A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators

We prove a general theorem on the relation between the bulk topological quantum number and the edge states in two dimensional insulators. It is shown that whenever there is a topological order in bulk, characterized by a non-vanishing Chern number, even if it is defined for a non-conserved quantity such as spin in the case of the spin Hall effect, one can always infer the existence of gapless edge states under certain twisted boundary conditions that allow tunneling between edges. This relation is robust against disorder and interactions, and it provides a unified topological classification of both the quantum (charge) Hall effect and the quantum spin Hall effect. In addition, it reconciles the apparent conflict between the stability of bulk topological order and the instability of gapless edge states in systems with open boundaries (as known happening in the spin Hall case). The consequences of time reversal invariance for bulk topological order and edge state dynamics are further studied in the present framework.Comment: A mistake corrected in reference

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

Journal ArticleWe 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

General theorem relating the bulk topological number to edge states in two-dimensional insulators

Journal ArticleWe prove a general theorem on the relation between the bulk topological quantum number and the edge states in two-dimensional insulators. It is shown that whenever there is a topological order in bulk, characterized by a nonvanishing Chern number, even if it is defined for a nonconserved quantity such as spin in the case of the spin Hall effect, one can always infer the existence of gapless edge states under certain twisted boundary conditions that allow tunneling between edges. This relation is robust against disorder and interactions, and it provides a unified topological classification of both the quantum (charge) Hall effect and the quantum spin Hall effect. In addition, it reconciles the apparent conflict between the stability of bulk topological order and the instability of gapless edge states in systems with open boundaries (a known happening in the spin Hall case). The consequences of time reversal invariance for bulk topological order and edge state dynamics are further studied in the present framework

Transitions between the quantum Hall states and insulators induced by periodic potentials

Journal ArticleTransitions between two quantum Hall states or between a quantum Hall state and a Mott insulator induced by periodic potentials are studied in the 1 /TV expansion. The transitions are found to be continuous in the large-TV limit and are described by a critical point that depends on a real parameter 0, which is determined by the topological orders in the quantum Hall states involved in the transition. Some critical exponents and universal quantities are calculated in the large-TV limit and shown to be 0 dependent