超导纳米线：量子限制和空间相关的Hartree-Fock势
Superconducting nanowires: quantum confinement and spatially dependent Hartree-Fock potential
摘要：
众所周知，在整体中，无论是否包括Hartree-Fock项，Bogoliubov-de Gennes方程的解都是相同的。在这里，哈特里-福克势是位置无关的，因此，对单电子能量和费米能级（化学势）的贡献是相同的。因此，从费米能级测量的单电子能量（它们控制溶液）保持不变。对于纳米结构的超导体，情况并非如此，其中量子限制打破了平移对称性并导致位置相关的Hartree-Fock势。在这种情况下，它对单电子能量的贡献取决于相关的量子数。我们数值求解了Bogoliubov-de Gennes方程与Hartree-Fock项的清洁超导纳米圆柱体，并发现代表临界超导温度的厚度依赖振荡的曲线的移位到更大的直径。
英文摘要：
It is well-known that in bulk, the solution of the Bogoliubov-de Gennes equations is the same whether or not the Hartree-Fock term is included. Here the Hartree-Fock potential is position independent and, so, gives the same contribution to both the single-electron energies and the Fermi level (the chemical potential). Thus, the single-electron energies measured from the Fermi level (they control the solution) stay the same. It is not the case for nanostructured superconductors, where quantum confinement breaks the translational symmetry and results in a position dependent Hartree-Fock potential. In this case its contribution to the single-electron energies depends on the relevant quantum numbers. We numerically solved the Bogoliubov-de Gennes equations with the Hartree-Fock term for a clean superconducting nanocylinder and found a shift of the curve representing the thickness-dependent oscillations of the critical superconducting temperature to larger diameters.
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