. Nevertheless, the QAH phase appeared at extremely low temperatures (less than 30 mK) due to the small band gap, weak magnetic coupling and low carrier mobility. These factors hinder further exploration of the exotic properties of the QAH phase and its applications.
The problems with weak magnetic coupling and small band gap could be overcome by adopting 4
d
and 5
d
transition metal atoms, which simultaneously have more extended
d
-orbitals and stronger relativistic spin-orbit coupling (SOC). Therefore, through
ab initio
density functional calculations, we have recently conducted a systematic search for high-temperature QAH phases in 4
d
and 5
d
transition metal oxides. Indeed, we discovered that layered rhodium oxide K
1/2
RhO
2
in the noncoplanar antiferromagnetic state is a QAH insulator with a large band gap of ~0.2 eV and a Néel temperature of a few tens of Kelvins [5] [Figure 2]. Furthermore, this QAH phase is found to be unconventional because it occurs in the antiferromagnetic state without the need for net magnetization and SOC. The quantum topological Hall effect caused by the nontrivial topology of the noncoplanar antiferromagnetic structure in the system is rather exotic [Figure 2(a)]. These findings thus show that 4
d
and 5
d
metal oxides are promising materials for exploring exotic quantum phases and for realizing advanced technological applications such as low-power consumption nanoelectronics and oxide spintronics.
Figure 1. Schematic diagrams of chiral conductive edge states in (a) the integer quantum Hall effect and (b) the quantum anomalous Hall effect. Note that the bulk regions are nonconductive due to either (a) Landau level quantization by the strong magnetic field (B
z
) or (b) ferromagnetism (M
z
) plus the relativistic spin-orbit coupling gap.
Figure 2. Layered K
1/2
RhO
2
. (a) Crystalline and antiferromagnetic structure. (b) Edge band diagram. The gapless chiral edge states are denoted by red and blue lines, and black lines represent the insulating bulk band structure. (c) Illustration of the chiral edge states (orange lines) labelled
a
and
b
in (b).
References
1. K. V. Klitzing, G. Dorda, and M. Pepper (1980). New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance.
Physical Review Letters,
45
(6), 494-497. DOI:10.1103/PhysRevLett.45.494.
2. D. J. Thouless, M. Kohmoto, M. P. Ni
ghtingale, and M. den Nijs (1982). Quantized Hall conductance in a two-dimensional periodic potential.
Physical Review Letters,
49
(6), 405-408. DOI:10.1103/PhysRevLett.49.405.
3. F. D. M. Haldane (1988). Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the ‘parity anomaly’.
Physical Review Letters,
61
(18), 2015-2018.
DOI:10.1103/PhysRevLett.61.2015.
4. Cui-Zu Chang, Jinsong Zhang, Xiao Feng, Jie Shen, Zuocheng Zhang, Minghua Guo, Kang Li, Yunbo Ou, Pang Wei, Li-Li Wang, Zhong-Qing Ji, Yang Feng, Shuaihua Ji, Xi Chen, Jinfeng Jia, Xi Dai, Zhong Fang, Shou-Cheng Zhang, Ke He, Yayu Wang, Li Lu, Xu-Cun Ma, Qi-Kun Xue (2013). Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator.
Science, 340
(6129),
167-170. DOI:10.1126/science.1234414.
5. Jian Zhou, Qi-Feng Liang, Hongming Weng, Y. B. Chen, Shu-Hua Yao, Yan-Feng Chen, Jinming Dong, and Guang-Yu Guo (2016).
Predicted quantum topological Hall effect and noncoplanar antiferromagnetism in K
0.5
RhO
2
.
Physical Review Letters, 116
(25), 256601. DOI:10.1103/PhysRevLett.116.256601
Professor Guang-Yu Guo
Department of Physics
gyguo@phys.ntu.edu.tw
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Quantum topological Hall effect in noncoplanar antiferromagnetic oxides
Keywords
Berry phase
ferromagnet
metals
states
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