Study of Inhomogeneous State of Two-Dimensional Electron Quantum Liquid

理论研究了二维电子液体在远程无序状态下的性质。这种类型的无序通常是由随机分布的杂质离子在具有较大间隔宽度的异质结构中产生的。二维电子液体的筛选有效地与产生的随机电位竞争。然而，在某些情况下，这种筛选是无效的，二维电子液体变得非常不均匀。在强磁场中，每当朗道能级的填充因子对应于整数或分数间隙时，就会发生这种状态。研究了非均匀态的不同表现：电导率张量在填充因子范围内的低温行为，其中所有间隙都被无序破坏；量子霍尔效应平台的宽度；表面声波的衰减；在长程无序存在下的维格纳晶体形成。将对介观系统的物理学进行理论研究，其中量子效应在宏观尺度上表现出来。特别地，将研究无序对在半导体连接处形成的二维电子液体性质的影响。

Theoretical research will be conducted on the properties of the two-dimensional electron liquid in the presence of long-range disorder. This type of disorder is usually created in heterostructures with large spacer width by randomly distributed remote impurity ions. Screening by the two-dimensional electron liquid competes effectively with the resultant random potential. However, in some cases this screening is not effective and the two- dimensional electron liquid becomes very inhomogeneous. In a strong magnetic field this state occurs each time the filling factor of the Landau level corresponds to an integer or a fractional gap. Different manifestations of the inhomogeneous state will be studied: the low temperature behavior of the conductivity tensor in the filling factor range where all gaps are destroyed by disorder; the width of the plateau of the quantum Hall effect; the attenuation of the surface acoustic waves; the Wigner crystal formation in the presence of the long range disorder. %%% Theoretical studies will be made on the physics of mesoscopic systems where quantum effects are manifest on a macroscopic scale. In particular, studies will be made on the effects of disorder on the properties of the two-dimensional electron liquid which forms at junctions between semiconductors.