外爾半金屬中相互交織的超導序與密度波序

這篇論文致力於去探討在外爾半金屬中互相交織的超導序與密度波序。我們使用了硒化鉍的材料做為我們的模型系統。我們能證明在時間反轉對稱被破壞的外爾半金屬可以產生出超導相，而且能更進一步的由一般超導的不穩定性來產生密度波。細節上，我們引入了一個負位能的交互作用力並且去探討超導相、超導密度波、電荷密度波和自旋密度波之間的競爭關係。我們基於平均場理論和數值計算去分析完整的相圖。我們發現超導密度波總是伴隨著電荷密度波，更發現自旋密度波並不會存在於系統中的基態。我們接著要分析負位能和聲子交互作用的不同。而為了要產生出聲子的吸引交互作用力，所以負位能交互作用力要更進一步的限制在費米面上的電子態。而相圖在定性上來說是相同的，它給出在時間反轉對稱被破壞的外爾半金屬通常能通過聲子交互作用力來變成超導相的結果，而且這個超導相是帶著質心動量不為零的古柏對。

關鍵字

超導相；超導密度波；電荷密度波

並列摘要

This thesis is devoted to exploring intertwined superconducting orders and density wave orders in the Weyl semimetal. We use Bi2Se3 as our model system. It is shown that for Weyl semimetals that break time reversal symmetry, in addition to the superconducting order, the usual superconducting instability will also induce density waves. Specifically, we introduce a negative U interaction and explore the competition between superconducting, pair density wave (PDW), charge density wave (CDW) and spin density wave (SDW). Based on the mean field theory and numerical calculation, we analyze the whole phase diagram. We find that PDW always accompanies CDW. In addition, SDW orders can not exist in the ground state of the system. Secondly, we analyze the difference between negative interaction and phonon mediated interaction. To simulate the phonon induced attractive interaction, the negative U interaction is further restricted to electronic states near the Fermi surface. The phase diagram is found to be qualitatively the same, indicating that Weyl semimetals that break time reversal symmetry can generally become superconducting with non-zero center of mass momentum Cooper pair simply through the phonon mediated interaction.