Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors

By Xiao-Liang Qi, Yong-Shi Wu, Shoucheng Zhang. 2005

576 citations recorded by the source corpus.

We propose models of two-dimensional paramagnetic semiconductors where the intrinsic spin Hall effect is exactly quantized in integer units of a topological charge. The model describes a topological insulator in the bulk and a ``holographic metal'' at the edge, where the number of extended edge states crossing the Fermi level is dictated by (exactly equal to) the bulk topological charge. We also demonstrate the spin Hall effect explicitly in terms of the spin accumulation caused by the adiabatic flux insertion.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/ebaec23b3a59d0ca6c6ddf5f309b93e5ef0e4b52

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Nathan Goldman
2. J. Dalibard
3. Zhong Wang
4. Di Xiao
5. Shoucheng Zhang
6. Q. Niu
7. Xiao-Liang Qi
8. M. Chang

In Materials Chemistry

1. Nathan Goldman
2. J. Dalibard
3. Di Xiao
4. Zhong Wang
5. Shoucheng Zhang
6. Q. Niu
7. Xiao-Liang Qi
8. Ze-Guo Chen

Citations in the corpus

• Artificial gauge fields in materials and engineered systems (2017, unknown): “(30) to a simple (integer) winding number, which can be directly evaluated from the Hamiltonian [241,242], as we now recall.”
• Periodically Driven Quantum Systems: Effective Hamiltonians and Engineered Gauge Fields (2014, background): “Adding terms to the static Hamiltonian Ĥ0 could also be envisaged to generate systems exhibiting the anomalous quantum Hall effect [38,74], the so-called Chern insulators.”
• A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions (2015, unknown): “nomalous Hall Effect has recently been observed in thin films of chromium-doped (Bi,Sb) 2Te 3 [8]. To illustrate the concepts of Chern insulators, we will use a toy model introduced by Qi, Wu and Zhang[24], which we call the QWZ model. This model is also important because it forms the basic building ”
• Non-Hermitian Chern Bands. (2018, unknown): “The Hermitian part is the Qi-Wu-Zhang model [92] (a variation of Haldane model [88]); the non-Hermitian parameters γx;y;z appear as “imaginary Zeeman fields” [93].”
• Bulk-Edge Correspondence for Two-Dimensional Topological Insulators (2012, background): “In [25] a correspondence between bulk and edge description is given.”
• Topological Nematic States and Non-Abelian Lattice Dislocations (2011, background): “Since Chern numbers are generic properties of any band structure, it is natural to expect that quantum Hall states can also be realized in lattice systems without an applied magnetic field [10,11], and indeed such ‘‘quantum anomalous Hall’’ (QAH) states may be realizable experimentally [12,13].”