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.

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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

Observation of confinment in condensed matter systems

It is well known that baryons are made of quarks. However, these quarks can not be directly observed due to a phenomenon called 'aymptotic freedom' or say 'confinement', which arises becasuse of increasing force strength with separation. It is interesting that, such confinement is not exclusive to high energy physics. It was recently observed occuring to condensed matter systems. This gives another example on how concepts are shared between various fields in physics.

a, The region between two spinons (domain walls) on a chain consists of reversed spins (coloured in red); if this chain is coupled antiferromagnetically to another chain, as in a spin ladder, these reversed spins cost energy owing to their parallel alignment with the spins on the neighbouring chain. This energy cost, which is proportional to the separation of the spinons, acts to confine the spinons. b,c, The structure of CaCu₂O₃ for the a–b plane (b) and the a–c plane (c). CaCu₂O₃ has orthorhombic symmetry with space group Pmmn and lattice parameters a=9.949 Å, b=4.078 Å and c=3.460 Å at T=10 K. The magnetic Cu²⁺ ions have spin=1/2 and are represented by the red spheres; they are coupled to each other by superexchange interactions through the O²⁻ ions (blue spheres) and the Cu–O bonds are represented by the solid black lines; the Ca²⁺ ions are not shown. The lattice parameters are shown in grey as well as the rung distance d_rung, which is approximately one third of the a lattice parameter. The structure consists of copper oxide layers stacked along the c direction, the ladders lie within this plane running parallel to b and neighbouring ladders are shifted by half a unit cell in a. The dotted black lines indicate the separate ladder units and the inter- and intraladder exchange interactions are labelled. The coupling along the legs, J_leg, occurs through superexchange interactions mediated by oxygen; the Cu–O–Cu bond angle is 180^°, giving rise to strong antiferromagnetic coupling (according to the Goodenough–Kanamori–Anderson rules). In contrast, the Cu–O–Cu bond along the rungs is 123^° and therefore J_rung is expected to be substantially weaker although still antiferromagnetic. In addition, a weak antiferromagnetic interaction, J_diag, is predicted between opposite copper ions within each plaquette of the ladder. The ladders are coupled together by a number of weaker interactions. Within the a–b plane, Cu²⁺ ions on neighbouring ladders are connected through Cu–O–Cu bonds that are 90^°, giving rise to a weak ferromagnetic J_inter. Note that J_inter is frustrated and competes with the much stronger J_leg; thus, its energy cancels in the Hamiltonian to first order. Weak interladder couplings J_c1 and J_c2 are also expected between ladders in the c direction. Finally, in common with other planar copper oxide materials, CaCu₂O₃ is expected to have a four-spin cyclic exchange interaction, J_cyclic, coupling the four copper ions that form each plaquette. Quantum chemistry calculations give the following exchange constants for CaCu₂O₃: J_leg=−147 to −134 meV; J_rung=−15 to −11.3 meV; J_cyclic=4 meV; J_inter<24 meV; J_diag=−0.2 meV; J_c1=0.1 meV; J_c2=0.8 meV (refs 19, 20). Susceptibility data fitted to a spin-1/2 Heisenberg chain model without other interactions provide good agreement with the data and suggest that J_leg is indeed the dominant interaction and has a value of −168 meV (ref. 22).

Nature Physics 6, 50 - 55 (2009)