Novel collective phenomena in Majorana fermion devices

Lead Research Organisation: University of Birmingham
Department Name: School of Physics and Astronomy

Abstract

The collective behaviour of many particles often gives rise to phenomena defying one's intuition based on the microscopic rules governing the system. A striking example is that of the emergence of new, exotic particles, with properties completely different from those of the individual constituents.

It is one of the most exciting recent discoveries that Majorana fermions, exotic particles of this kind, can emerge in certain superconductor structures. Majorana fermions, unlike the superconductor's electrons, are neutral, concealing the electric charge in a quantum mechanical, nonlocal manner. The excitement about these particles, beyond their fundamental science, is due to the prospects of taking advantage of this intrinsic quantum nonlocality in quantum computing applications.

Experimental work on systems designed to host 0D (confined from all directions) and 1D (extending along one direction) forms of Majorana fermions is ongoing, with the first promising signatures reported recently. Among the main goals of theoretical research motivated by these developments is to devise new methods and devices for detecting and manipulating Majorana fermions.

This theoretical research aims at exploring a novel avenue for studying Majorana fermions based on the observation that they can not only result, but also participate in, or even cause novel collective quantum phenomena. Focusing on the case where these are promoted by strong interactions of spatially localised ("impurity") nature, the research will explore new many particle physics arising (1) when conduction electrons are coupled to devices with 0D Majorana fermions and (2) in devices hosting 1D Majorana fermions.

The scientific goals are: to uncover and describe (e.g., via scattering properties, spatial and other organisation patterns) fundamentally new forms of collective behaviour; and to predict experimentally observable phenomena that can serve as in-depth tests of Majorana fermion features (such as nonlocality) and can influence the behaviour of devices aimed at Majorana fermion manipulation.

The proposed work, in addition to being directly relevant to ongoing Majorana fermion research, has the potential to provide new routes for cross-fertilisation between the communities working on Majorana fermions and strongly interacting systems.

Planned Impact

Majorana fermions have a range of features which are not only exotic, but also underlie a paradigm for a type of quantum bits (qubits) which are by their very nature protected from environmental disturbances and can be operated largely error free. The realisation of Majorana qubits will therefore overcome major challenges hindering currently available qubit alternatives.

The research focuses on uncovering and describing collective phenomena that can give in-depth information on Majorana qubits through straightforward measurements. Direct beneficiaries will include experimentalists currently working on creating Majorana qubits (including UK groups at Cambridge and UCL) and later quantum computers, who can use the results for quickly validating parts of their systems. These quick validations can, in the future, translate into commercial applications both in quantum computer assembly and maintenance.

Through their contribution to the developments towards creating a quantum computer, the results will have a range of indirect, though long-term, societal and economic impacts and benefits. These include
*infrastructural investments (both public and private) into data storage and communication, which will be necessary once current cryptographic technology becomes obsolete due to the superior code breaking abilities of quantum algorithms.
*societal benefits due to new simulation capabilities, used, e.g., for material design, drug discovery, or weather modelling. Bringing the benefits of quantum computation to society will, through the uptake of the new technology, of course also involve significant investment from high-tech companies.

In addition to these societal and economical impacts, the research will
*directly contribute to expanding scientific knowledge through exploring fundamentally new physics
*be a source of research skills transfer through collaborating with an early career researcher.

Publications


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Description Exact nonequilibrium transport in the topological Kondo effect:
I have introduced a novel exact approach to study collective phenomena in certain Majorana fermion devices far from equilibrium. Key predictions include universal scaling functions for the linear and differential conductance and the discovery of charge fractionalisation in the nonequilibrium current noise. The predictions from this approach are expected to greatly facilitate demonstrating the quantum dynamics of Majorana fermion qubits in solid-state experiments and thus constitute a key step towards constructing quantum information processing units based on Majorana fermions.

Signatures of time-reversal invariant topological superconductivity in the Josephson effect:
With Mr. Ehren Mellars we have predicted signatures in superconducting junctions involving certain symmetric counterparts of Majorana fermions. The predictions are exact and take only a few, independently measurable, physical parameters as inputs, such as the normal state conductance. The results are expected to aid searches for symmetric Majorana fermions in experiments.

Universality and quantized response in bosonic nonfractionalized tunneling:
With Dr. Shaoyu Yin, we have worked on theoretically establishing routes towards the creation and detection of novel collective states of bosonic particles called the boson integer quantum Hall effect. We have shown how these states can be created in a manner much closer to current experiments than previous suggestions, by highlighting the possibility of using optical lattices and single component bosons. We have discovered a great degree of universality in the tunneling of bosonic particles and shown that, in addition to the challenges posed by the consequent uniformity of features across a wide variety of bosonic tunneling setups, this also provides methods to unmask bosonic integer quantum Hall states through a quantised nonequilibrium signature.
Exploitation Route The work on Majorana fermions may greatly aid searches for novel forms of emergent particles and the demonstration of the potential for quantum computation. The work on bosonic systems may facilitate the creation and demonstration of novel collective phases with robust conducting properties in ultracold atom experiments.
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