MilliKelvin Experiments Utilising Vector Magnetic Field

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.

The purpose of this application is to fund a new facility to enhance our ability to investigate quantum physics with reference to the development of new quantum technologies. If successful there are many applications of this technology, in particular quantum data processing and computation has profound consequences for security and rapid assessment of large data bases.
A number of communities will benefit from this work as follows.
The knowledge community will gain considerably from progress in quantum information and spintronics communities as both are seeking new concepts and experimental results. Properties of entangled electrons will be of great interest to the user community of theoretical physicists. The information gained on the properties of semiconductor nanostructurers will be of significance to Material Scientists and Device Engineers, as the improvements in semiconductor growth can be implemented in the fabrication of high frequency GaAs devices used in mobile phones and other applications. Other communities who will benefit from entanglement based computation include those involved in cryptography, (companies and government establishments), and the medical/biological community who wish to search large data bases and perform parallel computations very quickly, for example crystallographic data bases.
The community developing new materials could benefit in our opening the facility for use in investigations of new materials such as Transparent Metal Oxides and Topological Insulators. The separation of the various conduction mechanisms will be an important help in the control of the growth and fabrication of these materials.
There could be benefit to the economy in that success in the experimental programme described here will stimulate sales of low temperature equipment and associated instrumentation and high magnetic field systems. The growth in the study of two-dimensional systems in recent years has fuelled growth of MBE and processing equipment as well as cryogenic systems, success here would
further increase this trend. The longer term development of devices based on the physics explored here could also give rise to sizeable economic benefits.
People will benefit in that there will be considerable advantages to the scientists employed on the grant and Ph.D students who will be associated with it. The science of this work gives rise to new expertise which will be of considerable assistance to Ph.D students and post-doctoral research workers in adjacent areas of physics. This is very important in the context of training given the global competition for skilled personnel and the increasing international competition in new technologies.
There are also benefits to society at large in view of the practical consequence of the quantum physics which is to be investigated. There is considerable interest in sections of the public about the implications of quantum theory such as entanglement, as well as the significance for understanding the meaning of concepts such as superposition of states. The popularity of recent books on these topics indicates the latent interest in the community at large. The generalisation and popularisation of the success of this project will be of considerable interest to this community. The PI has given general lectures on research and will continue to seek every opportunity of doing so in the future as part of an outreach policy.
EPSRC has recently identified Quantum Technology including Entanglement and Decoherence as a Grand Challenge, the equipment in this proposal will allow us to address these themes in a new manner with a new range of investigations.