Surprising Entropy Measurements Reveal Exotic Effect in “Magic-Angle” Graphene

Pomeranchuk Effect in Magic Angle Graphene

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Pomeranchuk result in magic angle graphene, exposing an unique shift in between 2 stages: A (Fermi) liquid stage, where the spatial positions of electrons are disordered however their magnetic minutes (arrows) are completely lined up, and a solid-like stage where the electrons are bought in area however their magnetic minutes are varying easily. Counterintuitively, the liquid stage changes to the solid-like stage upon heating. Credit: Weizmann Institute of Science

Researchers at the Weizmann Institute of Science and the Massachusetts Institute of Technology find an unexpected stage shift in twisted bilayer graphene.

Most products go from being solids to liquids when they are heated up. One unusual counter-example is helium-3, which can strengthen upon heating. This counterproductive and unique result, called the Pomeranchuk result, might now have actually discovered its electronic analog in a product called magic-angle graphene, states a group of scientists from the Weizmann Institute of Science led by Prof. Shahal Ilani, in cooperation with Prof. Pablo Jarillo-Herrero’s group at the Massachusetts Institute of Technology (MIT).

This result, released today (April 7, 2021) in Nature, comes thanks to the very first measurement of electronic entropy in an atomically-thin 2 dimensional product. “Entropy describes the level of disorder in a material and determines which of its phases is stable at different temperatures,” discusses Ilani. “Our team set up to measure the electronic entropy in magic angle graphene to resolve some of its outstanding mysteries, but discovered another surprise.”

Giant magnetic entropy

Entropy is a fundamental physical amounts that is hard to comprehend or determine straight. At low temperature levels, the majority of the degrees of flexibility in a performing product freeze out, and just the electrons add to the entropy. In bulk products, there is an abundance of electrons, and therefore it is possible to determine their heat capability and from that deduce the entropy. In an atomically-thin two-dimensional product, due to the little number of electrons, such a measurement ends up being very difficult. So far, no experiments was successful in determining the entropy in such systems.

To determine the entropy, the Weizmann group utilized a unique scanning microscopic lense consisting of a carbon nanotube single-electron transistor placed at the edge of a scanning probe cantilever. This instrument can spatially image the electrostatic capacity produced by electrons in a product, with an extraordinary level of sensitivity. Based on Maxwell’s relations that link the various thermodynamic homes of a product, one can utilize these electrostatic measurements to straight penetrate the entropy of the electrons.

“When we performed the measurements at high magnetic fields, the entropy looked absolutely normal, following the expected behavior of a conventional (Fermi) liquid of electrons, which is the most standard state in which electrons exist at low temperatures. Surprisingly, however, at zero magnetic field, the electrons exhibited giant excess entropy, whose presence was very mysterious.” states Ilani. This huge entropy emerged when the variety of electrons in the system had to do with one per each website of the synthetic “superlattice” formed in magic angle graphene.

Artificial “superlattice” in twisted layers of graphene

Graphene is a one atom thick crystal of carbon atoms organized in a hexagonal lattice. When 2 graphene sheets are put on top of each other with a little and unique, or “magic,” misalignment angle, a routine moiré pattern appears that functions as a synthetic “superlattice” for the electrons in the product. Moiré patterns are a popular result in materials and emerge anywhere one mesh overlays another at a small angle.

In magic angle graphene, the electrons are available in 4 tastes: spin “up” or spin “down,” and 2 “valleys.” Each moiré website can therefore hold up to 4 electrons, among each taste.

Researchers currently understood that this system acts as a basic insulator when all moiré websites are totally complete (4 electrons per website). In 2018, nevertheless, Prof. Jarillo-Herrero and coworkers found to their surprise that it can be insulating at other integer fillings (2 or 3 electrons per moiré website), which might just be discussed if a correlated state of electrons is formed. However, near a filling of one electron per moiré website, the large bulk of transportation measurements showed that the system is rather basic, acting as a common metal. This is precisely where the entropy measurements by the Weizmann-MIT group discovered the most unexpected outcomes.

“In contrast to the behavior seen in transport near a filling of one electron per moiré site, which is quite featureless, our measurements indicated that thermodynamically, the most dramatic phase transition occurs at this filling,” states Dr. Asaf Rozen, a lead author in this work. “We realized that near this filling, upon heating the material, a rather conventional Fermi liquid transforms into a correlated metal with a giant magnetic entropy. This giant entropy (of about 1 Boltzmann constant per lattice site) could only be explained if each moiré site has a degree of freedom that is completely free to fluctuate.”

An electronic analog of the Pomeranchuk result

“This unusual excess entropy reminded us of an exotic effect that was discovered about 70 years ago in helium-3,” states Weizmann theorist Prof. Erez Berg. “Most materials, when heated up, transform from a solid to a liquid. This is because a liquid always has more entropy than the solid, as the atoms move more erratically in the liquid than in the solid.” In helium-3, nevertheless, in a little part of the stage diagram, the product acts totally oppositely, and the greater temperature level stage is the strong. This habits, forecasted by Soviet theoretical physicist Isaak Pomeranchuk in the 1950s, can just be discussed by the presence of another “hidden” source of entropy in the system. In the case of helium-3, this entropy originates from the easily turning nuclear spins. “Each atom has a spin in its nucleus (an ‘arrow’ that can point in any direction),” discusses Berg. “In liquid helium-3, due to the Pauli exclusion principle, exactly half of the spins must point up and half must point down, so spins cannot freely rotate. In the solid phase, however, the atoms are localized and never come close to each other, so their nuclear spins can freely rotate.”

“The giant excess entropy that we observed in the correlated state with one electron per moiré site is analogous to the entropy in solid helium-3, but instead of atoms and nuclear spins, in the case of magic angle graphene we have electrons and electronic spins (or valley magnetic moments),” he states.

The magnetic stage diagram

To develop the relation with the Pomeranchuk result even more, the group carried out comprehensive measurements of the stage diagram. This was done by determining the “compressibility” of the electrons in the system- that is, how tough it is to squeeze extra electrons into a provided lattice website (such a measurement was shown in twisted bilayer graphene in the group’s previous work). This measurement exposed 2 unique stages separated by a sharp drop in the compressibility: a low-entropy, electronic liquid-like stage, and a high-entropy solid-like stage with totally free magnetic minutes. By following the drop in the compressibility, the scientists mapped the border in between the 2 stages as a function of temperature level and electromagnetic field, showing that the stage border acts exactly as gotten out of the Pomerachuk result.

“This new result challenges our understanding of magic angle graphene,” states Berg. “We imagined that the phases in this material were simple – either conducting or insulating, and expected that at such low temperatures, all the electronic fluctuations are frozen out. This turns out not to be the case, as the giant magnetic entropy shows.”

“The new findings will provide fresh insights into the physics of strongly correlated electron systems and perhaps even help explain how such fluctuating spins affect superconductivity,” he includes.

The scientists acknowledge that they do not yet understand how to describe the Pomeranchuk result in magic angle graphene. Is it precisely as in helium-3 because the electrons in the solid-like stage stay at a country mile from each other, permitting their magnetic minutes to remain totally totally free? “We are not sure,” confesses Ilani, “since the phase we have observed has a ‘spit personality’ – some of its properties are associated with itinerant electrons while others can only be explained by thinking of the electrons as being localized on a lattice.”

Reference: “Entropic evidence for a Pomeranchuk effect in magic-angle graphene” by Asaf Rozen, Jeong Min Park, Uri Zondiner, Yuan Cao, Daniel Rodan-Legrain, Takashi Taniguchi, Kenji Watanabe, Yuval Oreg, Ady Stern, Erez Berg, Pablo Jarillo-Herrero and Shahal Ilani, 7 April 2021, Nature.
DOI: 10.1038/s41586-021-03319-3

Prof. Shahal Ilani’s research study is supported by the Sagol Weizmann-MIT Bridge Program; the André Deloro Prize for Scientific Research; the Rosa and Emilio Segre Research Award; and the Leona M. and Harry B. Helmsley Charitable Trust.

Prof. Erez Berg’s research study is supported by Irving and Cherna Moskowitz.

Prof. Yuval Oreg’s research study is supported by the Lady Davis Professorial Chair of Experimental Physics. Prof. Oreg is the Head of the Maurice and Gabriella Goldschleger Center for Nanophysics.

Prof. Ady Stern’s research study is supported by the Veronika A. Rabl Physics Discretionary Fund and the Zuckerman STEM Leadership Program.