Andreev反射在非中心對稱超導體之量子傳輸性質

Abstract

本論文目的探討在計算單層蜂蜜巢狀結構(honeycomb lattice)上加入不同的自旋軌道耦合作用(SOC)與混合自旋單重態(spin-singlet)和三重態(-triplet)的超導之間的導電度(differential conductance)，其分析方法為BTK(G.E.Blonder, M.Tinkham, T.M.Klapwijk)所提出及C.W.J.Beenakker推廣至石墨烯上的計算，在正常態(Normal)和超導態(Superconducting state)的界面(interface)會發生獨特的量子現象稱為Andreev反射，原理是因超導的pairing gap引起電子電洞之間的轉換，在正常態反射出電洞(hole)且於超導態形成庫伯對(Cooper pair)並產生超導電流，是一個把耗散(disspative)的電流轉換成無耗散的超導電流的過程，造成穿過界面導電度增加。自旋軌道耦合包含Rashba和Kane-Mele兩種形式，兩種可使正常態變成具有拓樸絕性質，反鐵磁自旋交換耦合在相鄰的晶格引發自旋單重態d+id’波超導，Rashba自旋軌道耦合偏向產生自旋三重態p波超導，兩種超導具有手性/螺旋Majorana模邊界態(edge state)的拓樸性質。我們比較在三種極限下模型所計算出來的導電度：(i) Rashba自旋軌道耦合+自旋三重態超導 (ii) Kane-Mele和Rashba自旋軌道耦合+自旋單重態d+id’波超導 (iii) 同時擁有(i)和(ii)且兩者超導係數強度相當。我們發現在這三個情況下的導電度有不同的趨勢，其結果與可能夠被實現的材料，如Silicene，MoS2或參雜的石墨烯拓樸超導有關。

In this thesis, we investigate transport at an interface between monolayer honeycomb lattice with spin-orbit coupling (SOC) and superconductor with mixed spin-singlet and spin-triplet superconducting pairing and calculate the differential conductance (G/G0). Our analysis method is based on the BTK (G.E.Blonder, M.Tinkham, T.M.Klapwijk) and its extension to graphene by C.W.J.Beenakker. The quantum phenomenon called Andreev reflection (AR) at an interface between normal and superconducting side of tunneling junction is our focus. It converts an electron into hole excitation by the superconducting pairing potential. A hole is reflected in the normal side, and generates a Cooper pair which induces supercurrent in the superconducting side. It is a process that transfers disspative current into non-disspative supercurrent and increases the differential conductance. The SOC induces Rashba type and Kane-Mele type, and both leads to non-trivial topological properties. Antiferromagnetic spin-exchange coupling correlates neighbor site and leads to the spin-singlet d+id’-wave superconducting pairing. The Rashba SO coupling favors spin-triplet p-wave superconducting pairing. Both superconducting conditional states show topological non-trivial properties induce chiral/helical Majorana mode edge state. We compare AR calculation in three different limits of our general model : (i) Rashba SOC + spin-triplet p-wave pairing (ii) K.M. SOC + Rashba SOC + spin-singlet d+id’-wave pairing (iii) generic case with both (i) and (ii) on equal footing. We find different signatures of Andreev reflection conductance in these three cases. Our results are relevant to possible topological superconductor on Silicene, MoS2 and doped graphene.