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arXiv 0709.3164cond-mat.mes-hall
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量子霍尔边系统的输运:量子点接触之外

Transport through constricted quantum Hall edge systems: beyond the quantum point contact

Siddhartha Lal

摘要:

在最近的实验结果的惊喜的动机,我们研究运输的量子霍尔边缘系统的模型与栅极电压控制收缩。有限的反向散射电流在有限的边缘偏置解释从Landauer-Buttiker分析所产生的分裂所造成的散装($ν_{1}$)和收缩($ν_{2}$)量子霍尔流体区域的填充分数的差异的边缘电流。我们发展了一个流体力学理论的玻色子边缘模式的启发,这个模型。收缩区将入射的长波长手征边缘密度波激发分裂为围绕它的透射和反射边缘态,收缩区内部发生的两个边缘间隧穿过程之间的竞争由准粒子-准空穴(qp-qh)对称性引起,通过计算系统的边界理论得到解释.发现这种竞争决定了系统的强耦合构型。qp-qh对称无隙临界态的分界线被发现位于相关RG流到金属和绝缘配置的收缩系统之间。这构成了凯恩-费舍尔量子杂质模型的一个有趣的推广。RG相图的特征也通过计算系统的各种调制器和手征线性电导得到证实。通过这种方式,我们的结果发现与最近许多令人困惑的实验结果的情况下,$ν_{1}=1/3,~1$的协议。我们还讨论和预测的情况下,收缩系统与$ν_{2}=5/2$。

英文摘要:

Motivated by surprises in recent experimental findings, we study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained from a Landauer-Buttiker analysis as arising from the splitting of edge current caused by the difference in the filling fractions of the bulk ($ν_{1}$) and constriction ($ν_{2}$) quantum Hall fluid regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model. The constriction region splits the incident long-wavelength chiral edge density-wave excitations among the transmitting and reflecting edge states encircling it. The competition between two interedge tunneling processes taking place inside the constriction, related by a quasiparticle-quasihole (qp-qh) symmetry, is accounted for by computing the boundary theories of the system. This competition is found to determine the strong coupling configuration of the system. A separatrix of qp-qh symmetric gapless critical states is found to lie between the relevant RG flows to a metallic and an insulating configuration of the constriction system. This constitutes an interesting generalisation of the Kane-Fisher quantum impurity model. The features of the RG phase diagram are also confirmed by computing various correlators and chiral linear conductances of the system. In this way, our results find excellent agreement with many recent puzzling experimental results for the cases of $ν_{1}=1/3,~1$. We also discuss and make predictions for the case of a constriction system with $ν_{2}=5/2$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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