Study of the surface bound state of superfluid 3He-B by a new acrostic technique

3 He在大约1 mK时进入P波自旋三重态超流体相。超流体的序参量具有很大的内部自由度，因而可以有多种超流体相。然而，不幸的是，只有两个阶段实现; BW状态（B阶段）和ABM状态（A阶段）。超流~ 3 He-B对固体壁面非常敏感。波函数关于壁面的垂直分量Δ_k（k）在近壁处具有奇函数性质。也就是说，Δ_k（-k）=-Δ_k（k）。由于这一性质，当特征长度为相干长度的数倍时，Δ k（k）随着离壁距离的增加逐渐恢复到体值，而Δ k（k）不受壁的影响。λ通常为几纳米。作为Δ_k（k）的这种空间变化的结果，在壁位置处的差距内出现表面状态。这种表面态被称为Andreev表面束缚态，它是P波超流在边界处的典型特征。表面束缚态的性质主要取决于壁面处的边界条件。如果准粒子在壁面上的反射是漫射的（通常是在普通壁面上），则束缚态不像δ函数，而是具有更宽的能量宽度。当然，超流3 He-B的这些表面性质是理论预测的，还没有实验研究。原因是我们没有相关的探测技术。在本计画中，我们成功地侦测到这种表面束缚态，借由精确测量具有适当共振频率的交流切割石英换能器的声剪切运动。在阻抗的真实的部分和虚部的尖点处检测到表面束缚态的特征，用绿色函数模型对剪切阻抗的数值计算与实验结果很好地吻合。

3He sets into the P-wave spin-triplet super fluid phase at around 1 mK. Order parameter of the super fluid has a lot of internal degrees of freedom and hence it can have many superfluid phases. Unfortunately, however, there are only two phases realized ; BW-state(B-phase) and ABM-state(A-phase). Superfluid 3He-B is very sensitive against the solid wall. The perpendicular component of the wave function of with respect to the wall, which is denoted as Δ_〓(k), has a property of odd function near the wall. That is, Δ_〓(-k)=-Δ_〓(k). Due to this property, Δ_〓(k) gradually recovers to the bulk value as the distance from the wall increases with the characteristic length of several times of the coherence length ξ, whereasΔ_// exhibits no effect of the wall. ξ is typically several nanometers. As a result of this spatial variation of Δ_〓(k), there comes out the surface state inside the gap at the wall position. This surface state is called as "Andreev surface bound state", which is a typical feature of P-wave superfluid at the boundary. The property of the surface bound state crucially depends on the boundary condition at the wall. If the reflection of quasi-particles at the wall is diffusive(which is often the case with the ordinary wall), the bound state is not δ-function like, but has wider energy width. These surface properties of superfluid 3He-B is, of course, predicted by the theory, has not been studied experimentally yet. The reason is that we had no relevant probing techniques. In the present project, we succeeded in detecting this surface bound state, by the precise measurement of the acoustic shear motion of AC-cut quarts transducer with proper resonance frequencies. The signature of the surface bound state was detected as a kink of in the real part of the impedance and in the cusp of the imaginary part of it. The experimental result is well reproduced by the numerical calculation of the shear impedance by the Green function model.