We perform a microscopic study on the redistribution of electric charge near the surface of a model $d$-wave superconductor cut along the [110] direction, with a Fermi surface appropriate for cuprate superconductors, using the augmented quasiclassical equations. We identify two possible mechanisms for the redistribution of charged particles different from the well-known magnetic Hall effect, namely; the pair potential gradient (PPG) force due to surface effects on the pair potential and the pressure difference between the normal and superconducting regions arising from the slope of the density of states (SDOS) in the normal states at the Fermi level. Our present results show that in spite of the absence of supercurrents, electric charge is induced around the surface. Moreover, the charging effect due to the SDOS pressure dominates over that due to the PPG force for all the realistic electron-fillings $n=0.8$, $0.9$, and $1.15$, at all temperatures. In addition, for the filling $n=1.15$, the PPG force and the SDOS pressure contributions have the same negative signs, which gives a larger total surface charge i.e., both the sign and amount of the surface charge depends greatly on the Fermi-surface curvature. We have also calculated the local density of states (LDOS) within the augmented quasiclassical theory. Spatially varying local particle-hole asymmetry appears in the LDOS, which suggests the presence of electric charge.

中文翻译：

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由于 d 波超导体中的间隙抑制导致的零场表面电荷

我们使用增强的准经典方程对沿 [110] 方向切割的模型 $d$-wave 超导体表面附近的电荷重新分布进行微观研究，费米表面适合铜酸盐超导体。我们确定了与众所周知的磁霍尔效应不同的带电粒子重新分布的两种可能机制，即：由于对电势的表面效应和正常和超导区域之间的压力差，对电势梯度 (PPG) 力是由费米能级的正常态中的态密度 (SDOS) 的斜率引起的。我们目前的结果表明，尽管没有超电流，但在表面周围感应出电荷。而且，在所有温度下，对于所有实际电子填充 $n=0.8$、$0.9$ 和 $1.15$，由于 SDOS 压力引起的充电效应优于 PPG 力引起的充电效应。此外，对于填充 $n=1.15$，PPG 力和 SDOS 压力贡献具有相同的负号，这给出了更大的总表面电荷，即表面电荷的符号和数量在很大程度上取决于费米。表面曲率。我们还计算了增强准经典理论中的局部状态密度 (LDOS)。LDOS 中出现空间变化的局部粒子-空穴不对称性，这表明存在电荷。PPG 力和 SDOS 压力贡献具有相同的负号，这给出了更大的总表面电荷，即表面电荷的符号和数量在很大程度上取决于费米表面曲率。我们还计算了增强准经典理论中的局部状态密度 (LDOS)。LDOS 中出现空间变化的局部粒子-空穴不对称性，这表明存在电荷。PPG 力和 SDOS 压力贡献具有相同的负号，这给出了更大的总表面电荷，即表面电荷的符号和数量在很大程度上取决于费米表面曲率。我们还计算了增强准经典理论中的局部状态密度 (LDOS)。LDOS 中出现空间变化的局部粒子-空穴不对称性，这表明存在电荷。