Bi2Se3超薄薄膜在S波超导邻近效应下的拓扑性质研究

Three dimensional topological insulator is a special kind of material with both bulk insulating gap and chiral semi-metal surface state. This new topological phase of mater is experimentally comfirmed in Bi2Se3, Bi2Te3 and Sb2Te3. In 2008, perfessor Fu Liang proposed that, one can construct a spinless chiral P-wave superconductor when a S-wave superconductor is deposited on the surface of Bi2Se3. After his first theoratical proposal, many theoratical and experimental researches have focused on the behavior of a single chiral surface state of Bi2Se3 film while S-wave cooper pairs are induced due to the proximity effect. This requires that Bi2Se3 film should be relatively thick since the coupling of the two surfaces states can break the chirallity of the surface states. However, when the thickness of Bi2Se3 film is below the critical value, the origional proposal of the hamiltonian of spinless chiral P-wave superconductor is invalid since the chirallity of the surface states is broken. We are interested in the behavior of elementary excitations in this case, i.e, Bi2Se3 ultra-thin film -- S wave superconductor heterostructure. We want to include the two surfaces and the coupling between them simultaneously, by expanding the dimention of the Hilbert space. In this new space, we might be able to construct a hamiltonian of spinfull chiral P-wave supercondutor by performing unitary transformation when S-wave cooper pairs are introduced. We have to emphasize that this “spin” is not a real spin of electron, it is a pseudo spin made by the degree of the two surface states. Hence, we expect to find some extraodinary properties in this system, such as novel Majorana fermions.

三维拓扑绝缘体是一种同时具有绝缘体态和手征半金属表面态的三维材料，这种物质态已经在Bi2Se3等材料中被实验所证实。2008年傅亮教授等学者提出，可以在Bi2Se3的表面，通过超导的邻近作用引入S波超导配对，构建出无自旋的手征P波超导体。这一理论也被之后的实验所证实。目前的理论与实验工作都要求Bi2Se3薄膜具有一定的厚度，否则手征半金属态就会由于上下表面态之间的耦合受到破坏。而我们感兴趣的正是这种Bi2Se3超薄薄膜－S波超导体系统中的准粒子行为。由于手征半金属表面态的缺失，原本的P波超导有效哈密顿量不再成立。我们希望通过扩大系统的维度，在哈密顿量中同时考虑上下表面的贡献以及它们之间的耦合作用，在引入S波超导配对之后，可以变换成有效的自旋手征P波超导哈密顿量。这里的“自旋”并不是真正的自旋，而是由上下表面构成的赝自旋，我们期望能找到一些不同寻常的性质，比如奇异的Majorana费米子等。

三维拓扑绝缘体是一种同时具有绝缘体态和手征半金属表面态的三维材料，这种物质态已经在Bi2Se3等材料中被实验所证实。2008年傅亮教授等学者提出，可以在Bi2Se3的表面，通过超导的邻近作用引入S波超导配对，构建出无自旋的手征P波超导体。这一理论也被之后的实验所证实。目前的理论与实验工作都要求Bi2Se3薄膜具有一定的厚度，否则手征半金属态就会由于上下表面态之间的耦合受到破坏。而我们感兴趣的正是这种Bi2Se3超薄薄膜－S波超导体系统中的准粒子行为。通过研究我们发现，在Bi2Se3超薄薄膜和普通绝缘体薄膜的多层共建系统中，电子的行为更接近Weyl费米子行为，它在S波超导的邻近效应下，更符合Weyl费米的S波配对规则。针对这一发现，我们就Weyl费米子本身的拓扑性质进行了深入的研究，并发现Weyl费米子与非共振光场的相互作用会强烈的影响它的拓扑结构。我们采用Floquet理论，在Dirac型半金属中通过加入非共振激光的办法使得Dirac点劈裂成为两个独立的Weyl点，从而人工的创造出了Weyl半金属。进而我们在Weyl半金属中加入共振激光，采用旋转波近似的方法，我们发现在原来的共振能级处，并没有类似普通半导体的那种全能隙打开，而是会在动量空间的产生四个独立的Weyl点，这些新增的Weyl点可以为我们研究Weyl半金属的拓扑性质带来新的丰富的研究内容。随后我们将加入S波超导，通过邻近效应讨论实现P波超导体的可能性。