Dirac Electrons Come Back to Life in Magic-Angle Graphene – Unusual Breaking of Symmetry

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Dirac Electrons

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The symmetry-breaking stage shift in magic-angle graphene. The 4 ‘flavors’ of Dirac electrons filling their energy levels are represented by 4 ‘liquids’ filling cone-shaped glasses. Credit: Weizmann Institute of Science

A brand-new symmetry-broken moms and dad state found in twisted bilayer graphene.

In 2018 it was found that 2 layers of graphene twisted one with regard to the other by a “magic” angle reveal a range of fascinating quantum stages, consisting of superconductivity, magnetism, and insulating habits. Now a group of scientists from the Weizmann Institute of Science led by Prof. Shahal Ilani of the Condensed Matter Physics Department, in partnership with Prof. Pablo Jarillo-Herrero’s group at MIT, have actually found that these quantum stages come down from a formerly unidentified high-energy “parent state,” with an uncommon breaking of balance.

Graphene is a flat crystal of carbon, simply one atom thick. When 2 sheets of this product are put on top of each other, misaligned at little angle, a regular “moiré” pattern appears. This pattern supplies a synthetic lattice for the electrons in the product. In this twisted bilayer system the electrons can be found in 4 “flavors”: spins “up” or “down,” integrated with 2 “valleys” that come from the graphene’s hexagonal lattice. As an outcome, each moiré website can hold up to 4 electrons, among each taste.

While scientists currently understood that the system acts as an easy insulator when all the moiré websites are totally complete (4 electrons per website), Jarillo-Herrero and his coworkers found to their surprise, in 2018, that at a particular “magic” angle, the twisted system likewise ends up being insulating at other integer fillings (2 or 3 electrons per moiré website). This habits, displayed by magic-angle twisted bilayer graphene (MATBG), cannot be discussed by single particle physics, and is frequently referred to as a “correlated Mott insulator.” Even more unexpected was the discovery of unique superconductivity near to these fillings. These findings resulted in a flurry of research study activity intending to respond to the huge concern: what is the nature of the brand-new unique states found in MATBG and comparable twisted systems?

Imaging magic-angle graphene electrons with a carbon nanotube detector

The Weizmann group set out to comprehend how engaging electrons act in MATBG utilizing a unique kind of microscopic lense that uses a carbon nanotube single-electron transistor, placed at the edge of a scanning probe cantilever. This instrument can image, in genuine area, the electrical capacity produced by electrons in a product with severe level of sensitivity.

“Using this tool, we could image for the first time the ‘compressibility’ of the electrons in this system – that is, how hard it is to squeeze additional electrons into a given point in space,” discusses Ilani. “Roughly speaking, the compressibility of electrons reflects the phase they are in: In an insulator, electrons are incompressible, whereas in a metal they are highly compressible.”

Compressibility likewise exposes the “effective mass” of electrons. For example, in routine graphene the electrons are exceptionally “light,” and hence act like independent particles that virtually overlook the existence of their fellow electrons. In magic-angle graphene, on the other hand, electrons are thought to be exceptionally “heavy” and their habits is hence controlled by interactions with other electrons ‒ a reality that lots of scientists credit to the unique stages discovered in this product. The Weizmann group for that reason anticipated the compressibility to reveal a really easy pattern as a function of electron filling: interchanging in between a highly-compressible metal with heavy electrons and incompressible Mott insulators that appear at each integer moiré lattice filling. 

To their surprise, they observed a greatly various pattern. Instead of a symmetric shift from metal to insulator and back to metal, they observed a sharp, uneven dive in the electronic compressibility near the integer fillings.

“This means that the nature of the carriers before and after this transition is markedly different,” states research study lead author Uri Zondiner. “Before the transition the carriers are extremely heavy, and after it they seem to be extremely light, reminiscent of the ‘Dirac electrons’ that are present in graphene.”

The very same habits was seen to repeat near every integer filling, where heavy providers suddenly paved the way and light Dirac-like electrons reappeared.

But how can such an abrupt modification in the nature of the providers be comprehended? To address this concern, the group interacted with Weizmann theorists Profs. Erez Berg, Yuval Oreg and Ady Stern, and Dr. Raquel Quiroez; in addition to Prof. Felix von-Oppen of Freie Universität Berlin. They built an easy design, exposing that electrons fill the energy bands in MATBG in an extremely uncommon “Sisyphean” way: when electrons begin filling from the “Dirac point” (the point at which the valence and conduction bands simply touch each other), they act usually, being dispersed similarly amongst the 4 possible tastes. “However, when the filling nears that of an integer number of electrons per moiré superlattice site, a dramatic phase transition occurs,” discusses research study lead author Asaf Rozen. “In this transition, one flavor ‘grabs’ all the carriers from its peers, ‘resetting’ them back to the charge-neutral Dirac point.”  

“Left with no electrons, the three remaining flavors need to start refilling again from scratch. They do so until another phase transition occurs, where this time one of the remaining three flavors grabs all the carriers from its peers, pushing them back to square one. Electrons thus need to climb a mountain like Sisyphus, being constantly pushed back to the starting point in which they revert to the behavior of light Dirac electrons,” states Rozen. While this system remains in an extremely symmetric state at low provider fillings, in which all the electronic tastes are similarly occupied, with more filling it experiences a waterfall of symmetry-breaking stage shifts that consistently lower its balance.

A “parent state”

“What is most surprising is that the phase transitions and Dirac revivals that we discovered appear at temperatures well above the onset of the superconducting and correlated insulating states observed so far,” states Ilani. “This indicates that the broken symmetry state we have seen is, in fact, the ‘parent state’ out of which the more fragile superconducting and correlated insulating ground states emerge.”

The strange method which the balance is broken has essential ramifications for the nature of the insulating and superconducting states in this twisted system.

“For example, it is well known that stronger superconductivity arises when electrons are heavier. Our experiment, however, demonstrates the exact opposite: superconductivity appears in this magic-angle graphene system after a phase transition has revived the light Dirac electrons. How this happens, and what it tells us about the nature of superconductivity in this system compared to other more conventional forms of superconductivity remain interesting open questions,” states Zondiner.

A comparable waterfall of stage shifts was reported in another paper released in the very same Nature problem by Prof. Ali Yazdani and coworkers at Princeton University. “The Princeton team studied MATBG using a completely different experimental technique, based on a highly-sensitive scanning tunneling microscope, so it is very reassuring to see that complementary techniques lead to analogous observations,” states Ilani.

The Weizmann and MIT scientists state they will now utilize their scanning nanotube single-electron-transistor platform to respond to these and other standard concerns about electrons in numerous twisted-layer systems: What is the relationship in between the compressibility of electrons and their evident transportation residential or commercial properties? What is the nature of the correlated states that form in these systems at low temperature levels? And what are the basic quasiparticles that comprise these states?

Reference: “Cascade of phase transitions and Dirac revivals in magic-angle graphene” by U. Zondiner, A. Rozen, D. Rodan-Legrain, Y. Cao, R. Queiroz, T. Taniguchi, K. Watanabe, Y. Oreg, F. von Oppen, Ady Stern, E. Berg, P. Jarillo-Herrero and S. Ilani, 11 June 2020, Nature.
DOI: 10.1038/s41586-020-2373-y

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



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