Research Reveals “Wigner Glass” Arrangement of Electrons in Cuprates

Cuprates, a family of copper-oxide ceramics sharing a common elementary unit of oxygen and copper atoms in a flat square lattice, have been investigated for their potential to be superconducting at comparatively high temperatures.

However, in their pristine state, they are a unique type of insulator—a material that does not conduct electricity readily—called a Mott insulator.

Upon adding electrical charge carriers—either electrons or “holes”, or the lack of electrons—to an insulator through a process known as doping, the insulator might turn into a metal, which conducts electricity readily, or a semiconductor, which can conduct electricity based on the environment. However, cuprates act neither like a normal metal nor like a normal insulator due to strong interactions between their electrons. In order to prevent the large energy cost that arises from these interactions, the electrons impulsively organize into a collective state in which the motion of each particle is linked to all the other particles.

The superconducting state is one such example in which electrons move together and drift with zero net friction upon applying a potential—a zero-resistance state which is a characteristic that defines a superconductor. Another collective electronic state is a “charge density wave,” a term that originated from the wave-like modulation in the density of electrons, where electrons “freeze” into static and periodic patterns while hindering electron flow simultaneously. Since this state is antagonistic to the superconducting state, it is vital to investigate and understand. The charge-density waves in cuprates choose to align to the atomic rows of oxygen and copper atoms that form the basic crystal structure, where wave “crests” occur every three to five unit cells, based on the material and doping level.

Scientists at MIT chanced upon an unexpected discovery when they used a method called resonant X-ray scattering to investigate these charge-density waves in two different cuprate compounds, praseodymium copper oxide (Pr₂CuO₄ or PCO) and neodymium copper oxide (Nd₂CuO₄ or NCO) doped with additional electrons. Their study demonstrated a phase of the material in which the electrons fall into a disordered, or “glassy,” arrangement, called a “Wigner glass.” The outcomes of the study were recently reported in a paper published in Nature Physics.

In resonant X-ray scattering, a diffraction technique that was developed recently, crystallography is conducted on electrons instead of performing it widely on the atoms as in traditional X-ray diffraction. “In the limit of low concentration of doped electrons, we observed a completely new and unexpected form of electronic phase which is neither a superfluid nor a crystal, but it rather has the characteristics of a Wigner glass. In this phase, the electrons form a collective state without any orientational preference,” stated Riccardo Comin, the senior author of the paper and assistant professor of physics at MIT. An amorphous glass of electrons such as this is totally unheard of in this class of materials, he added.

This phenomenon occurs only in a narrow window of electron doping.

Intriguingly, this exotic new state only exists in a small region of the electronic phase diagram of this material, and when more electrons are doped in the [copper oxide] planes, a more conventional electronic crystal is recovered, whose ripples align to the crystallographic axes of the underlying atomic lattice.

Min Gu Kang, Study Lead Author, Graduate Student, MIT.

The MIT group, including Comin, graduate student Kang, and postdoc Jonathan Pelliciari, developed the project and headed the majority of experiments. Their study was rendered possible by the contributions of scientists from different institutions and facilities across the globe. Resonant X-ray scattering measurements were carried out at a number of synchrotron facilities, including the Berlin Electron Storage Ring in Germany, the Canadian Light Source in Saskatoon, Saskatchewan, Canada, and the Advanced Light Source, in Berkeley, California. The copper-oxide thin film samples were grown at NTT Basic Research Laboratories in Japan. Theoretical analysis was designed by scientists at the Indian Institute of Science in India.

According to Comin, the theory put forward explains the part played by the electronic band structure in regulating the periodic spacing and deficiency of orientational preference of the density waves as a function of doping level in this material.

Our theory suggests that these electronic ripples are initially formed with irregular shapes and are likely nucleated around defects or impurities in the material. When the density of carriers increases, the electrons manage to find a more highly-ordered arrangement that minimizes the total energy of the system, thereby restoring the more conventional charge density waves that have been observed universally in all families of copper-oxide superconductors.

Riccardo Comin, Assistant Professor of Physics, MIT.

“I was completely blown away by Riccardo’s results on NCO and PCO,” stated Peter Abbamonte, Fox Family Professor in Engineering at the University of Illinois at Urbana-Champaign, who created the resonant soft X-ray scattering technique. Observing that charge density wave (CDW) order in cuprates has been the core of the field for more than a decade, Abbamonte, who did not take part in this study, explained that it was earlier perceived that the CDW order is tied to the crystal lattice, suggesting that the charge density wave must point in one of two perpendicular directions, but not in between. This traditional wisdom is hinged on 20 years of resonant scattering and scanning tunneling microscopy experiments that have always revealed this to be the case, he noted.

Comin’s studies on these specific electron-doped cuprates revealed that in the glassy phase, the charge order could point toward any direction, without regards to the crystal lattice in which it exists.

The more precise statement is that the CDW order parameter is not Ising-like (that is, taking only discrete values, in this case two: x or y), as has always been assumed, but is more like an X-Y order parameter (that is, free to choose any value on a continuous range, such as all directions between x and y as is the case here) that is only weakly influenced by the crystal.

Peter Abbamonte, Fox Family Professor in Engineering, University of Illinois at Urbana-Champaign.

“It is going to take some time for the community to fully digest this realization and its implications for understanding the relevance of CDW order,” added Abbamonte. “What is clear is Riccardo’s paper is going to lead to a serious re-reckoning of the rules of the game, and in this sense is a major advance for the field.”

Superconductors have a tremendous, largely unexploited potential for transformative applications like magnetic sensing and medical diagnostic imaging, quantum computing, plasma and nuclear fusion power technologies, and lossless energy transport.

Overall, our study has revealed yet another manifestation of the exquisite quantum character of charge carriers in high-temperature superconductors, which ultimately arises from the nature of the electronic interactions. The detailed behavior of electrons uncovered in this work provides new insights on how high-temperature superconductivity is born out of a Mott insulator, and promises to bridge a gap between regions of the phase diagram with very contrasting phenomenologies.

Riccardo Comin, Assistant Professor of Physics, MIT.