University of Illinois team finds Wigner crystal—not Mott insulator—in 'magic-angle' graphene

Siv Schwink
9/24/2018

University of Illinois at Urbana-Champaign Professor of Physics Philip Phillips (right) and graduate student Bikash Padhi pose in the Institute for Condensed Matter Theory on the Urbana campus. Credit: Siv Schwink, University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign Professor of Physics Philip Phillips (right) and graduate student Bikash Padhi pose in the Institute for Condensed Matter Theory on the Urbana campus. Credit: Siv Schwink, University of Illinois at Urbana-Champaign
Recently, a team of scientists led by Pablo Jarillo-Herrero at the Massachusetts Institute of Technology (MIT) created a huge stir in the field of condensed matter physics when they showed that two sheets of graphene twisted at specific angles—dubbed “magic-angle” graphene—display two emergent phases of matter not observed in single sheets of graphene. Graphene is a honeycomb lattice of carbon atoms—it’s essentially a one-atom-thick layer of graphite, the dark, flaky material in pencils. 

In two articles published online in March 2018 and appearing in the April 5, 2018 issue of the journal Nature, the team reported the twisted bilayer graphene (tBLG) exhibits an unconventional superconducting phase, akin to what is seen in high-temperature superconducting cuprates. This phase is obtained by doping (injecting electrons into) an insulating state, which the MIT group interpreted as an example of Mott insulation. A joint team of scientists at UCSB and Columbia University has reproduced the remarkable MIT results. The discovery holds promise for the eventual development of room-temperature superconductors and a host of other equally groundbreaking applications.

Researchers at the University of Illinois at Urbana-Champaign have recently shown that the insulating behavior reported by the MIT team has been misattributed. Professor Philip Phillips, a noted expert in the physics of Mott insulators, says a careful review of the MIT experimental data by his team revealed that the insulating behavior of the “magic-angle” graphene is not Mott insulation, but something even more profounda Wigner crystal.

“People have been looking for clear examples of Wigner crystals since Wigner first predicted them in the 1930s,” Phillips asserts. “I think this is even more exciting than if it were a Mott insulator.”

Lead author of the U of I study, graduate student Bikash Padhi, explains, “When one sheet of graphene is twisted on top of another, moiré patterns emerge as a result of the offset in the honeycomb structure. By artificially injecting electrons into these sheets, the MIT group obtained novel phases of matter which can be understood by studying these extra electrons on the bed of this moiré pattern. By increasing the electron density, the MIT group observed an insulating state when two and three electrons reside in a moiré unit cell.  They argued this behavior is an example of Mott physics.”

Why can’t it be Mott physics?

Proposed Wigner crystals for magic-angle bilayer graphene. Leftmost figure, the criterion for observing this lattice structure is not satisfied experimentally, resulting in metallic transport when a single electron occupies a moiré cell. The remaining two figures show the insulating state, explaining the experimental observation when 2 or 3 electrons are in a moiré cell. Credit: Philip Phillips, University of Illinois at Ubana-Champaign
Proposed Wigner crystals for magic-angle bilayer graphene. Leftmost figure, the criterion for observing this lattice structure is not satisfied experimentally, resulting in metallic transport when a single electron occupies a moiré cell. The remaining two figures show the insulating state, explaining the experimental observation when 2 or 3 electrons are in a moiré cell. Credit: Philip Phillips, University of Illinois at Ubana-Champaign
Phillips explains, “Mott insulators are a class of materials that should be conductive if electronic interactions are not taken into account, but once that’s taken into account, are insulating instead. There are two primary reasons why we suspect the tBLG does not form a Mott insulatorthe observed metal-insulator transition offers only one characteristic energy scale, whereas conventional Mott insulators are described by two scales. Next, in the MIT report, in contrast to what one expects for a Mott system, there was no insulator when there was only one electron per unit cell. This is fundamentally inconsistent with Mottness.”

The accompanying figure displays the crystalline states that explain these data.

What is a Wigner crystal?

Zorbing, rolling and bouncing in an inflated transparent ball, has become popular around the world. Bikash Padhi, a University of Illinois at Urbana-Champaign graduate student in theoretical condensed matter physics, compares Wigner crystallization to swelling zorbs in a closed field, where the zorb passengers are electrons and the zorb itself is a measure of each electron's repulsion to other electrons. Credit: Username:Rodw/Wikimedia Commons/Public Domain
Zorbing, rolling and bouncing in an inflated transparent ball, has become popular around the world. Bikash Padhi, a University of Illinois at Urbana-Champaign graduate student in theoretical condensed matter physics, compares Wigner crystallization to swelling zorbs in a closed field, where the zorb passengers are electrons and the zorb itself is a measure of each electron's repulsion to other electrons. Credit: Username:Rodw/Wikimedia Commons/Public Domain
To understand Wigner crystals, Padhi offers this analogy: “Imagine a group of people each inside a large orb and running around in a closed room. If this orb is small they can move freely but as it grows bigger one may collide more frequently than before and eventually there might be a point when all of them are stuck at their positions since any small movement will be immediately prevented by the next person. This is basically what a crystal is. The people here are electrons, and the orb is a measure of their repulsion.”

Phillips credits Padhi with providing the impetus for the study. Chandan Setty, who was until recently a postdoctoral researcher working in Phillips' group at the Institute for Condensed Matter Theory in Urbana, also made significant contributions to the study, according to Phillips.

These results were pre-published online in the journal Nano Letters in the article, “Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization not Mott Insulation,” on September 5, 2018, with the final official publication to be included in the journal’s October 2018 issue.

This research was funded by the Center for Emergent Superconductivity, a Department of Energy–funded Energy Frontier Research Center, and by the National Science Foundation. The conclusions presented are those of the researchers and not necessarily those of the funding agencies.

Recent News

  • Accolades

Physics Professor Nadya Mason has been selected a University Scholar by the Office of the Vice President for Academic Affairs at the University of Illinois at Urbana-Champaign. The highest honor bestowed on faculty by the university, this award recognizes faculty who have made significant contributions in their fields of research and teaching, in line with the university’s reputation for leading-edge innovation and excellence. Mason is one of five faculty members on the Urbana campus to be named to this honor in this selection round.

  • Accolades

The 347 scientists from around the globe who worked together to capture the first-ever image of a black hole have won the 2020 Breakthrough Prize in Fundamental Physics. The Breakthrough Prize Foundation announced today that members of the international Event Horizon Telescope (EHT) Collaboration were selected for this honor, with the citation: “For the first image of a supermassive black hole, taken by means of an Earth-sized alliance of telescopes.”

The $3-million prize will be shared equally among all contributing scientists named on the six EHT papers published on April 10, 2019, in conjunction with the public unveiling of the black hole image—the first direct evidence of a supermassive black hole and its shadow.In addition to Gammie, U of I’s EHT research team members named Breakthrough Prize laureates include current physics graduate students George Wong and Ben Prather; current astronomy graduate student Andrew Nadolski; former astronomy graduate students Ben Ryan (now an R&D scientist at Los Alamos National Laboratory), Dimitrios Psaltis (now an astronomy professor at The University of Arizona), and Hotaka Shiokawa (now a data scientist at Rakuten Institute of Technology); and former physics postdoctoral researchers Monika Moscibrodzka (now an astrophysics professor at Radboud University, the Netherlands) and Roman Gold (now a postdoctoral researcher at Goethe University Frankfurt am Main, Germany). Each of these scientists will receive upwards of $8,600 in prize money.

  • Accolades

Humankind’s first image of a monster black hole, the tangled proteins that cause destructive neurodegenerative diseases, and the pathways telling our brains we’re in pain are among the discoveries honored by this year’s Breakthrough Prizes.

With $3 million accompanying each major prize, the Breakthrough Prizes are the most lucrative in science. Bankrolled by Silicon Valley titans, including Yuri Milner and Mark Zuckerberg, the prizes honor cutting-edge achievements in life sciences, physics, and mathematics. And unlike some other well-known science prizes, it’s not unusual for the Breakthrough team to honor teams rather than a few select individuals.

  • Accolades

The Department of Physics at the University of Illinois at Urbana-Champaign has established the Gary Kelly Staff Excellence Award to recognize staff members who demonstrate exceptional job performance and dedication in support of departmental goals. The annual award will be presented for the first time at the 2019 Fall Physics Reception to up to two outstanding staff members; the award comprises a commemorative plaque and $2,000 for each recipient. The Gary Kelly Staff Excellence Award is funded by a generous estate gift from Illinois Physics alumnus Gary Kelly (MS, 1974).  

 

Illinois Physics Associate Head for Administration Jennifer Jorstad comments, “This award was created to recognize the hard work that the civil service and academic professional staff contribute to the mission of the department. Many of our staff go above and beyond their regular job responsibilities in order to serve the department. Those strong performers deserve to be recognized.”