二维圆柱约瑟夫森结阵列中的持续电流
Persistent current in a 2D Josephson junction array wrapped around a cylinder
摘要：
研究了圆柱体周围约瑟夫森结阵列中的持续电流。阵列的$T=0$量子统计力学等效于在有效温度$T^{*}=\sqrt{2JU}$下2+1维中经典$xy$自旋系统的统计力学，其中$J$是结的约瑟夫森能量，而$U$是超导岛的充电能量。它是研究分析和数值上的晶格包含超过一百万个网站。对于弱无序和$T^{*}\ll J$，数值计算的持续电流对无序和$T^{*}$的依赖性与自旋波近似下的分析结果在定量上一致。高$T^{*}$和/或强无序行为由对应于2+1维涡旋环的瞬子主导。电流在量子相变到库珀对绝缘相时被完全破坏。
英文摘要：
We study persistent currents in a Josephson junction array wrapped around a cylinder. The $T=0$ quantum statistical mechanics of the array is equivalent to the statistical mechanics of a classical $xy$ spin system in 2+1 dimensions at the effective temperature $T^{*}=\sqrt{2JU}$, with $J$ being the Josephson energy of the junction and $U$ being the charging energy of the superconducting island. It is investigated analytically and numerically on lattices containing over one million sites. For weak disorder and $T^{*}\ll J$ the dependence of the persistent current on disorder and $T^{*}$ computed numerically agrees quantitatively with the analytical result derived within the spin-wave approximation. The high-$T^{*}$ and/or strong-disorder behavior is dominated by instantons corresponding to the vortex loops in 2+1 dimensions. The current becomes destroyed completely at the quantum phase transition into the Cooper-pair insulating phase.
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