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.