Ezawa Motohiko, Tanaka Yukio, Nagaosa Naoto
Department of Applied Physics, University of Tokyo, Hongo 7-3-1, 113-8656, Japan.
Sci Rep. 2013 Sep 27;3:2790. doi: 10.1038/srep02790.
Topological phase transition is accompanied with a change of topological numbers. According to the bulk-edge correspondence, the gap closing and the breakdown of the adiabaticity are necessary at the phase transition point to make the topological number ill-defined. However, the gap closing is not always needed. In this paper, we show that two topological distinct phases can be continuously connected without gap closing, provided the symmetry of the system changes during the process. Here we propose the generic principles how this is possible by demonstrating various examples such as 1D polyacetylene with the charge-density-wave order, 2D silicene with the antiferromagnetic order, 2D silicene or quantum well made of HgTe with superconducting proximity effects and 3D superconductor Cu doped Bi2Se3. It is argued that such an unusual phenomenon can occur when we detour around the gap closing point provided the connection of the topological numbers is lost along the detour path.
拓扑相变伴随着拓扑数的变化。根据体边对应关系，在相变点处能隙关闭和绝热性的破坏是使拓扑数定义不明确所必需的。然而，并不总是需要能隙关闭。在本文中，我们表明，只要系统的对称性在过程中发生变化，两个拓扑不同的相可以在无能隙关闭的情况下连续连接。在这里，我们通过展示各种例子，如具有电荷密度波序的一维聚乙炔、具有反铁磁序的二维硅烯、具有超导邻近效应的二维硅烯或由HgTe制成的量子阱以及三维超导体Cu掺杂的Bi2Se3，提出了这种情况如何可能的一般原理。有人认为，当我们绕开能隙关闭点时，如果沿着绕行路径拓扑数的连接丢失，就会出现这种不寻常的现象。
