Leonid Rokhinson - US grants

Spin is a fascinating property of matter which has no classical analog and which is largely ignored in mainstream charge-based electronics. As the scalability of conventional devices nears exhaustion, the spin degree of freedom moves to the forefront of research in the quest to find alternative device paradigms. Holes
in semiconductor nanostructures are especially attractive for future implementation of spintronic devices due to their potentially very long spin relaxation times. The goal of this proposal is to understand mechanisms of spin interactions in p-type semiconductor nanostructures, to develop functional spin-based quantum devices, and to develop a versatile educational program closely integrated with this research project.

Semiconductor nanostructures provide a unique controllable environment where a single spin can be isolated and fundamental aspects of its interactions can be investigated. Hole nanostructures have a peculiar set of parameters and symmetries that are largely unexplored. Strong anisotropy of exchange interaction, effective mass and $g$-factor for high index crystallographic axises will allow the applicant to investigate different mechanisms contributing to spin relaxation and to devise efficient methods of spin manipulation. Applications relevant to the emerging fields of spintronics and quantum information processing will be investigated.

Educational activities are an essential part of the proposed career development plan and are closely integrated with the proposed research program, which include (i) training of graduate and undergraduate students in state-of-the-art experimental techniques via their direct involvement in the proposed research program, (ii) development of a special course ``Physics of Low-dimensional Systems'' and (iii) development of an enrichment program for K-12 students.

Intellectual Merit of the project is to demonstrate key technology toward development of novel multifunctional devices based on antiferromagnetic (AF) semiconductors. The proposed devices will combine non-volatile magnetic memory with electronic transistor functionality in a single device, thus resolving current dichotomy between logic circuitry and memory implementations. For operation devices will utilize phase transitions which, combined with sup-ps intrinsic magnetization dynamics, will offer THz speeds in both functionality domains. The devices will also have a potential to improve on basic transistor switching characteristics if gate-induced coupled phase transitions are realized. Finally, these magnetic devices will have no fringing fields, thus allowing high density packaging. The proposed devices are metal-oxide-AF-semiconductor field-effect transistors, MOS(AF)FET, where mobile carriers are induced into an AF semiconductor by electrostatic gating. This functionality will enable electrical detection of the magnetization axis in collinear AF materials for the first time. At high carrier concentrations we expect a succession of metal-insulator, antiferromagneticferromagnetic (AF-FM) and structural phase transitions, which will allow electrostatic control of both electrical and magnetic properties of the AF host. Of a special interest for fast memory recording is a possibility to rotate the magnetization axis in multi-axis collinear AF by means of AF-FM phase transition, where magnetic torque will be generated by a few tesla intrinsic exchange fields. For prototype demonstrations we will focus on NiO. NiO is a technologically relevant room temperature collinear AF semiconductor which can be epitaxially grown on readily available MgO substrates. The focus of EAGER proposal is to fabricate and characterize NiO?based MOS(AF)FET and to demonstrate electrical detection of AF magnetization axis.

The broader impact of this project will be development of the enabling technology for the investigation of electrostatically-induced AF-FM phase transition, study of fundamental physics of coupled phase transitions, and analysis of magnetization dynamics in AF semiconductors. A student working on the project will be involved in a truly interdisciplinary research, bridging fields of material science, semiconductor physics and magnetism. The PI is developing a new graduate course on physics of magnetic semiconductors which will be disseminated to a wider audience using NSF-sponsored nanoHUB.org facility at Purdue University.

****TECHNICAL ABSTRACT****
This project will address topologically non-trivial properties of degenerate states in low dimensional hole gases. Non-Abelian phases will be measured in double-ring interferometric devices, where the contribution of Abelian phases can be minimized. Excitations with non-Abelian statistics will be studied in 1D semiconducting wires proximity-coupled to a conventional superconductor. Complementary experiments exploring the energy spectrum of bound states and phase-energy relation of Josephson junctions will be performed. Several fabrication approaches are proposed to reduce effects of localization, the major complication in mesoscopic devices. Finally, an interplay between non-Abelian nature of the wavefunction and non-Abelian statistics of excitation will be investigated. This project will support a PhD student who will be trained in semiconductor physics, fabrication and measurement techniques, including low temperature high magnetic field techniques, vacuum technology, low noise electrical characterization, scanning probe and electron-beam nanolithography. This broad experience will prepare the student for a successful career in technology or academia. An outreach program includes development of nanotechnology demonstrations and accompanying materials for high school students and physics teachers.

****NON-TECHNICAL ABSTRACT****
Quantum statistics, spin and symmetry of the wavefunction are central to the quantum mechanical understanding of the world. In most systems phases accumulated by a particle along a trajectory are additive and exchange of two particles amounts to a multiplication by a phase factor. However, over the last few decades it has been realized that in very special settings the accumulated phase depends on the topology of the system and particle exchanges do not have to commute, meaning the outcome of permutations depends on the order of the particle exchanges. The main objective of this work is to engineer a new state of matter where exotic particles with non-commuting properties can exist. New techniques to detect particles with these unconventional properties will be also developed. If successful, the research will enable development of a topological quantum bit, a key element of a revolutionary concept of a fault-tolerant quantum computer, which promises to increase computational power for some resource-intensive tasks exponentially, especially for encryption algorithms paramount for national security. The project will train a PhD student working at the edge of nanotechnology, which is the best hands-on training in science and engineering for a successful career in technology or academia. An outreach program includes development of nanotechnology demonstrations and accompanying materials for high school students and physics teachers.

Non-technical:
This award from the Condensed Matter Physics program of the Division of Materials Research supports Purdue University with a research project which aims to create and manipulate exotic particles known as Majorana particles. Majorana particles are an important class of fundamental particles originally proposed in particle physics (such as in the study of neutrinos) as having the unique property of being their own anti-particle but have not been conclusively found despite decades of research. Recently, it has been realized that it is possible to create analogues of such elusive particles using realistic material systems. Besides their fundamental interests, such "condensed matter" analogues of Majorana particles could potentially be used as quantum "bits" (qubits) to build a robust quantum computer, which would revolutionize our ability to perform computation and solve many complicated problems with dramatically increased speed and reduced energy cost. This project aims to create and manipulate Majorana particles using nanowires of a novel type of insulator, "topological insulators", interfaced with superconductors. Such "topological superconductor nanowires" promise to offer a robust experimental material system to realize the Majorana particles and to manipulate them for possible future applications in quantum computing. The project will also enhance collaborations across multiple disciplines in physics and engineering, with other institutions and international partners. Several graduate and undergraduate students, from both physics and engineering, including those from underrepresented groups, are expected to actively participate and be trained. Outreach activities will also involve high school and undergraduate college students and teachers.

Technical:
Realizing and manipulating analogues of "Majorana particles" (MPs, originally proposed in a particle physics context) in condensed matter systems has attracted strong attention for both fundamental interests and for potential applications to enable fault-tolerant topological quantum computing (TQC). This project aims to realize and detect MPs in "topological superconducting quantum wires" consisting of topological insulator nanoribbons (TINR) coupled to s-wave superconductors, with supercurrent carried by a unique 1D spin-helical mode. Recent theories have suggested that such a setup has several important advantages and is among the most promising experimental systems to host MPs. The properties of MP will be investigated by tunneling spectroscopy, and dc and ac Josephson effects. The proposed research could establish a new, robust experimental platform to realize MP, to explore their novel physics and topological phase transitions, and pave the way for their applications in TQC. The project will also enhance collaborations across multiple disciplines in physics and engineering, with other institutions and international partners. Several graduate and undergraduate students, from both physics and engineering, including those from underrepresented groups, are expected to actively participate and be trained. Outreach activities will also involve high school and undergraduate college students and teachers.

Non-technical Abstract:
Electrons are charged particles, and two electrons brought close to each other repel according to the Coulomb's law. Behavior of a large number of electrons may be much more complex and sometimes counterintuitive. For example, lattice vibrations can change repulsive interactions into attractive resulting in superconductivity, a state with no resistance to electrical current. In two dimensional systems, where electrons are confined to a thin sheet of material, even more exotic states can develop in high magnetic fields. At some fields resistance vanishes, as in superconductors, but transverse (Hall) resistance remains non-zero and is quantized. Some of these states may be superconductors of a very special type, where charges are fractions of an electron charge, something impossible in a three dimensional world. After many years of studies these states are still poorly understood, primarily due to a very limited amount of tools that can be used to investigate these fragile states. Yet some of these states may possess properties necessarily to create fault tolerant quantum computers. In the past with NSF support, the PI's group developed a technology to form high quality electrical contacts between conventional superconductors and two dimensional electron systems. Our research team is now using superconductivity as a new tool to probe exotic states at high magnetic fields, a regime previously not accessible to experimental scrutiny.
This research can potentially lead to the development of quantum bits where quantum information is encoded in the topology of the system. Such quantum bits are predicted to be inherently fault-tolerant. Educational and outreach goals include training students in a multidisciplinary program and organization of a Summer Physics Camp for middle school students.


Technical Abstract:
Among all the experimental systems high mobility two-dimensional electron gases (2DEG) play a unique role of a model system where strong electron-electron correlations lead to the formation of a plethora of exotic states at high magnetic fields, some of them predicted to form unconventional superconducting states. The PI's group's recent breakthrough in the fabrication of transparent ohmic superconducting contacts to high mobility 2DEG in GaAs opens this previously inaccessible regime of superconductor-2DEG interface to experimental scrutiny. Preliminary results indicate the limited understanding of Cooper pair injection into a quantum Hall effect regime. The research objectives include detailed investigation of interplay between topologically distinct superconductivity and strongly correlated fractional quantum Hall effect, a previously inaccessible regime where exciting new physics is waiting to be discovered. This research can potentially lead to the development of a new platform where high order non-Abelian excitations can be realized, a prerequisite for topologically protected fault-tolerant quantum computing. Educational and outreach goals include training students in a multidisciplinary program and organization of a Summer Physics Camp for middle school students.

Nontechnical Abstract: Quantum statistics is central to the quantum mechanical understanding of the world. All known particles have so-called Abelian statistics, meaning that result of several consecutive particle exchanges does not depend on the order of the exchanges. Recently it has been proposed that particles with non-Abelian statistics can be realized in some exotic systems, and signatures of simplest such non-Abelian particles - Majorana fermions - have been reported. The main driving force in the search for these elusive excitations, apart from scientific curiosity, is a possibility to realize a fault tolerant quantum computer. Qubits based on Majorana fermions have their limitations, and the main objective on this proposal is to develop a new system where more computationally useful higher order non-Abelian excitations can be realized.

Technical Abstract: The main objective of the proposed research is to develop a system where high-order non-Abelian excitations can be realized and manipulated. The non-Abelian statistics (the notion that a result of consecutive exchanges of several identical particles depends on the order of the exchanges) is at the heart of a revolutionary concept to realize a fault-tolerant quantum computer. Current efforts are focused on the development of Majorana-based qubits, the simplest non-Abelian particles. Majorana-based qubits are not computationally universal, though, and higher order non-Abelions are required to realize a universal gate. Specifically, spin transitions in the fractional quantum Hall effect regime will be explored to realize a reconfigurable network of helical channels with fractionalized charged excitations. Demonstration of induced superconductivity in these channels will be the major milestone. Quantum statistics of excitations formed at a boundary of trivial and topologically non-trivial superconductors will be investigated in multi-gate devices, where network of topological channels can be reconfigured within a two-dimensional plane.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

Non-technical Abstract:
Statistical properties are central to the quantum mechanical understanding of the world. All known particles have so-called Abelian statistics, meaning that result of several consecutive particle exchanges does not depend on the order of the exchanges. Recently it has been proposed that particles with non-Abelian statistics can be realized in some exotic systems, and signatures of simplest non-Abelian particles ? Majorana fermions ? have been reported. The main driving force in the search for these elusive excitations, apart from scientific curiosity, is a possibility to realize a fault tolerant quantum computer. Qubits based on Majorana fermions are not computationally universal,, which means one cannot perform all the operations with these fault tolerant qubits alone. The main objective of this proposal is to develop a new system where more computationally complete higher order non-Abelian excitations can be realized. Outreach to local Indiana schools and training of students in convergent skills of quantum materials synthesis and characterization, quantum computing and quantum technologies is planned.

Technical Abstract:
The objective of the proposed research is to develop a system where high-order non-Abelian excitations can be realized and manipulated. Specifically, spin transitions in the fractional quantum Hall effect regime will be explored to realize a reconfigurable network of helical channels with fractionalized charged excitations. Demonstration of induced superconductivity in these channels will be a major milestone. An intricate interplay between superconductivity and integer and strongly interacting fractional quantum Hall states will be investigated. While signatures of Majorana fermions, the simplest type of excitations with non-Abelian statistics, have been seen in recent experiments, current experiments fall short of demonstrating non-Abelian exchange statistics. This proposal will address development of a system where high order non-Abelian excitations (parafermions) can be realized and manipulated. Outreach to local Indiana schools and training of students in convergent skills of quantum materials synthesis and characterization, quantum computing and quantum technologies is planned.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.