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Superconductivity is an advantageous physical phenomenon observed in some materials, which entails an electrical resistance of zero below specific critical temperatures. This phenomenon is known to arise following the formation of so-called Cooper pairs (i.e., pairs of electrons).

There are two known types of superconductivity, known as conventional and unconventional superconductivity. In conventional superconductors, the formation of Cooper pairs is mediated by the interaction between electrons and phonons (i.e., vibrations in a crystal's lattice), as explained by Bardeen-Cooper-Schrieffer (BCS) theory.

Unconventional superconductors, on the other hand, are materials that exhibit a superconductivity that is not prompted by electron–phonon interactions. While many past studies have tried to shed light on the mechanisms underpinning unconventional superconductivity, its underlying physics remains poorly understood.

Researchers at Massachusetts Institute of Technology (MIT), Harvard University and the National Institute for Materials Science in Japan recently set out to better understand the mechanisms behind the unconventional superconductivity observed in twisted graphene moiré heterostructures, material consisting of stacked graphene sheets twisted at an angle of approximately 1.1°.

Their paper, in ÌÇÐÄÊÓƵical Review Letters, unveils a large and tunable kinetic inductance (i.e., a resistance to changes in current prompted by the inertia of charge carriers) in twisted trilayer graphene, offering new insight about the underpinnings of superconductivity in moiré materials.

"It was quite a moment when Pablo Jarillo-Herrero and his team made public a ," Paritosh Karnatak, co-senior author of the paper, told ÌÇÐÄÊÓƵ. "They demonstrated that two graphene layers twisted with respect to each other at a particular, small angle showed superconductivity in a certain doping range (number density of charge carriers), and other unexpected, correlated states.

"This discovery immediately caught our attention since our research group had been working for some years already on graphene monolayer and bilayer stacks, and we were quite experienced in the physics of superconductivity and the use of such materials for superconducting devices."

After learning about the work by Jarillo-Herrero and his colleagues, the researchers set out to conduct their own research focusing on the superconductivity of twisted graphene moiré materials. They were particularly intrigued by results indicating that these materials are unconventional superconductors that in some ways resemble high-Tc superconductors (i.e., materials exhibiting zero resistance at temperatures significantly higher than those predicted by conventional superconductivity theories).

"In the twisted graphene superconductor one can change the doping state just by tuning a knob, in practice by changing a gate voltage, while this is not possible in a solid-state high-Tc superconductor, where one must grow a new crystal for each desired doping," said Karnatak. "Our primary objective was thus to see if we could realize superconducting junctions, often generically called Josephson junctions, in a magic angle twisted graphene stack and, through the characterization of the junctions, reveal some properties of this superconducting state."

As part of their study, Karnatak and his colleagues first realized superconducting junctions in magic angle twisted graphene. These junctions are regions in which two superconducting materials (i.e., leads) are connected, separated only by a thin barrier.

"We used superconducting leads made from a conventional superconductor," explained Christian Schönenberger, co-senior author of the paper. "The two leads are narrowed down to a scale below one micrometer and they are also separated from each other by a short distance, typically also in the micrometer or sub-micrometer scale. In between the 'tips' of the two leads sits the MATG stack. The doping of the stack can be controlled by another gate electrode, also fabricated close to the junction."

If the MATG stack in superconducting junctions is not superconducting, but is instead made up of a normal metal, the devices are referred to as S-N-S junctions. In this context, "S" stands for "superconductor," while "N" stands for "normal metal."

"The two S's in the notation S-N-S denote the two leads that connect to the N part, the normal metal part," said Schönenberger. "If, on the other hand, the stack becomes superconducting, we term the junction a weak link and denote it as S-S'-S, where S' refers to the superconducting MATG stack.

"By measuring the supercurrent as a function of (phase) bias, one obtains characteristic properties of the junctions, and, most importantly, an S-N-S and an S-S'-S junction display different supercurrent dependencies. In our experiment, we resolve this difference by showing that a junction with MATG turns into a weak link, an S-S'-S device, when entering the phase space (controlled by temperature and doping state) where the resistance drops to small values, indicative of a superconducting state."

The observation of a low resistance in these junctions, such as that reported by the researchers, hints at the presence of superconductivity. However, this low resistance alone is not a proof of superconductivity, thus the team also had to demonstrate that their material expelled magnetic fields.

"This is exactly what we demonstrated," said Schönenberger. "The weak-link characteristics shows that the material behaves as an inductor, and not as a resistor, whose value we deduce in the experiment."

Ultimately, Karnatak, Schönenberger and their colleagues were able to quantify the kinetic inductance of magic angle twisted trilayer graphene, which is inductance that arises from the inertia of paired electrons in the superconducting state. Notably, the kinetic inductance they measured reached values almost 50 times larger than those observed in known superconductors with a high kinetic inductance.

This is a highly promising result, as high kinetic inductance superconductors are typically advantageous for the development of quantum technologies. Earlier studies suggest that they could be particularly promising for advancing single photon detectors, superconducting quantum bit platforms and quantum sensing systems.

"Given the gate tunability of the superconductor, we study the inverse scaling relationship between the kinetic inductance and the critical current (the maximum at which a superconductor becomes a normal conductor) in a single device," said Schönenberger.

"This inverse relation between the kinetic inductance and the critical current also reveals the coherence length of the superconductor—roughly speaking the 'size' of the electron pairs responsible for the superconducting state. We measure a larger coherence length than reported in earlier studies, using different experimental methods, on this material."

While the mechanisms "binding" electrons in unconventional superconductors are not yet clear, this recent study could help to uncover them. Specifically, it introduces experimental methods to quantify kinetic inductance in superconductors and measure the length of their coherence.

"We believe that our study will lead to small steps in the direction of providing hints for understanding superconductivity in these materials and perhaps towards the search for other novel superconductors," said Schönenberger.

The recent work by Karnatak, Schönenberger and their colleagues could soon inspire further studies assessing the kinetic inductance and quantum coherence in moiré superconductors. The researchers are now planning to continue investigating the underpinnings of superconductivity in twisted trilayer graphene and other twisted graphene moiré heterostructures.

"While we show that this material shows large kinetic inductance values, its application potential in quantum technologies depends on its characteristics at high (microwave) frequencies," said Karnatak. "We are performing such experiments by building superconducting circuits at high frequencies."

The material studied by the researchers does not exist in nature and needs to be carefully engineered in laboratory settings, thus it might not be ideal for the large-scale development of quantum technologies. As it also easily relaxes back into its natural state and is prone to disorder, eventually material scientists will need to identify other easily sourced graphene-based materials that exhibit similar characteristics.

"The discovery of superconductivity in these 'twisted' materials compelled researchers to look harder at other naturally occurring graphitic materials," added Karnatak. "In fact, superconductivity was also recently discovered in many other graphite-based materials that have been studied for nearly two decades. These materials may be more practical for both fundamental research and perhaps practical applications. We are keen on studying these materials with the experimental tools that we have developed."

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