In a new discovery regarding graphene, two research teams independently discovered a particular graphene system whose electrons "freeze" as temperature rises.

The first team, an international collaboration between Israel, the US, and Japan, discovered that stacking a graphene layer on top of another, and then twisting the top layer resulted in a graphene system where electrons freeze with rising temperature.

In an attempt to further understand this baffling observation, this first research team found that the entropy at the near-insulating phase of the system was about half of what was theoretically expected from free-electron spins.

As for the second team, also with members from Israel, the US, and Japan, they found the same graphene system and further studies revealed that a large magnetic moment existed in the insulating material.

Both studies appear in the journal Nature, April 7. One report was titled "Isospin Pomeranchuk effect in twisted bilayer graphene" and the other was "Entropic evidence for a Pomeranchuk effect in magic-angle graphene." Additionally, Biao Lian from Princeton University's Department of Physics published his News and Views articles on the two studies appearing in the same journal.

Moiré pattern arising from the superposition of two graphene lattices twisted by 4°.
(Photo: Ponor via Wikimedia Commons)

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Observing the Isospin Pomeranchuk Effect in Twisted Bilayer Graphene

A general observation for condensed-matter systems is that in higher temperatures, these systems often lean towards disorder. This, in turn, creates an upper critical temperature for a number of physical phenomena such as the material's magnetic properties and potential for superconductivity.

However, a noted exception for these tendencies is the so-called "Pomeranchuk effect," originally observed in liquid helium (3He), which freezes instead upon exposure to increasing temperature. This is attributed to the large entropy of liquid helium's paramagnetic solid phase, its "solid phase" having higher than average nuclear spin entropy, leading to the unusual behavior.

The research team, including members from the University of California at Santa Barbara and Brown University from the United States, the National Institute for Materials Science from Japan, and the Weizmann Institute of Science in Israel, demonstrated a similar phenomenon - this time in the context of spin dynamics and valley isospins for magic-angle twisted bilayer graphene (MATBG).

Aside from observing how electrons "freeze" with increasing temperature, researchers also noted that the entropy - expressed in units of Boltzmann's constant - is approximately half from disordered free-electron spins.

Additional Entropic Evidence from an Independent Study

The second research team - from Weizmann Institute of Science, Massachusetts Institute of Technology, and the National Insitute of Materials Science in Japan - also observed the Pomeranchuk effect in MATBG.

This study, however, used a combination of local and global electronic measurements of entropy to demonstrate that near the filling of one electron per moire unit cell, there exists a notable increase in the electronic entropy - about one Boltzmann constant per unit cell.

Additionally, this excess entropy is eventually "quenched" by an in-plane magnetic field, which creates a magnetic moment in the material. This moment is marked by a steep drop in the MATBG compressibility in relation to electron density.

Researchers also observed the discrepancy between the energy scales that characterize the observed properties in MATBG. The "compressibility jump" occurs at temperatures of about 30 Kelvin (about minus 243.15 degrees Celsius), while the bandwidth of the material's magnetic excitation occurs at about 3 Kelvin (about minus 270.15 degrees Celsius) or less.


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