中觀超導結內超導電流特性的微觀研究

Abstract

本論文提出一種用微觀方式來研究中觀超導結內超導 電流特性的 方法（以下稱為微觀法）。此方法的特色是能 夠仔細分析量子傳輸的 中間散射過程，而其計算電流的公 式是可以嚴謹地推導出來的，不像 其它的 Landauer-type 傳導方法是由適用於半導體的公式推廣而來 。對於 SNS 超導結，微觀法和其它的傳導法給出相同的結果。但是 ， 就對稱的 SNSNS 超導結而言，這兩類方法得到的超導電 流卻 不同。更進一步的分析顯示，在兩個超導電極之間， 若再有 Andreev 反射，則量子傳輸就不能用一般的傳導 法來處理。所以，中觀超導 結裡的傳輸應該是散射的，而 非傳導的。 中觀超導結這種系統非常適合探討和超導體能隙函數 的相位有關的新 物理。在本論文中，我們用微觀法來計算 SNSNS 超導結的電流—相位 差關係（以下稱為電相圖）。 不論結構對稱與否，中間超導層的相位 φ2 對電相圖有特 殊的影響。尤其在不對稱的結構裡，φ2 更是無法 用直觀 的對稱想法來選定。為了決定 φ2，我們提議用一種守恆 條件，要求在兩個非超導區計算的電流必須相等。結果顯 示，φ2 是 兩個超導電極的相位差 φ 的多值函數。此性 質對超導結的電相圖有 重大的效應。 絕對零溫時， SNSNS 電相圖 只有唯一的分支，週期是 4π。當中間超導層的長度 L2 不是很長時， 此電相圖會顯 現出與 Andreev 能階穿隧有關的特性。而不對稱超導結 的 電相圖還有另外兩種特性。一、截斷的特性，尤其當 L2 很長 或不對稱的程度較高時更為顯著。這種截斷的特性影 響著超導結的臨 界電流大小。二、在被截斷以外的部份， 不對稱和對稱超導結的電相 圖只有幾個百分點的差異（在 這裡所比較的是非超導區的總長度以及 L2 相同的超導結 ）。這種特性和其它參數所對應的靈敏變化呈現明 顯的對 比。 當溫度高於絕對零度時，上述的截斷特性和 Andreev 能階穿隧的特性 仍然存在。不過，更重要的是，有限溫度 的效應導致新而不同的 φ2 值產生。結果，對稱超導結的 電相圖被修改成有二條分支，而其週期 各為 2π 和 4π。 至於不對稱 SNSNS 超導結的電相圖則有更加不同 的修改。 該電相圖有二條分支，而週期都是 2π。這些結果已經在 不同的極限情況下驗證成立。我們也嘗試找出這些由溫度 所引起的差 異的物理原因。最後，我們預期這些 φ2 的新 奇效應在其它結構的中 觀超導結裡， 甚至超導超晶格中， 都會顯現。 A microscopic approach to the study of the supercurrent characteristics in mesoscopic superconducting junctions (MSJ) has been established in this thesis. In this approach, all contributing physical processes are treated as the scattering of quasiparticles while the current is calculated from a microscopically derived current expression. These processes include Andreev reflections, which correspond to the tunneling of Cooper pairs. An example for the discrepancy between our approach and the transmission approach is found in a double superconductor-normal-metal-superconductor (SNS) junction. These two approaches, however, give the same results in a single SNS junction. Our analysis shows that the additional Andreev reflections occurring within the region between the two superconducting end-electrodes lead to the discrepancy. Thus we conclude that in general MSJ structures, transport is scattering, rather than transport is transmission. The MSJ structures provide a valuable opportunity for the exploration of new physics that are associated with the phases of the gap function of the constituent superconductors. We have studied the current-phase relations (CPR) of both symmetric and asymmetric SNSNS junctions. It is found that the phase of the middle superconductor plays a very special role in shaping the CPR features. The lack of configuration symmetry in asymmetric SNSNS junctions forbid an intuitive choice of values for the phase φ2 of the middle superconductor. To determine φ2, we propose a current-conserving condition that requires the currents evaluated in the two normal regions to be the same. Applying this current-conserving condition to both the symmetric and the asymmetric SNSNS junctions, we find that φ2 is a multi-valued function of φ, the phase difference between the two superconducting end-electrodes. This has significant effects on the CPR of the junctions. At T = 0, the CPR has one branch which has a φ-period of 4π. It exhibits prominent features associated with Andreev-level tunneling when the length L2 of the middle superconductor is not too long. The asymmetric junctions have two additional features. First, the CPR has a cutoff feature, which is more pronounced for longer L2 and for higher degree of junction asymmetry. This cutoff feature affects the critical current of the junctions. Second, in regions other than the cutoff region, the CPR of the asymmetric junctions deviates only within a few percent from the CPR of the symmetric junction which has the same total length in the normal regions, and the same L2. This is in contrast with the greater sensitivity the CPR has to other choices of the junction parameters. At finite T, both the cutoff and the Andreev-level tunneling features remain robust. But, more importantly, the finite-temperature effects lead to additional but distinctly new φ2 values. As a consequence, the CPR for a symmetric junction is modified and has two branches, with φ-periods of 2π and 4π, respectively. However, the CPR for an asymmetric junction is modified differently. It has two branches, each with a φ-period of 2π. The validity of these results has been checked rigorously in various limiting cases. The physical reason for these temperature-induced differences is explored. These interesting effects of φ2 are expected to persist in other MSJ structures and also in superconducting superlattices.