平衡表面电流和U（1）对称性的作用：求和规则和表面扰动
Equilibrium Surface Current and Role of U(1) Symmetry: sum rule and surface perturbations
摘要：
我们讨论了在没有时间反演对称性的系统中，表面扰动对平衡表面电流的影响，这些电流对轨道磁化和轨道角动量有贡献。我们表明，在一个U（1）粒子数守恒系统中，在表面的无序和其他扰动不影响平衡表面电流和相应的轨道磁化由于一个求和规则，这是类似于Luttinger定理。另一方面，对于超流体，求和规则不再适用，因此表面质量流和相应的轨道角动量可以依赖于表面的细节。
英文摘要：
We discuss effects of surface perturbations on equilibrium surface currents which contribute to orbital magnetization and orbital angular momentum in systems without time reversal symmetry. We show that, in a U(1) particle number conserving system, disorder and other perturbations at a surface do not affect the equilibrium surface current and corresponding orbital magnetization due to a sum rule which is analogous to Luttinger's theorem. On the other hand, for a superfluid, the sum rule is no longer applicable and hence the surface mass current and corresponding orbital angular momentum can depend on details of a surface.
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