球狀拓樸絕緣體中由空間曲率造成之渦流態

由於拓樸絕緣體有特殊的電子表面態，拓樸絕緣體近年來已有許多廣泛的研究。在這篇論文之中，我們主要會去探討拓樸絕緣體三碲化二銻(Sb2Te3)，所引發的超導體現象。藉由探討電子在曲面上配對，了解率於性質所造成的影響。我們因此選定了最簡單的曲面幾何-球型幾何來進行探討。由於球面的曲率會造成電子看到等效磁單極磁場於球心產生，也因此有別傳統的超導體渦流態，系可以在不用外加磁場情形下產生穩定。因為馬約拉那費米子有非阿貝爾群統計的性質，科學家們預測子可以用來應於量計算中的位元操作，能會對現有很大突破，科學家們紛試著找到馬約拉那費米子。而由於馬約拉那費米子在二維系統中可能會存在於 P-wave 配對的超導體渦流態中，因此我們將會下去探討是否有馬約拉那費米子存在於我們的系統渦流態中。藉由均場定理，我們可以分析我們的系統對於曲面上的超導體。我們考慮系統中有聲子交互作用力以及庫倫排斥力，並發現隨著交互作用的大小不同均勻超導態和渦流態彼此會有所競爭。我們在此論文中提供了相關的理論計算以及分析，並於最後呈現了不同曲率對於不同溫度的相圖。此研究幫助了我們了解到電子於曲面上的超導體電子配對的機制。未來我們也將再近一步對於這個題目有所改善及推廣。

關鍵字

拓樸絕緣體；曲率；磁單極；馬約拉那費米子

並列摘要

There have been intensive researches recently on topological insulators which have symmetry-protected electronic surface state. In this thesis, we would like to investigate the geometrical effect of superconductivity on the surface of topological insulators. The surface states enable us to realize the dependence of pairing symmetry on different geometry of the surface. In particular, we are interested in the effect of curvature on the topological superconductivity . Due to the so-called spin-connection effect , the curvature generates a gauge eld via a local transformation of spin quantization direction. As a result, electrons of the local frame experience an effective magnetic field even if there is no external magnetic field. In this thesis, we consider the superconductivity of topological insulator induced by spherical geometry. The curvature effectively introduces a magnetic monopole at the center with opposite magnitudes for spin up and down electrons on a sphere. By using the effective Dirac Hamiltonian that includes the gauge field due to monopoles, we solve mean-field equations for superconductivity on a sphere with phonon-mediated interaction and Coulomb interaction. It is found that the competition between electron-phonon coupling and Coulomb interaction leads to a region in phase space that p-wave superconductivity can be stabilized. Furthermore, depending on the radius of sphere, vortices will be induced on the sphere with one Majorana zero mode being trapped in the core. Finally, phase diagram in the radius versus temperature space for topological superconducting orders is constructed.

並列關鍵字

Topological ； Superconductor ； Curvature ； Magnetic ； Monopole ； Majorana ； zero ； mode

參考文獻

1. L. Zhao, H. Deng, I. Korzhovska, M. Begliarbekov, Z. Chen, E. Andrade,E.Rosenthal, A. Pasupathy, V. Oganesyan, and L Krusin-Elbaum1, Nat. Commun. 6, 8279 (2015).