Entropy measurements reveal exotic effect in ‘magic-angle’ graphene: Researchers discover a surprising phase transition in twisted bilayer graphene

Most supplies go from being solids to liquids when they’re heated. One uncommon counter-example is helium-3, which might solidify upon heating. This counterintuitive and unique impact, referred to as the Pomeranchuk impact, might now have discovered its digital analogue in a cloth referred to as magic-angle graphene, says a crew of researchers from the Weizmann Institute of Science led by Prof. Shahal Ilani, in collaboration with Prof. Pablo Jarillo-Herrero’s group on the Massachusetts Institute of Know-how (MIT).

This end result, printed in the present day in Nature, comes due to the primary ever measurement of digital entropy in an atomically-thin two dimensional materials. “Entropy describes the extent of dysfunction in a cloth and determines which of its phases is secure at completely different temperatures,” explains Ilani. “Our crew set as much as measure the digital entropy in magic angle graphene to resolve a few of its excellent mysteries, however found one other shock”.

Big magnetic entropy

Entropy is a fundamental bodily portions that isn’t simple to know or measure immediately. At low temperatures, a lot of the levels of freedom in a conducting materials freeze out, and solely the electrons contribute to the entropy. In bulk supplies, there may be an abundance of electrons, and thus it’s doable to measure their warmth capability and from that deduce the entropy. In an atomically-thin two-dimensional materials, as a result of small variety of electrons, such a measurement turns into extraordinarily difficult. Thus far, no experiments succeeded in measuring the entropy in such programs.

To measure the entropy, the Weizmann crew used a novel scanning microscope comprising of a carbon nanotube single-electron transistor positioned on the fringe of a scanning probe cantilever. This instrument can spatially picture the electrostatic potential produced by electrons in a cloth, with an unprecedented sensitivity. Based mostly on Maxwell’s relations that join the completely different thermodynamic properties of a cloth, one can use these electrostatic measurements to immediately probe the entropy of the electrons.

“After we carried out the measurements at excessive magnetic fields, the entropy regarded completely regular, following the anticipated behaviour of a standard (Fermi) liquid of electrons, which is essentially the most commonplace state through which electrons exist at low temperatures. Surprisingly, nevertheless, at zero magnetic area, the electrons exhibited large extra entropy, whose presence was very mysterious.” says Ilani. This large entropy emerged when the variety of electrons within the system was about one per every website of the factitious “superlattice” fashioned in magic angle graphene.


Synthetic “superlattice” in twisted layers of graphene

Graphene is a one atom thick crystal of carbon atoms organized in a hexagonal lattice. When two graphene sheets are positioned on high of one another with a small and particular, or “magic”, misalignment angle, a periodic moiré sample seems that acts as a man-made “superlattice” for the electrons within the materials. Moiré patterns are a preferred impact in materials and emerge wherever one mesh overlays one other at a slight angle.

In magic angle graphene, the electrons are available in 4 flavours: spin “up” or spin “down”, and two “valleys”. Every moiré website can thus maintain as much as 4 electrons, one in every of every flavour.

Researchers already knew that this technique behaves as a easy insulator when all moiré websites are utterly full (4 electrons per website). In 2018, nevertheless, Prof. Jarillo-Herrero and colleagues found to their shock that it may be insulating at different integer fillings (two or three electrons per moiré website), which may solely be defined if a correlated state of electrons is fashioned. Nonetheless, close to a filling of 1 electron per moiré website, the overwhelming majority of transport measurements indicated that the system is sort of easy, behaving as an bizarre metallic. That is precisely the place the entropy measurements by the Weizmann-MIT crew discovered essentially the most stunning outcomes.

“In distinction to the behaviour seen in transport close to a filling of 1 electron per moiré website, which is sort of featureless, our measurements indicated that thermodynamically, essentially the most dramatic part transition happens at this filling”, says Dr. Asaf Rozen, a lead writer on this work. “We realized that close to this filling, upon heating the fabric, a relatively standard Fermi liquid transforms right into a correlated metallic with an enormous magnetic entropy. This large entropy (of about 1 Boltzmann fixed per lattice website) may solely be defined if every moiré website has a level of freedom that’s utterly free to fluctuate”.


An digital analogue of the Pomeranchuk impact

“This uncommon extra entropy reminded us of an unique impact that was found about 70 years in the past in helium-3”, says Weizmann theorist Prof. Erez Berg. “Most supplies, when heated up, remodel from a strong to a liquid. It’s because a liquid all the time has extra entropy than the strong, because the atoms transfer extra erratically within the liquid than within the strong.” In helium-3, nevertheless, in a small a part of the part diagram, the fabric behaves utterly oppositely, and the upper temperature part is the strong. This behaviour, predicted by Soviet theoretical physicist Isaak Pomeranchuk within the Fifties, can solely be defined by the existence of one other “hidden” supply of entropy within the system. Within the case of helium-3, this entropy comes from the freely rotating nuclear spins. “Every atom has a spin in its nucleus (an ‘arrow’ that may level in any course),” explains Berg. “In liquid helium-3, as a result of Pauli exclusion precept, precisely half of the spins should level up and half should level down, so spins can not freely rotate. Within the strong part, nevertheless, the atoms are localized and by no means come shut to one another, so their nuclear spins can freely rotate.”

“The enormous extra entropy that we noticed within the correlated state with one electron per moiré website is analogous to the entropy in strong helium-3, however as an alternative of atoms and nuclear spins, within the case of magic angle graphene we’ve got electrons and digital spins (or valley magnetic moments)”, he says.

The magnetic part diagram

To ascertain the relation with the Pomeranchuk impact additional, the crew carried out detailed measurements of the part diagram. This was accomplished by measuring the “compressibility” of the electrons within the system- that’s, how exhausting it’s to squeeze extra electrons right into a given lattice website (such a measurement was demonstrated in twisted bilayer graphene within the crew’s earlier work). This measurement revealed two distinct phases separated by a pointy drop within the compressibility: a low-entropy, digital liquid-like part, and a high-entropy solid-like part with free magnetic moments. By following the drop within the compressibility, the researchers mapped the boundary between the 2 phases as a operate of temperature and magnetic area, demonstrating that the part boundary behaves exactly as anticipated from the Pomerachuk impact.

“This new end result challenges our understanding of magic angle graphene,” says Berg. “We imagined that the phases on this materials had been easy – both conducting or insulating, and anticipated that at such low temperatures, all of the digital fluctuations are frozen out. This seems to not be the case, as the large magnetic entropy exhibits”.

“The brand new findings will present contemporary insights into the physics of strongly correlated electron programs and even perhaps assist clarify how such fluctuating spins have an effect on superconductivity,” he provides.

The researchers acknowledge that they don’t but know the right way to clarify the Pomeranchuk impact in magic angle graphene. Is it precisely as in helium-3 in that the electrons within the solid-like part stay at a fantastic distance from one another, permitting their magnetic moments to remain utterly free? “We aren’t positive,” admits Ilani, “for the reason that part we’ve got noticed has a ‘spit character’ – a few of its properties are related to itinerant electrons whereas others can solely be defined by considering of the electrons as being localized on a lattice”.