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The study of topological property of band insulators is an interesting branchof condensed matter physics. Two types of topologically nontrivial insulatorshave been extensively studied. The first type is characterized by a nonzeroTKNN invariant or Chern number[1] which is directly related to the quantizationof Hall conductance in the integer quantum Hall effect. Haledane propose amodel with this type of band structure even in the absence of a macroscopicmagnetic field[2]. We refer to such materials "Chern insulator". The secondtype called "Z2 topological insulators" is proposed recently[3, 4]. Quantumspin Hall effect has been predicted and observed in such systems.[5, 6].Despite the recent intensively study there are still some fundamental problemsthat aren't quite clear about Z2 insulators even at the single-particle level.For example, it's claimed that Z2 insulators will return to its origin stateafter two cycles, thus coupling to the reservoirs is important for the Z2insulators to continuously pump spin[7]. Theoretical and experimental resultsshow quantum spin Hall effect is an edge state transport property of thematerials and coupling to the reservoir seems not play an important role. Sothe Z2 picture is not satisfactory in explaining these phenomena. We study therelationship of the ground states of Z2 insulators and that of Chern insulator.Combined with the results of recent researches on polarization of Cherninsulators[8] and topology of edge states[9] we propose a coherent physicspicture of topological insulators.

A Coherent Physics Picture of Topological Insulators at Single-Particle Level