MilliKelvin Experiments Utilising Vector Magnetic Field

在强磁场作用下，二维电子气在低温下产生了许多引人注目的物理效应，例如整数量子霍尔效应和分数量子霍尔效应。在这项工作中，我们建议研究半导体纳米结构在毫开尔文温度下的电子性质，在强磁场存在的情况下，当电子气平面和磁场之间的夹角可以改变时。这将开辟一个新的物理研究范围，因为场的方向会影响电子系统的不同性质。例如，自旋分裂由总场决定，而波函数受横跨电子气的场分量的影响。如果使用电子气的耦合层，那么层间耦合会受到平行于平面的场分量的影响。这将允许更大程度地探索许多效应。在大多数情况下，半导体中的电子可以被认为是自由的，它们的能量由它们的总数和它们的有效质量决定，相互排斥只略微改变了这一自由电子图景。然而，理论表明，在较低的载流子浓度下，排斥力可能会主导电子在固体中的扩散方式，在足够低的温度下，电子可以将自己排列成规则的阵列。这被称为维格纳晶体，或维格纳晶格，以维格纳第一个预测这种现象的人的名字命名。在一维中，电子形成一条单线，维格纳晶体是电子寻求规则周期的微不足道的例子。然而，随着限制的减弱，或电子斥力的增加，当电子试图最大化它们的分离时，电子线可能会扭曲。在极限情况下，这行分裂成两个或多个单独的行。当限制改变时，通过跟随电导值，可以得到作为限制势的函数的能级的移动。这已经被观察到了，我们把由于电子-电子排斥而形成的两排称为初始维格纳晶格，IWL。对能级运动的结果的分析表明，在形成两个单独的行之前，形成了杂化态，其中在两个行之间共享两个电子，使得它们形成扭曲的单行。量子力学规定，以这种方式共享的两个电子必须具有相反的自旋，因此它们可能会被纠缠，因此它们各自“知道”对方所处的量子态。现在，有人建议研究IWL，并对电子纠缠的杂化态进行磁性修改。在类似的研究中，将研究电子的各种性质，例如自旋非相干区域，当温度导致自旋快速和随机旋转时出现，因此它不再是一个定义的量子参数。无序的电子局域化很大程度上受到磁场的影响，磁场可以驱动系统绝缘，或者相反，在低场下消除电子波的干扰特性，后一种效应导致绝缘样品的导电性增加。这种设备的灵活性将应用于新材料的研究，其中表面和体相的贡献可以通过改变磁场方向来确定。表面导电层中的能级分裂会随着横向分量的变化而变化，而体属性则由总场决定。

Many striking physical effects have been found using a two dimensional electron gas at low temperatures in the presence of a strong magnetic field, for example the Integer and Fractional Quantum Hall effects. In this work we propose to investigate electronic properties of semiconductor nanostructures at milliKelvin temperatures in the presence of a high magnetic field when the angle between the plane of the electron gas and the field can be altered. This will open up a new range of physical investigations as the direction of the field affects different properties of the electron system. For example, the spin splitting is determined by the total field whereas the wavefunction is affected by the field component transverse to the electron gas. If coupled layers of electron gas are used then the interlayer coupling is affected by the component of field parallel to the plane.This will allow a much greater exploration of a number of effects. In most situations electrons in semiconductors can be regarded as free with their energy determined by their total number and their effective mass with the mutual repulsion only slightly modifying this free electron picture. However at low values of carrier concentration the repulsion can dominate the manner in which the electrons diffuse in the solid, theory has shown that at sufficiently low temperatures the electrons can arrange themselves into a regular array. This is termed a Wigner Crystal, or Wigner Lattice, after Wigner who first predicted such a phenomenon.In one dimension the electrons form a single line and the Wigner Crystal is the trivial case of the electrons seeking a regular periodicity. However, as the confinement weakens, or the electron repulsion increases, so it is possible for the line of electrons to distort as electrons attempt to maximise their separation. In the limit the row splits into two or more separate rows.By following the values of conductance as the confinement is changed so the movement of energy levels can be obtained as a function of confinement potential. This has been observed and we call the two rows formed as a result of the electron-electron repulsion the Incipient Wigner Lattice, IWL. Analysis of the results on the movement of energy levels has shown that prior to the formation of the two separate rows a hybridised state is formed in which two electrons are shared between the two rows such that they form a distorted single row. Quantum Mechanics dictates that two electrons shared in this way must have opposite spins and they can be entangled as a consequence of which they each "know" the quantum state the other is in..It is now proposed to study the IWL and magnetically modify the hybrid state in which the electrons are entangled. In similar studies a variety of properties of electrons will be investigated such as the spin incoherent regime which occurs when temperature causes the spins to rotate rapidly and randomly and so it is no longer a defined quantum parameter. The localisation of electrons by disorder is very much affected by a magnetic field which can drive a system insulating or conversely at low fields remove the interference characteristic of electron waves, This latter effect results in an insulating sample increasing in conductivity.The flexibility of this facility will be applied to the study of new materials where the surface and bulk contributions to the overall properties can be determined by varying the field direction. Energy level splittings in a surface conduction layer will vary as the transverse component whereas the bulk properties are determined by the total field.