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

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 theories 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.

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.