2006年11月14日 · In the 2D quantum spin Hall phase and the 3D strong topological insulator these states are robust and are insensitive to weak disorder and interactions. In this paper we show that the presence of inversion symmetry greatly simplifies the …

2007年7月2日 · In the two-dimensional quantum spin-Hall phase and the three-dimensional strong topological insulator, these states are robust and are insensitive to weak disorder and interactions. In this paper, we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the ${Z}_{2}$ invariants.

In the two-dimensional quantum spin-Hall phase and the three-dimensional strong topological insulator, these states are robust and are insensitive to weak disorder and interactions. In this paper, we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the Z2 invariants.

In this paper we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the Z2 invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wavefunctions at …

We discuss specifically the example of insulators with inversion sym-metry which is found to act as an antiunitary symmetry on the entanglement spectrum. A Kramers degeneracy can then arise even when time-reversal symmetry is absent. This degeneracy persists for interacting systems.

2011年6月28日 · We analyze translationally invariant insulators with inversion symmetry that fall outside the current established classification of topological insulators. These insulators exhibit no edge or surface modes in the energy spectrum and hence they are not edge metals when the Fermi level is in the bulk gap.

2014年4月11日 · In this paper we show that 1D and 2D insulators with the simplest point-group symmetry, inversion, have a Z ≥ classification. In 2D, we identify a relative winding number that is solely protected by inversion symmetry.

2006年11月14日 · In the two-dimensional quantum spin-Hall phase and the three-dimensional strong topological insulator, these states are robust and are insensitive to weak disorder and interactions. In this paper, we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the ${Z}_{2}$ invariants.

2024年11月1日 · We explore a large family of one-dimensional (1D) topological crystalline insulators (TCIs) classified by Z invariants under space-time inversion symmetry. This finding stands in marked contrast to the conventional classification of 1D band topology protected by inversion symmetry and characterized by Z2 -quantized polarization (Berry-Zak phase).

In this Lecture Note, the term (TI) specifically refers to the insulator with its topol-ogy protected solely by time-reversal symmetry. A re-lated term is topological crystalline insulator, in which the topology is protected by crystalline symmetry. We will first study 2D TI, then 3D TI. The edge states of the TIs is the subject of next Lect.