Superconducting substances resemble the carpool lane on a busy highway. Just like passengers who share rides, paired electrons can evade the typical congestion, gliding through the material without any friction.
However, akin to carpools, the flow of electron pairs is influenced by various factors, such as the concentration of pairs traversing the material. This “superfluid rigidity,” or the facility with which a stream of electron pairs can navigate, is a crucial indicator of a material’s superconductivity.
Researchers at MIT and Harvard University have now successfully measured superfluid rigidity for the initial time in “magic-angle” graphene — substances formed by overlaying two or more atomically thin sheets of graphene twisted at the precise angle to unlock a range of remarkable characteristics, including unconventional superconductivity.
This superconductivity renders magic-angle graphene a potential cornerstone for upcoming quantum-computing technologies, yet the precise mechanism of how the material becomes superconducting remains unclear. Understanding the superfluid rigidity of the material will aid scientists in uncovering the superconductivity mechanism in magic-angle graphene.
The findings from the team imply that the superconductivity in magic-angle graphene is predominantly dictated by quantum geometry, which pertains to the theoretical “shape” of quantum states that can manifest within a specific material.
The outcomes, which are discussed today in the journal Nature, represent the inaugural instance of researchers directly measuring superfluid rigidity in a two-dimensional material. In achieving this, the team devised a novel experimental technique that can now be employed to perform similar assessments on other two-dimensional superconducting materials.
“There exists an entire class of 2D superconductors waiting to be explored, and we are merely beginning,” states study co-lead author Joel Wang, a research scientist in MIT’s Research Laboratory of Electronics (RLE).
The study’s co-authors from both MIT’s primary campus and MIT Lincoln Laboratory encompass co-lead author and former RLE postdoctoral researcher Miuko Tanaka, alongside Thao Dinh, Daniel Rodan-Legrain, Sameia Zaman, Max Hays, Bharath Kannan, Aziza Almanakly, David Kim, Bethany Niedzielski, Kyle Serniak, Mollie Schwartz, Jeffrey Grover, Terry Orlando, Simon Gustavsson, Pablo Jarillo-Herrero, and William D. Oliver, alongside Kenji Watanabe and Takashi Taniguchi from the National Institute for Materials Science in Japan.
Magic resonance
Since its initial isolation and characterization in 2004, graphene has emerged as an extraordinary material. The substance consists of a single, atom-thin layer of graphite arranged in an intricate lattice of carbon atoms resembling chicken wire. This straightforward structure can display an array of extraordinary characteristics in terms of its strength, durability, and capacity to conduct electricity and heat.
In 2018, Jarillo-Herrero and his team discovered that when two graphene sheets are stacked at a specific “magic” angle, the twisted arrangement — now termed magic-angle twisted bilayer graphene, or MATBG — reveals entirely novel attributes, including superconductivity, wherein electrons form pairs instead of repelling each other as seen in conventional materials. These so-called Cooper pairs can create a superfluid, with the potential for superconductivity, implying they could flow through the material as a seamless, frictionless current.
“Yet, despite the fact that Cooper pairs experience no resistance, some force, in the form of an electric field, must be applied for the current to flow,” Wang clarifies. “Superfluid rigidity indicates how effortlessly these particles can be set in motion to facilitate superconductivity.”
Currently, scientists can gauge superfluid rigidity in superconducting substances using techniques that generally involve positioning the material within a microwave resonator — a device characterized by a resonance frequency where an electrical signal oscillates at microwave frequencies, akin to a vibrating violin string. When a superconducting material is inserted into a microwave resonator, it can alter the device’s resonance frequency, particularly its “kinetic inductance,” by an amount that scientists can directly correlate with the material’s superfluid rigidity.
Nevertheless, such methodologies have thus far only been suitable for large, thick material samples. The MIT team recognized that a new strategy would be necessary to evaluate superfluid rigidity in atomically thin substances such as MATBG.
“In comparison to MATBG, the usual superconductors examined with resonators are 10 to 100 times thicker and cover a larger area,” Wang asserts. “We were uncertain if such a minuscule material would generate any measurable inductance.”
A captured signal
The difficulty in measuring superfluid rigidity in MATBG lies in the challenge of integrating the incredibly fragile material onto the surface of the microwave resonator as seamlessly as possible.
“For this to function, you need to establish an ideally lossless — i.e., superconducting — connection between the two materials,” Wang clarifies. “Otherwise, the microwave signal you transmit will be diminished or may simply bounce back instead of penetrating into your target material.”
Will Oliver’s team at MIT has been developing techniques to accurately connect extremely fragile, two-dimensional materials, aiming to create new types of quantum bits for future quantum-computing applications. For their latest study, Tanaka, Wang, and their colleagues utilized these methods to connect a tiny sample of MATBG to the tip of an aluminum microwave resonator seamlessly. To accomplish this, the group initially employed traditional techniques to fabricate MATBG, then enclosed the structure between two insulating layers of hexagonal boron nitride, preserving MATBG’s atomic characteristics and properties.
“Aluminum is a commonly used material in our superconducting quantum computing research, such as aluminum resonators for reading out aluminum quantum bits (qubits),” Oliver elaborates. “Thus, we thought, why not construct most of the resonator from aluminum, which is quite manageable for us, and then add a little MATBG to the tip? This proved to be a wise decision.”
“To contact the MATBG, we etch it very precisely, akin to slicing through layers of a cake with a sharp knife,” Wang notes. “We expose a side of the freshly cut MATBG, onto which we subsequently deposit aluminum — the same material as the resonator — to establish a strong connection and form an aluminum lead.”
The researchers then linked the aluminum leads of the MATBG structure to the larger aluminum microwave resonator. They transmitted a microwave signal through the resonator and observed the ensuing shift in its resonance frequency, from which they could deduce the kinetic inductance of the MATBG.
Upon converting the measured inductance into a superfluid rigidity value, the researchers discovered it was significantly greater than what traditional superconductivity theories had anticipated. They suspected that this excess was related to MATBG’s quantum geometry — the manner in which the quantum states of electrons interconnect.
“We noted a tenfold increase in superfluid rigidity compared to standard expectations, with a temperature dependency consistent with predictions made by the theory of quantum geometry,” Tanaka remarks. “This served as a ‘smoking gun’ indicating the influence of quantum geometry on superfluid rigidity in this two-dimensional material.”
“This work exemplifies how sophisticated quantum technology currently applied in quantum circuits can be leveraged to explore condensed matter systems comprised of strongly interacting particles,” emphasizes Jarillo-Herrero.
This research received support, in part, from the U.S. Army Research Office, the National Science Foundation, the U.S. Air Force Office of Scientific Research, and the U.S. Under Secretary of Defense for Research and Engineering. The work was conducted, in part, using facilities at MIT.nano.
A related study on magic-angle twisted trilayer graphene (MATTG), conducted by a collaboration between Philip Kim’s group at Harvard University and Jarillo-Herrero’s group at MIT appears in the same issue of Nature.