Laboratory for Neutron Scattering, Paul Scherrer Institut, 5232 Villigen, Switzerland.
Nat Commun. 2010 Jul 27;1:45. doi: 10.1038/ncomms1047.
Many prominent phenomena originate from geometrical effects rather than from local physics. For example, the 'hairy ball' (HB) theorem asserts that a hairy sphere cannot be combed without introducing at least one singularity, and is fulfilled by the atmospheric circulation with the existence of stratospheric polar vortices and the fact that there is always at least one place on Earth where the horizontal wind is still. In this study, we examine the consequences of the HB theorem for the lattice of flux lines that form when a magnetic field is applied to a type-II superconducting crystal. We find that discontinuities must exist in lattice shape as a function of field direction relative to the crystal. Extraordinary, 'unconventional' flux line lattice shapes that spontaneously break the underlying crystal symmetry are thus remarkably likely across all type-II superconductors, both conventional and unconventional.
许多显著的现象源于几何效应而非局部物理。例如，“毛球”（HB）定理断言，在不引入至少一个奇点的情况下，一个毛茸茸的球体不可能被梳理，这一现象在大气环流中得到了验证，其存在平流层极地涡旋，以及地球上总是存在至少一个地方水平风静止的事实。在这项研究中，我们研究了 HB 定理对磁场施加到 II 型超导晶体时形成的磁通线晶格的影响。我们发现，晶格形状相对于晶体的磁场方向必须存在不连续性。因此，在所有 II 型超导体中，无论是传统的还是非传统的，都极有可能出现异常的、“非常规的”通量线晶格形状，这些形状会自发地破坏基础晶体对称性。
