探求非中心對稱超導體存在p-wave有序參數的可能性

Abstract

根據理論計算，擁有非心對稱之結構的材料，其不對稱的自旋-軌道耦合會使得有序參數多了雙能隙以及同向異性的能隙兩種可能性。所以我們針對三個擁有α-Mn結構的非中心對稱超導體，Re24Ti5、Re21.75Ta7.25和Re24.9Hf4.1進行低溫比熱量測，並且利用不同的有序參數去擬合超導態電子比熱，而比熱可以用s-波對來描述， 2∆⁄(k_B T_c ) 依序為3.68 ± 0.01、3.70 ± 0.07以及3.69。從略大於BCS理論值的 ∆C/(γ_n T_c)、2∆⁄(k_B T_c ) 與電子-聲子耦合係數 λ_ep，我們可以得知，庫柏對的電子-聲子是一moderate coupling。我們利用WHH理論 (H_c2 (0)=9.01±0.22 T) 與 γ(H) (H_c2 (0)=9.84±0.60 T) 得到Re24.9Hf4.1的上臨界磁場之數值具有一致性。 而描述非中心對稱超導體比熱的有序參數除了s-波對之外，還可以用雙能隙以及同向異性的能隙。Re24Ti5的大小能隙與 k_B T_c 的比值，分別為 (2∆_L)⁄(k_B T_c=) 3.87±0.07 與 (2∆_S)⁄(k_B T_c=) 3.5±0.06，Re24.9Hf4.1的 (2∆_L)⁄(k_B T_c=) 3.97±0.04、(2∆_S)⁄(k_B T_c=) 3.41±0.04。對Re24Ti5、Re21.75Ta7.25還有Re24.9Hf4.1而言，同向異性的能隙 2∆⁄(k_B T_c ) 皆同s-波對的結果，而能隙的同向異性程度 α 各別是 0.070 ± 0.025、0.149 ± 0.033和0.106 ± 0.015。即使這三個超導體皆為dirty limit，但是參考擁有雙能隙同時又為dirty limit的MgB2的例子，使我們不全然排除p-wave有序參數在Re24Ti5與Re24.9Hf4.1中的存在。

According to theoretical calculations, the asymmetric spin-orbit coupling from non-centrosymmetric structure may lead to an order parameter of two gaps or an anisotropic gap. Low temperature specific heat C(T,H) of Re24Ti5, Re21.75Ta7.25 and Re24.9Hf4.1 were investigated, and we fitted their superconducting electronic specific heat by various order parameter symmetries. These compounds are the of non-centrosymmetric superconductors with α-Mn structure. The specific heat can be well described within the context of an isotropic s-wave for all three compounds, and the 2∆⁄(k_B T_c ) is equal to 3.68 ± 0.01 for Re24Ti5, 3.70 ± 0.07 for Re21.75Ta7.25 and 3.69 for Re24.9Hf4.1. The results of ∆C/(γ_n T_c), 2∆⁄(k_B T_c ) and electron-phonon coupling λ_ep indicate a moderate coupling in these compounds. For Re24.9Hf4.1, the upper critical field H_c2 (0)=9.01±0.22 T was estimated from the Werthamer-Helfand-Hohenberg (WHH), consistent with H_c2 (0)=9.84±0.60 T from γ(H). For two-gap fitting results, the results of Re24Ti5 are (2∆_L)⁄(k_B T_c=) 3.87±.07 and (2∆_S)⁄(k_B T_c=) 3.50±0.06, and those of Re24.9Hf4.1 are (2∆_L)⁄(k_B T_c=) 3.97±0.04 and (2∆_S)⁄(k_B T_c=) 3.41±0.04. As for the fitting of the anisotropic gap, all values of 2∆⁄(k_B T_c ) are the same as those with s-wave, but the individual gap anisotropic α is 0.070 ± 0.025 for Re24Ti5, 0.149 ± 0.033 for Re21.75Ta7.25 and 0.106 ± 0.015 for Re24.9Hf4.1, respectively. Although we found these superconductors are within at the dirty limit, the existence of p-wave order parameter in Re21.75Ta7.25 and Re24.9Hf4.1 cannot be totally excluded considering the case of the two-gap superconductor MgB2 which is also at the dirty limit.