Beyond Luttinger Liquids-spin-charge separation at high excitation energies

Lead Research Organisation: University of Cambridge
Department Name: Physics

Abstract

It is an astonishing fact that although an isolated electron is, as far as we can tell, indivisible, a collection of electrons constrained to move only in a narrow wire appear to dissociate into two new types of particle. These two particles carry separately the magnetism (or spin) of the electron and its electric charge and are called spinons and holons. These form the building blocks of a new state of matter known as a Tomonaga-Luttinger liquid. For decades our understanding of this Luttinger liquid has been entirely theoretical, resting on simplified models of how electrons behave, since even with the world's most powerful computers we are unable to solve exactly the behaviour of more than a handful of electrons-such is the complexity of the many-electron Schrödinger equation. Advances in semiconductor physics have made it possible in recent years to set up the necessary conditions to create a Luttinger liquid and observe the phenomenon of spin-charge separation directly. This we achieved in 2009 in a collaboration that brought together the experimentalist and theorist who are the principal investigators on this proposal. The experiment worked by injecting electrons into an array of wires (via quantum mechanical tunnelling) and mapping out where they subsequently go by varying the magnetic field and voltage. Though the experiment was a success, it raised a number of intriguing questions-only with the experimental results in front of us could we see the shortcomings of current theory. It is those questions that underpin this proposal.
The most surprising observation is that, while the approximate theories that predict spin-charge separation are only valid for the lowest-energy excitations, we saw hints in the experiment that spin-charge separation extends to higher energies. The key question is: how high in energy can we track the spinon and holon? If they are unusually stable then what causes this stability and can we understand it mathematically? Also, the theoies all assume the wires are infinitely long. Our proposal involves studying a range of lengths to address how the excitations are influenced by the ends of the wire when it is short. That may be the vital step necessary to explain a 15 year-old mystery of the "0.7" step-like feature in the conductance of quantum wires. At the heart of this proposal is an improved device for measuring spin-charge separation, and recent theoretical ideas that develop mathematical machinery to allow us to calculate properties away from the low-energy limit of narrow wires. This theory needs to be related to the new tunnelling experiment of the proposal.
Our new devices will also allow two new types of experiment to be undertaken. We will measure the tunnelling both into and out of a one-dimensional wire, from which it is possible to understand how the novel excitations relax back to equilibrium. We will also measure the drag forces between two 1D wires, which again will help characterise the distinct spinon and holon properties. There are preliminary theoretical predictions for both experiments, which we will test.
The implications of the proposal extend beyond the boundaries of the Luttinger-liquid state. Other types of metal (so called "bad metals") also show, at high temperatures, properties that naively only belong at low energies and temperatures. If we can understand how this works in the one-dimensional Luttinger liquid (where typically we have more mathematical techniques to deploy) it could point to a solution of that much harder problem. Similarly, the techniques of manipulating very narrow wires and stabilising their unusual quantum properties are also what would be required to make a proposed type of quantum computer. Like the Luttinger liquid, the wires in question also have very unusual excitations but these have been constructed to be robust at high temperatures through a type of topological protection reminiscent of that which prevents a Möbius strip from unwinding.

Planned Impact

This proposal combines experiment and theory in an area of fundamental physics. It is work that impacts across a number of themes within the recent Grand Challenges for Physics published by EPSRC. One Grand Challenge is "Emergence and physics far from equilibrium". Emergence describes the new ordering principles that often arise in complex interacting systems making them more than the simple sum of their constituent parts. The phenomenon of spin-charge separation is a common theoretical example of emergence: our experimental work has demonstrated that an electron, which when isolated has its charge and spin locked together, can break apart in one-dimensional (1D) wires, by interacting with all the other electrons there. If we are to exploit this we must first understand the boundaries of the phenomenon. This proposal does this by considering the role of temperature and wire length and compares these to theoretical expectations developed alongside the experiments.
This proposal also probes this emergent behaviour beyond the low-energy regime via tunnelling at high voltage. This driven system is therefore away from equilibrium yet because of the small probability of tunnelling it can still be treated mathematically. This proposal thus represents a route to understanding a type of emergence and non-equilibrium physics from starting points that are understood and with a controlled path into the unknown. Progress here will represent impact in understanding this grand challenge.
Both emergence and physics beyond equilibrium demand a close interplay between theorists and experimentalists. The new theoretical ideas are likely to be inspired by experiment, thus the training of theoretical physicists who can work effectively with experimental teams is a key path to long-term impact.
The other grand challenge to be addressed is "Quantum physics for new quantum technologies". This work has the potential to be more applied than the fundamental physics challenge above. Novel excitations in 1D wires currently represent a highly promising path to entangled quantum bits that would be required in a quantum computer.
This proposal extends state-of-the-art fabrication techniques which will be necessary if such schemes are to come to fruition. Thus a further aspect of this proposal's impact in the UK is its contribution to the strength of semiconductor and quantum research in UK universities, by developing fabrication techniques, providing expertise and skilled personnel, and supporting the materials growth and fabrication infrastructure in the Semiconductor Physics group in Cambridge, which supplies many groups in the UK with high quality MBE-grown material and with electron-beam patterned samples.
The postdocs who will work on this project will become highly skilled researchers. They will learn skills that will be very useful to them in their future jobs, whether those be in other research groups or in industry. The project will give them experience not only of experimental techniques such as nanofabrication and low-temperature, low-noise measurements, and of using complex, high-technology equipment, or of advanced theory and modelling, but also of planning projects, designing devices and interpreting and discussing results based on a deep understanding of the physics involved. It will also involve trouble-shooting, report-writing and development of presentation skills. This supply of trained researchers will enhance the research capacity, knowledge and skills of high-technology companies and research laboratories in the UK.

Publications

10 25 50
 
Description It is an astonishing fact that although an isolated electron is indivisible, a collection of electrons constrained to move only in a narrow wire appear to dissociate into two new types of particle. These two particles carry separately the magnetism (or spin) of the electron and its electric charge and are called spinons and holons. These form the building blocks of a new state of matter known as a Tomonaga-Luttinger liquid. For decades our understanding of this Luttinger liquid has been entirely theoretical, resting on simplified models of how electrons behave. Having previously measured this spin-charge separation directly, we have now developed our device designs and fabrication techniques to allow detailed comparison with new theoretical advances, which predict extra curves (replicas of the usual dispersion relation for 1D wires in the absence of interactions) in plots of energy vs momentum. The theorists in our team have calculated that the magnitude of these replicas should increase strongly as the wire length is decreased, and indeed, in the shorter wires measured, we observe the start of the strongest replica. This is a completely new observation and it will give a boost to both experimental and theoretical work on interacting 1D systems in this new regime. In addition, the theory predicts a power-law dependence on energy, and we are accumulating evidence that confirms this. As a spin-off of this work, we have developed a method for reliably fabricating large numbers of "air bridges" that join metal features on our devices, and this may be useful in making other types of research devices.
Exploitation Route We have presented the work at conferences and Departmental seminars in the USA, Germany, Luxembourg and Italy. Papers have been published in Nature Communications, Physical Review Letters and Physical Review B, one more is very close to being accepted for Nature Communications, and at least two more are in preparation.
The impacts of the proposal extend beyond the boundaries of the Luttinger-liquid state. Other types of metal (so called "bad metals") also show, at high temperatures, properties that naively only belong at low energies and temperatures. The new theoretical techniques being brought to be bear on the one-dimensional interacting system (by our team and our collaborators) could lead eventually to a solution of that much harder problem. Similarly, the techniques of manipulating very narrow wires and stabilising their unusual quantum properties are also what would be required to make a proposed type of quantum computer. Like the Luttinger liquid, the wires in question also have very unusual excitations but these have been constructed to be robust at high temperatures through a type of topological protection reminiscent of that which prevents a Möbius strip from unwinding. For the next decade the impact will be mainly on academic researchers (theorists and experimentalists), but after that the results may help with the development of exotic quantum systems for commercial use, exploiting quantum computation or topological insulators. Another, more direct, impact is the training of two skilled postdoctoral researchers (one theorist and one experimentalist), and one PhD student, who may all be very useful to industry in the UK and beyond.
Sectors Digital/Communication/Information Technologies (including Software),Electronics

URL http://www.sp.phy.cam.ac.uk/research/1d-transport/SCseparation
 
Title Arrays of air bridges 
Description We have developed a reliable technique for making large arrays of "air bridges" to connect metal tracks on a chip together without touching the surface or other metal track in between. The technique avoids the need for an insulating layer beneath the metal track that bridges the two tracks, as it forms a bridge with an air gap beneath it. This technique is only intended for research devices and has been shown to work well for sub-micron width bridges spanning several microns, at cryogenic temperatures (down to 50 mK). 
Type Of Material Technology assay or reagent 
Provided To Others? No  
Impact This technique has enabled us to make arrays of very short (<5 micron) 1D wires to investigate interaction effects in this grant and in subsequent developments of the work. 
 
Description Talk at Royal Holloway, University of London 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact 30 people attended my talk to a research group at RHUL, aimed at fostering a collaboration with a research group there to enable my samples to be measured in their unique low-temperature cryostat. We have since provided samples and the collaboration is ongoing.
Year(s) Of Engagement Activity 2017
 
Description Talk at the German Physical Society Spring Meeting conference 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact 40 people attended a 15-minute conference talk. There were various questions afterwards.
Year(s) Of Engagement Activity 2018
 
Description Talk at the US APS March Meeting conference 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I gave a contributed talk at the conference to academics, postdocs and PhD students working in related scientific areas.
Year(s) Of Engagement Activity 2017
URL http://meetings.aps.org/Meeting/MAR17/Session/P37b.14
 
Description Talk at the University of Cambridge 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact 60 members of my Department attended my talk, which was aimed at increasing interactions and collaborations between members of the Department.
Year(s) Of Engagement Activity 2018
 
Description Talk at the University of Frankfurt 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I was invited to give a talk at the Physics Department to academics, postdocs and PhD students working in related scientific areas.
Year(s) Of Engagement Activity 2016
 
Description Talk at the University of Lancaster, UK 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Postgraduate students
Results and Impact I gave an invited talk at the University of Lancaster, UK, on the topic of the grant, to researchers at the Department of Physics. 40 postgraduate students, postdocs and academic staff attended. There were questions and discussion afterwards.
Year(s) Of Engagement Activity 2018
 
Description Talk at the University of Luxemburg 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I was invited to give a talk at the Physics Department to academics, postdocs and PhD students working in related scientific areas.
Year(s) Of Engagement Activity 2016