Interacting electrons that are confined to move in a one-dimensional structure do not simply jam together like cars in rush hour. Inelastic X-ray scattering shows that the electrons act as if they split into separate fractional entities. See Letter p.82
In physics, a phenomenon is often best explained by reducing it to its simplest version. For example, to understand the quantum-mechanical motion of non-interacting electrons in a crystalline solid, the case of a one-dimensional crystal lattice suffices to introduce the concept of electronic band structure, which describes the range of energies that the electrons may have in the solid. But when it comes to interacting electrons, this approach fails. Coulomb repulsion between any two electrons is much stronger in one-dimensional solids than in their higher-dimensional counterparts, and many-body effects emerge that lead to an apparent fractionalization of the electron1,2,3,4,5. With this fractionalization, the electron's spin and charge seem to form separate quasiparticles — spinons and holons, respectively — that move independently of each other and have different velocities. In a paper published on Nature's website today, Schlappa et al.6 describe an experiment that takes the idea of electronic fractionalization a step further by revealing that electrons can split into a third form of quasiparticle, the orbiton.*
Schlappa and colleagues observe orbitons in a copper oxide (Sr2CuO3) containing a one-dimensional chain of copper oxide building blocks (CuO3), in which the valence electrons reside in the 3d electronic shell of the central copper atoms (Fig. 1). In a free atom there are five 3d orbitals, which are energetically degenerate — that is, they all have the same energy. However, in a CuO3 unit, the electrical field of the oxygen ions around each copper atom lifts this degeneracy, generating an intra-shell energy spectrum. In the chain's ground state, the 3d electrons in all of the CuO3 units are in the same, lowest-energy 3d state, with their spin orientation alternating between neighbouring units as a result of antiferromagnetic interactions.
In such a system, electrons can be locally excited between the energetically different 3d states, leaving one of the CuO3 units in a state known as crystal-field excitation. To achieve this excitation, Schlappa et al. shone X-rays on the CuO3 chain using a technique called resonant inelastic X-ray scattering. The method is similar to conventional optical Raman scattering, but owing to the short wavelengths of X-rays, it provides information not only about a sample's electronic excitations, but also about the excitations' spatial dynamics.
Traditionally, crystal-field excitations in 3d-metal compounds have been viewed as localized objects that stay fixed to the atomic site at which they were generated. But Schlappa and colleagues6 provide clear evidence that, in one dimension, such entities break up into two independent, mobile fragments immediately after excitation. These fragments are the spinon, which is a local disturbance of the spin arrangement of the electron ensemble, and the orbiton, a collective response of all 3d electrons in the chain, which carries the 3d intra-shell excitation. The authors find that the separation of the spinon and the orbiton and their ensuing dynamical behaviour are in excellent agreement with theoretical expectations.
The concept of orbitons as collective orbital excitations in 3d-metal compounds, which is similar to that of spin waves in magnetically ordered systems, was introduced more than a decade ago7. However, for a long time their propagating character escaped unambiguous experimental verification, because previous work8 had been directed at materials of higher dimensions than the one-dimensional system studied here. In such systems, intricate coupling of the initial intra-shell 3d excitation to magnetic excitations tends to immobilize the orbitons, preventing their observation as propagating entities. The spinon–orbiton separation reported by Schlappa et al. not only establishes a new aspect of one-dimensional electron fractionalization, but also provides the first clear observation of moving orbitons in a solid.
It should be noted that this observation has become possible only through the enormous advances made in resonant inelastic X-ray scattering during the past few years, notably through pioneering work at the Swiss Light Source facility at the Paul Scherrer Institute in Villigen, Switzerland, where the authors' experiments6 were conducted. Schlappa and colleagues' results thus highlight the increasingly crucial role of resonant inelastic X-ray scattering in the study of electronic excitations, just as inelastic neutron scattering is the method of choice in the study of magnetic and lattice excitations8.
Finally, are there any practical implications for spinon–orbiton separation? As the microelectronics industry moves towards ever-increasing miniaturization, electronic devices and the conducting connections between them will eventually reach quantum-mechanical limits. When the diameter of the connections reaches atomic dimensions, the transport of charge in them — and also of spin and heat — will no longer follow the laws for macroscopic (three-dimensional) conductors, and one-dimensional electron fractionalization will become relevant. Whether such fractionalization can be used for new device functionalities in quantum computing or spin electronics remains to be seen.
*This article and the paper under discussion6 were published online on 18 April 2012.
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Physics Reports (2018)