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arXiv 2207.08239cond-mat.mes-hall
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石墨烯圆盘中亚Sharvin电荷输运理论

Theory of the sub-Sharvin charge transport in graphene disks

Adam Rycerz, Piotr Witkowski

摘要:

多模状态下的弹道石墨烯样品显示出亚Sharvin电荷传输,其特征在于与二维电子气中的标准Sharvin接触相比,电导降低了$π/4$的因子,并且散粒噪声功率提高到$F\approx{}1/8$($F$为Fano因子)[Phys.Rev.B104,165413(2021)]。在这里,我们考虑石墨烯中的盘形(Corbino)设置,具有内半径$r_1$和外半径$r_2$,发现对于任何$r_1<r_2$,多模电导略微增强,达到$r_1\ll{}r_2$的Sharvin值的$(4\!-\!π)\approx{}0.8684$。在相同的极限下,Fano因子减小,接近$(9π-28)/(12-3π)\approx{}0.1065<1/8$。假设狄拉克费米子在非对称双势垒上的非相干散射,导出了任意$r_1/r_2$比的封闭近似表达式,并与模式匹配法的精确数值结果进行了比较。Sub-Sharvin值将恢复到窄磁盘限制$r_1/r_2\rightarrow{}1$中。对于实验上可访问的半径比$0.5\leqslant{}r_1/r_2\leqslant{}0.8$的电导和Fano因子都明显接近预测值的$r_1\ll{}r_2$限制,但仍然不同于标准Sharvin传输特性。通过数值模拟研究了静电势垒从矩形变为抛物线时的系统行为,并证明了从亚Sharvin输运区到标准Sharvin输运区的交叉。一个有限的磁盘部分的影响进行了讨论。

英文摘要:

Ballistic graphene samples in a multimode regime show the sub-Sharvin charge transport, characterized by the conductance reduced by a factor of $π/4$ comparing to standard Sharvin contacts in two-dimensional electron gas, and the shot-noise power enhanced up to $F\approx{}1/8$ (with $F$ the Fano factor) [Phys. Rev. B 104, 165413 (2021)]. Here we consider the disk-shaped (Corbino) setup in graphene, with inner radius $r_1$ and outer radius $r_2$, finding that the multimode conductance is slightly enhanced for any $r_1<r_2$, reaching $(4\!-\!π)\approx{}0.8684$ of the Sharvin value for $r_1\ll{}r_2$. At the same limit, the Fano factor is reduced, approaching $(9π-28)/(12-3π)\approx{}0.1065<1/8$. Closed-form approximating expressions for any $r_1/r_2$ ratio are derived supposing incoherent scattering of Dirac fermions on asymmetric double barrier and compared with exact numerical results following from the mode-matching method. Sub-Sharvin values are restored in the narrow-disk limit $r_1/r_2\rightarrow{}1$. For experimentally-accessible radii ratios $0.5\leqslant{}r_1/r_2\leqslant{}0.8$ both the conductance and the Fano factor are noticeably closer to the values predicted for the $r_1\ll{}r_2$ limit, yet still differ from standard Sharvin transport characteristics. The system behavior upon tuning the electrostatic potential barrier from a rectangular to parabolic shape is studied numerically, and the crossover from the sub-Sharvin to standard Sharvin transport regime is demonstrated. Implications for a finite section of the disk are also discussed.

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