拓扑超导体的基态和元激发性质

Topological insulator is a phase discovered recently with nontrivial topological order characterized by a Z2 index. Its discovery brougt the study of topological phases to the forefront of condensed matter physics. In 2010, a new superconductor CuxBi2Se3 is prepared. CuxBi2Se3 is the first superconductor (T_C=3.8K) obtained by doping a topological insulator. Since then, it is guessed that this superconductor might have nontrivial topological order. Later, the superconducting phase of Bi2Te3 is also found under high pressure. One important property of topolgical superconductors is that they might support charge neutral topological excitations known as Majorana fermions. The Majorana fermion is widely considered as the most promising candidate to realize quantum computation. Because of this potential for application and also for its fundamental interest, topological superconductors have attracted a lot of attention. In this project, we will study the properties of the superconducting phase of typical two dimensional and three dimensional topological insulators, including their pairing symmetries and the elementary excitations therein. On one hand, we will study the pairing instability of the three dimensional topological insulators Bi2X3 (X is Se or Te). We will determine the pairing symmetries under various possible mechanisms and then analyze the ground state and elementary excitations. On the other hand, we would study the symmetry breaking transitions in the two dimensional honeycomb lattice with spin-orbit coupling and strong electron correlation (i.e., the Kane-Mele-Hubbard model). We would pay special attention to the phase diagrams of the undoped and doped systems in the strong correlation limit. For some superconducting phases with nontrivial topological characters, we would study further their elementary excitations and transport properties.

拓扑绝缘体是时间反演不变的系统中存在的具有非平庸Z2拓扑序的相。2010年由掺杂拓扑绝缘体Bi2Se3得到了转变温度为3.8K的超导体CuxBi2Se3。人们猜想其中的配对可能是拓扑非平庸的。拓扑超导体中的马拉约那费米子元激发是实现拓扑量子计算的最有希望的载体。应用前景和基础研究上的重要性使得拓扑超导体的研究吸引了众多的关注。本项目中，我们将研究典型的二维和三维拓扑绝缘体的超导相的性质，包括其配对对称性和元激发性质等。一方面，我们将研究三维拓扑绝缘体Bi2X3（X为Se或Te）由一些特定的配对机制导致的配对的对称性及其非平庸的基态和元激发性质。另一方面，我们将研究具有自旋轨道耦合和电子强关联的二维六角蜂窝晶格中的对称破缺相，特别是该系统在强关联极限情况下的零掺杂和掺杂相图。对于相图中一些拓扑非平庸的超导相，我们将进一步研究其元激发和输运性质。

2010年，通过向拓扑绝缘体Bi2Se3掺铜，得到了转变温度为3.8K的超导体CuxBi2Se3。随后不久，人们发现加压可以更容易地把一些拓扑绝缘体，如Bi2Se3和Bi2Te3等，也转变为超导体。考虑到这些超导体正常态的拓扑性质，人们猜测其中的超导配对可能也是拓扑非平庸的。而拓扑超导体中的元激发—马约拉那费米子—是实现拓扑量子计算的理想载体。因而，超导拓扑绝缘体，作为拓扑超导体家族的可能的新成员，吸引了众多的关注。本项目中，我们研究了典型的二维和三维拓扑绝缘体的超导相的性质，包括其配对对称性和元激发性质等。一方面，我们研究了三维拓扑绝缘体Bi2X3（X为Se或Te）由一些特定的配对机制导致的配对的对称性及其非平庸的基态和元激发性质。例如，考虑短程库仑排斥型相互作用，我们的计算表明超导拓扑绝缘体的主要配对通道是各向异性的自旋单重态配对。由于材料内禀的自旋轨道相互作用，几种不同的配对通道总是同时存在。一种奇特的轨道宇称和空间宇称都为奇的配对通道支持表面Andreev束缚态。另外，为了更深入地把握超导拓扑绝缘体的表面态性质，我们提出了一种构造超导拓扑绝缘体的低能有效模型的简便方法。根据这种方法，我们不仅可以很容易地判断某种配对是否支持表面束缚态，而且还预言实际的超导拓扑绝缘体可以支持两对表面Andreev束缚态。另一方面，我们研究了具有自旋轨道耦合和电子强关联的二维六角蜂窝晶格（Kane-Mele-Hubbard模型）的对称破缺相。我们通过Schrieffer-Wolff变换构造出了该模型在强关联极限情况下的低能有效模型，并进行了平均场处理。这部分工作我们还没有得到最后的结果。