利特尔-帕克斯效应：修订间差异

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== 实验 ==
== 实验 ==
[[File:LPcylinderv5.jpg|缩略图|利特尔-帕克斯实验的示意图。]]
[[File:LPcylinderv5.jpg|缩略图|利特尔-帕克斯实验的示意图。]]
利特尔和帕克斯制备样品的方法较为巧妙：首先将一滴G.E. 7031[[水泥]]置于两根电线的末端后猛地一拽，可以拉制出直径约为一微米的丝线。将丝线固定在一个可以旋转的凹槽中，就可以在表面上蒸出厚度均匀金属薄膜。但是，由于900 [[埃|Å]] 厚度的[[锡]]无法连续覆盖水泥表面，他们需要先在上面覆盖25 Å 的[[金]]后，才能生长出厚度375 Å 的锡。然后，他们测量了超导转变温度附近的样品的电阻随着磁场的变化，观察到了阻值的周期性振荡。
利特尔和帕克斯制备样品的方法较为巧妙：首先将一滴G.E. 7031[[水泥]]置于两根电线的末端后猛地一拽，可以拉制出直径约为一微米的丝线。将丝线固定在一个可以旋转的凹槽中，就可以在表面上蒸出厚度均匀金属薄膜。但是，由于900 [[埃|Å]] 厚度的[[锡]]无法连续覆盖水泥表面，他们需要先在上面覆盖25 Å 的[[金]]后，才能生长出厚度375 Å 的锡。然后，他们测量了超导转变温度附近的样品的电阻随着磁场的变化，观察到阻值的周期性振荡。<ref name="Little">


F·伦敦结合[[伦敦方程]]，认为类磁通的取值是离散的；而从类磁通的量子化，以及[[BCS理论]]，可以预测出利特尔-帕克斯实验中样品的超导转变温度 T<sub>c</sub> 的周期性行为<ref name="Tinkham">{{cite book|title=Introduction to Superconductivity, Second Edition|last=Tinkham|first=M.|publisher=McGraw-Hill|year=1996|isbn=0486435032|location=New York, NY}}</ref>。实际上，最初的实验并没有测量 T<sub>c</sub>，而只是测量了电阻；之后的分析<ref>{{cite journal|last1=Groff|first1=R. P.|last2=Parks|first2=R. D.|title=Fluxoid Quantization and Field-Induced Depairing in a Hollow Superconducting Microcylinder|journal=Physical Review|date=1968-12-10|volume=176|issue=2|pages=567–580|doi=10.1103/PhysRev.176.567}}</ref>在考虑了各方面因素对 T<sub>c</sub> 的影响后，令人满意地解决了这一系列的问题。
The LP effect is a result of collective quantum behavior of superconducting electrons. It reflects the general fact that it is the [[磁通量量子|fluxoid]] rather than the flux which is quantized in superconductors.<ref name="Tinkham">{{cite book|title=Introduction to Superconductivity, Second Edition|last=Tinkham|first=M.|publisher=McGraw-Hill|year=1996|isbn=0486435032|location=New York, NY}}</ref>


The LP effect can be seen as a result of the requirement that quantum physics be invariant with respect to the [[庫侖規範|gauge choice]] for the [[电磁四维势|electromagnetic potential]], of which the [[磁矢势|magnetic vector potential]] '''A''' forms part.
The LP effect can be seen as a result of the requirement that quantum physics be invariant with respect to the [[庫侖規範|gauge choice]] for the [[电磁四维势|electromagnetic potential]], of which the [[磁矢势|magnetic vector potential]] '''A''' forms part.
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Electromagnetic theory implies that a particle with electric charge ''q'' travelling along some path ''P'' in a region with zero [[磁場|magnetic field]] '''B''', but non-zero '''A''' (by <math>\mathbf{B} = 0 = \nabla \times \mathbf{A}</math>), acquires a phase shift <math>\varphi</math>, given in [[国际单位制|SI]] units by
Electromagnetic theory implies that a particle with electric charge ''q'' travelling along some path ''P'' in a region with zero [[磁場|magnetic field]] '''B''', but non-zero '''A''' (by <math>\mathbf{B} = 0 = \nabla \times \mathbf{A}</math>), acquires a phase shift <math>\varphi</math>, given in [[国际单位制|SI]] units by
: <math>\varphi = \frac{q}{\hbar} \int_P \mathbf{A} \cdot d\mathbf{x},</math>
: <math>\varphi = \frac{q}{\hbar} \int_P \mathbf{A} \cdot d\mathbf{x},</math>
In a superconductor, the electrons form a quantum superconducting condensate, called a [[BCS理论|Bardeen–Cooper–Schrieffer (BCS) condensate]]. In the BCS condensate all electrons behave coherently, i.e. as one particle. Thus the phase of the collective BCS wavefunction behaves under the influence of the vector potential '''A''' in the same way as the phase of a single electron. Therefore the BCS condensate flowing around a closed path in a multiply connected superconducting sample acquires a phase difference Δ''φ'' determined by the [[磁通量|magnetic flux]] ''Φ<sub>B</sub>'' through the area enclosed by the path (via [[斯托克斯定理|Stokes' theorem]] and <math>\nabla \times \mathbf{A} = \mathbf{B}</math>), and given by:
In a superconductor, the electrons form a quantum superconducting condensate, called a [[BCS理论]]. In the BCS condensate all electrons behave coherently, i.e. as one particle. Thus the phase of the collective BCS wavefunction behaves under the influence of the vector potential '''A''' in the same way as the phase of a single electron. Therefore the BCS condensate flowing around a closed path in a multiply connected superconducting sample acquires a phase difference Δ''φ'' determined by the [[磁通量|magnetic flux]] ''Φ<sub>B</sub>'' through the area enclosed by the path (via [[斯托克斯定理|Stokes' theorem]] and <math>\nabla \times \mathbf{A} = \mathbf{B}</math>), and given by:
: <math>\Delta\varphi = \frac{q\Phi_B}{\hbar}.</math>
: <math>\Delta\varphi = \frac{q\Phi_B}{\hbar}.</math>
This phase effect is responsible for the [[磁通量量子|quantized-flux]] requirement and the LP effect in [[超导现象|superconducting]] loops and empty cylinders. The quantization occurs because the superconducting wave function must be single valued in a loop or an empty superconducting cylinder: its phase difference Δ''φ'' around a closed loop must be an integer multiple of 2π, with the charge ''q'' = 2''e'' for the [[BCS理论|BCS]] electronic superconducting pairs.
This phase effect is responsible for the [[磁通量量子|quantized-flux]] requirement and the LP effect in [[超导现象|superconducting]] loops and empty cylinders. The quantization occurs because the superconducting wave function must be single valued in a loop or an empty superconducting cylinder: its phase difference Δ''φ'' around a closed loop must be an integer multiple of 2π, with the charge ''q'' = 2''e'' for the [[BCS理论|BCS]] electronic superconducting pairs.

2018年2月5日 (一) 23:39的版本

利特尔-帕克斯效应（Little–Parks effect），或利特尔-帕克斯实验，是由威廉·A·利特尔和罗兰·D·帕克斯于1962年完成的一个超导实验[1]。实验中，一个由超导材料制成的空心薄壳圆柱体被置于与其轴平行的磁場中。利特尔和帕克斯在实验中观测到圆柱体的电阻随着磁场强度呈现周期性的变化。利特尔-帕克斯效应不但是最初的几个能够说明BCS理论中库柏对假设的重要性的实验[2]，且验证了类磁通（fluxoid）的量子化[注 1][5]。

历史

1950年，弗里茨·伦敦在他的文章中预言：在多连通的超导体中，类磁通（fluxoid）的取值是离散的，且为hc/e*的整数倍[6]。他对类磁通Φ'的定义如下：

其中 为传统意义上的磁通量。弗里茨·伦敦当时假设有效电荷e*的大小为e。1961年，Deaver 和 Fairbank 的实验[7][8]验证了e* = 2e，将类磁通量子确定为hc/2e，即磁通量量子。

然而，因为 Deaver 和 Fairbank 的实验使用的空心圆柱体的外壳较厚，所以类磁通Φ'中的 Js 一项等于零[5]。在此条件下，类磁通Φ'与磁通量Φ无法被区分。因此， Deaver 和 Fairbank 的实验只能说明磁通量的取值是离散的。1962年，利特尔和帕克斯制备了薄壳空心圆柱状的超导体进行实验，成功证实了类磁通Φ'（而非磁通量Φ）的量子化。他们测量了样品在超导转变温度附近的磁阻随着磁场的变化，观察到的阻值出现了周期为 hc/2e 的振荡。

实验

利特尔-帕克斯实验的示意图。

利特尔和帕克斯制备样品的方法较为巧妙：首先将一滴G.E. 7031水泥置于两根电线的末端后猛地一拽，可以拉制出直径约为一微米的丝线。将丝线固定在一个可以旋转的凹槽中，就可以在表面上蒸出厚度均匀金属薄膜。但是，由于900 Å 厚度的锡无法连续覆盖水泥表面，他们需要先在上面覆盖25 Å 的金后，才能生长出厚度375 Å 的锡。然后，他们测量了超导转变温度附近的样品的电阻随着磁场的变化，观察到阻值的周期性振荡。引用错误：没有找到与<ref>对应的</ref>标签。实际上，最初的实验并没有测量 Tc，而只是测量了电阻；之后的分析[9]在考虑了各方面因素对 Tc 的影响后，令人满意地解决了这一系列的问题。

The LP effect can be seen as a result of the requirement that quantum physics be invariant with respect to the gauge choice for the electromagnetic potential, of which the magnetic vector potential A forms part.

Electromagnetic theory implies that a particle with electric charge q travelling along some path P in a region with zero magnetic field B, but non-zero A (by ), acquires a phase shift , given in SI units by

In a superconductor, the electrons form a quantum superconducting condensate, called a BCS理论. In the BCS condensate all electrons behave coherently, i.e. as one particle. Thus the phase of the collective BCS wavefunction behaves under the influence of the vector potential A in the same way as the phase of a single electron. Therefore the BCS condensate flowing around a closed path in a multiply connected superconducting sample acquires a phase difference Δφ determined by the magnetic flux ΦB through the area enclosed by the path (via Stokes' theorem and ), and given by:

This phase effect is responsible for the quantized-flux requirement and the LP effect in superconducting loops and empty cylinders. The quantization occurs because the superconducting wave function must be single valued in a loop or an empty superconducting cylinder: its phase difference Δφ around a closed loop must be an integer multiple of 2π, with the charge q = 2e for the BCS electronic superconducting pairs.

If the period of the Little–Parks oscillations is 2π with respect to the superconducting phase variable, from the formula above it follows that the period with respect to the magnetic flux is the same as the magnetic flux quantum, namely

Applications

Little–Parks oscillations is a widely used proof mechanism of Cooper pairing. One of the good example is the study of the Superconductor Insulator Transition.[10][11][2]

Typical LP oscillations for different temperatures

The challenge here is to separate LP oscillations from weak (anti-)localization (Altshuler et al. results, where authors observed the Aharonov–Bohm effect in a dirty metallic films).

注释

  1. ^ 需要指出的是，fluxoid的定义略微不同于磁通量：对于较厚的第一类超导体，fluxoid与flux相等；而在利特尔-帕克斯实验中所用的空心薄壳圆柱体形状的超导体，或是在第二类超导体中，则严格来说只有fluxiod是量子化的。虽然磁通量量子（flux quantum）有时也被称作“fluxoid”，例如Kittel所著《Introduction to Solid State Physics》的第281页[3]；以及Ashcroft与Mermin所著《Solid State Physics》的第749页[4]，但这是不准确的。Tinkham在《Introduction to Superconductivity》的第127页明确指出利特尔-帕克斯实验验证的是fluxoid量子化，不能与flux的量子化混为一谈。

参考资料

  1. ^ W. A. Little and R. D. Parks, “Observation of Quantum Periodicity in the Transition Temperature of a Superconducting Cylinder”, Physical Review Letters 9, 9 (1962), doi:10.1103/PhysRevLett.9.9
  2. ^ 2.0 2.1 Gurovich, Doron; Tikhonov, Konstantin; Mahalu, Diana; Shahar, Dan. Little-Parks Oscillations in a Single Ring in the vicinity of the Superconductor-Insulator Transition. Physical Review B. 2014-11-20, 91. doi:10.1103/PhysRevB.91.174505. 
  3. ^ Kittel, Charles. Introduction to Solid State Physics sixth. John Wiley and Sons. 1986. ISBN 0-471-87474-4. 
  4. ^ Neil W. Ashcroft; N. David Mermin. Solid state physics 27. repr. New York: Holt, Rinehart and Winston. 1977: 749. ISBN 0030839939. 
  5. ^ 5.0 5.1 引用错误：没有为名为Tinkham的参考文献提供内容
  6. ^ HUDSON, R. P. Superfluids: Macroscopic Theory of Superconductivity, Vol. I. Fritz London. New York: Wiley; London: Chapman & Hall, 1950. 161 pp. $5.00. Science. 1951-04-20, 113 (2938): 447–447. doi:10.1126/science.113.2938.447. 
  7. ^ Lindley, David. Focus: Landmarks—Superconductor Quantizes Magnetic Field. Physics. 2015-10-23, 8 [2018-01-31]. 
  8. ^ Deaver, Bascom S.; Fairbank, William M. Experimental Evidence for Quantized Flux in Superconducting Cylinders. Physical Review Letters. 1961-07-15, 7 (2): 43–46. doi:10.1103/PhysRevLett.7.43. 
  9. ^ Groff, R. P.; Parks, R. D. Fluxoid Quantization and Field-Induced Depairing in a Hollow Superconducting Microcylinder. Physical Review. 1968-12-10, 176 (2): 567–580. doi:10.1103/PhysRev.176.567. 
  10. ^ Kopnov, G.; Cohen, O.; Ovadia, M.; Lee, K. Hong; Wong, C. C.; Shahar, D. Little-Parks Oscillations in an Insulator. Physical Review Letters. 2012-10-17, 109 (16). doi:10.1103/PhysRevLett.109.167002. 
  11. ^ Sochnikov, Ilya; Shaulov, Avner; Yeshurun, Yosef; Logvenov, Gennady; Božović, Ivan. Large oscillations of the magnetoresistance in nanopatterned high-temperature superconducting films. Nature Nanotechnology. 2010-06-13, 5 (7): 516. doi:10.1038/nnano.2010.111 （英语）. 

[[Category:凝聚体物理学]] [[Category:超导]]

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