Edge states in graphene

Graphene offers more [http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.107.236806]:

In condensed matter systems, topology often gives rise to gapless excitations at the edge (in 2D) or the surface (in 3D). Such excitations in the 2D fractional quantum Hall state should manifest in the edge behaving as a Luttinger liquid, in which tunneling is determined by a universal power law related to an attribute—the filling factor—of the magnetic flux through, and the number of electrons in, the 2D state.

However, no such behavior has yet been observed at the edges of 2D semiconductor heterostructures, the most-studied quantum Hall systems. Theorists say that in these systems the conflicting interplay between the confinement potential, attracting each electron towards the center, and the Coulomb force, pushing them apart from each other, modifies the edge itself. This process—edge reconstruction—disturbs the universal Luttinger liquid picture in the experimentally accessible distance scales.

In a paper in Physical Review Letters, Zi-Xiang Hu, at Princeton University, and his colleagues tell us that we may, after all, be able to see chiral Luttinger behavior in another system in which fractional quantum Hall effect has been observed—graphene. In graphene, electrons are confined by metallic gates that are placed a specific distance away. By contrast, in semiconductors, electrons are confined by dopants. This one difference should make graphene less susceptible to edge reconstruction and reveal the fractional quantum Hall state. The authors say that experimentalists should therefore finally see the elusive universal edge behavior in the experimentally accessible state with filling factor 1/3. – Sami Mitra

spin charge separation in purple bronze

Spin charge separation has been a very old concept. It actually has been confirmed in various 1D systems. One manifestation allowing for experimental detection is the violation of Wiedemann-Franz Law, which states that the heat and electricity are carried by the same entities, i.e., electrons. But this law will break down in 1D systems.

http://bristol.ac.uk/news/2011/7777.html

The origin of this empirical observation did not become clear however until the discovery of the electron and the advent of quantum physics in the early twentieth century. Electrons have a spin and a charge. When they move through a metal they cause an electrical current because of the moving charge. In addition, the moving electrons also carry heat through the metal but now it is via both the charge and the spin. So a moving electron must carry both heat and charge: that is why the ratio does not vary from metal to metal.

For the past 150-plus years, the Wiedemann-Franz law has proved to be remarkably robust, the ratio varying at most by around 50 per cent amongst the thousands of metallic systems studied.

In 1996, American physicists C. L. Kane and Matthew Fisher made a theoretical prediction that if you confine electrons to individual atomic chains, the Wiedemann-Franz law could be strongly violated. In this one-dimensional world, the electrons split into two distinct components or excitations, one carrying spin but not charge (the spinon), the other carrying charge but not spin (the holon). When the holon encounters an impurity in the chain of atoms it has no choice but for its motion to be reflected. The spinon, on the other hand, has the ability to tunnel through the impurity and then continue along the chain. This means that heat is conducted easily along the chain but charge is not. This gives rise to a violation of the Wiedemann-Franz law that grows with decreasing temperature.

The experimental group, led by Professor Nigel Hussey of the Correlated Electron Systems Group at the University of Bristol, tested this prediction on a purple bronze material comprising atomic chains along which the electrons prefer to travel.

Remarkably, the researchers found that the material conducted heat 100,000 times better than would have been expected if it had obeyed the Wiedemann-Franz law like other metals. Not only does this remarkable capability of this compound to conduct heat have potential from a technological perspective, such unprecedented violation of the Wiedemann-Franz law provides striking evidence for this unusual separation of the spin and charge of an electron in the one-dimensional world.

Professor Hussey said: “One can create purely one-dimensional atomic chains on substrates, or free-standing two-dimensional sheets, like graphene, but in a three-dimensional complex solid, there will always be some residual coupling between individual chains of atoms within the complex that allow the electrons to move in three-dimensional space.

“In this purple bronze, however, nature has conspired to limit this coupling to such an extent that the electrons are effectively confined to individual chains and thus creating a one-dimensional world inside the three-dimensional complex. The goal now is to find a way, for example, using pressure or chemical substitution, to increase the ability of the electrons to hop between adjacent chains and to study the evolution of the spin and charge states as the three-dimensional world is restored within the material.”

Paper

‘Gross violation of the Wiedemann-Franz law in a quasi-one-dimensional conductor’ by Nicholas Wakeham, Alimamy F. Bangura, Xiaofeng Xu, Jean-Francois Mercure, Martha Greenblatt and Nigel E. Hussey in Nature Communications

1D is special

1D means enough space but little mobility. One always blocks another even if a bit of interaction gets in the way. And this makes the boundary between bosons and fermions fuzzy. Fermions naturally set hurdles to their compatriots for exclusion principle. While bosons, although without that famous principle, will also demobilize their partners in the presence of strong repulsions. If so, fermions and bosons will resemble each other. This is indeed what happens in this setup proposed in this work [Phys. Rev. Lett. 106, 153601 (2011) ]!

In this work we show that light-matter excitations (polaritons) generated inside a hollow-core onedimensional fiber filled with two types of atoms, can exhibit Luttinger liquid behavior. We first explain how to prepare and drive this quantum-optical system to a strongly interacting regime, described by a bosonic two-component Lieb-Liniger model. Utilizing the connection between strongly interacting bosonic and fermionic systems, we then show how spin-charge separation could be observed by probing the correlations in the polaritons. This is performed by first mapping the polaritons to propagating photon pulses and then measuring the effective photonic spin and charge densities and velocities by analyzing the correlations in the emitted photon spectrum. The necessary regime of interactions is achievable with
current quantum-optical technology.