Superconducting materials are like a carpool lane in a densely populated state. Like passengers riding together, electrons that pair up can bypass normal traffic and move through materials with zero friction.
But like carpools, how easily electron pairs can flow depends on a number of conditions, including the density of the pairs moving in the material. This “superfluid stiffness,” or the ease with which electron pairs flow, is a key measure of a material’s superconductivity.
Physicists from MIT and Harvard University have now, for the first time, directly measured the stiffness of a superfluid in “magic angle” graphene – materials made of two or more atomically thin sheets of graphene that are twisted together at exactly the right angle to enable a set of exceptional properties, including unconventional superconductivity.
This superconductivity makes magic-angle graphene a promising building block for future quantum computing devices, but exactly how the material becomes superconducting is not well understood. Knowledge of the material’s superfluid stiffness helps scientists identify the mechanism of superconductivity in magic-angle graphene.
The team’s measurements show that graphene’s magic-angle superconductivity is largely controlled by quantum geometry, which refers to the conceptual “shape” of quantum states that can exist in a particular material.
The results, published today in the journal Nature , are the first time scientists have directly measured the stiffness of a superfluid in a two-dimensional material. To do this, the team developed a new experimental method that can now be used to make similar measurements of other two-dimensional superconducting materials.
“There’s a whole family of 2D superconductors waiting to be explored, and we’re really just scratching the surface,” says study co-author Joel Wang, a research scientist at MIT’s Research Laboratory for Electronics (RLE).
Co-authors of the study from MIT’s main campus and MIT’s Lincoln Laboratory include co-author and former RLE postdoc Miyoko Tanaka, as well as Tao Dean, Daniel Rodan-Legrin, Samia Zaman, Max Heiss, Bharat Kanan, Aziza Almanacli, David Kim Warsky, Bettinkley, David Kimo Warsky, Jarillo Gurey-Horland’rero, and William D. Oliver, along with Kenji Watanabe and Takashi Taniguchi from the National Institute for Materials Science in Japan.
Magical resonance
Since its first isolation and identification in 2004, graphene has emerged as a remarkable material. The material is actually an atomically thin sheet of graphite, made up of a precise chicken wire of carbon atoms. This simple configuration can demonstrate a set of extraordinary properties in terms of graphene’s strength, durability, and ability to conduct electricity and heat.
In 2018, Jarillo-Herrero and his colleagues discovered that when two sheets of graphene are stacked at a precise “magic” angle, the twisted structure—now known as magic-angle twisted bilayer graphene, or MATBG—exhibits entirely new properties, including superconductivity in everyday life, like electrons. These so-called Cooper pairs can form a superfluid with a superconducting potential, meaning they can move through the material like a fluid, effortlessly and without friction.
“But even though Cooper pairs have no resistance, you have to apply pressure in the form of an electric field to get the current flowing,” Wang explains. The stiffness of a superfluid refers to how easy it is to move these particles to drive superconductivity.
Today, scientists can measure the stiffness of superconducting materials using methods that generally involve placing the material in a microwave resonator—a device with a specific resonant frequency in which an electrical signal oscillates at microwave frequencies, much like a vibrating violin string. When a superconducting material is placed in a microwave resonator, it can change the resonant frequency of the device, and specifically its “kinetic inductance,” to such an extent that scientists can directly relate this to the material’s superfluid stiffness.
Until now, however, such approaches have only been compatible with large, thick samples of materials. The MIT team realized they needed a new approach to measuring the stiffness of superfluids in atomically thin materials like MATBG.
“Compared to MATBG, a typical superconductor probed with resonators is 10 to 100 times thicker and has a larger surface area,” says Wang. We were unsure whether such a small material would even produce any measurable inductance.
Recorded signal
The challenge of measuring superfluid stiffness in MATBG is related to connecting very fine materials to the surface of the microwave resonator as smoothly as possible.
“You want to create an ideal lossless contact—that is, a superconductor—between the two materials,” Wang explains. Otherwise, the microwave signal you send out will be degraded or even reflected back instead of reaching the material you’re looking for.
Will Oliver’s group at MIT is developing techniques for precisely bonding extremely thin, two-dimensional materials with the goal of creating new types of quantum bits for future quantum computing devices. For their new study, Tanaka, Wang, and their colleagues used these techniques to seamlessly attach a small sample of MATBG to the end of an aluminum microwave resonator. To do this, the group first used conventional methods to assemble the MATBG, then sandwiched the structure between two insulating layers of hexagonal boron nitride to help preserve the atomic structure and properties of the MATBG.
“Aluminum is a material that we regularly use in research on superconducting quantum computers, for example, aluminum resonators for reading aluminum quantum bits (qubits),” Oliver explains. So we thought, why not make most of the resonator out of aluminum, which is relatively easy for us, and then add a little MATBG at the end? “It turned out to be a good idea.”
“To call a MATBG, we carve it very sharply, like cutting layers of a cake with a very sharp knife,” says Wang. We expose one side of the freshly cut MATBG, and then place aluminum—the same resonant material—on top to make good contact and form an aluminum lead.
The researchers then connected the aluminum conductors of the MATBG structure to a larger aluminum microwave resonator. They sent a microwave signal through the resonator and measured the resulting change in its resonant frequency, from which they could infer the kinetic inductance of the MATBG.
But when they converted the measured inductance into a value for the stiffness of the superfluid, the researchers found that it was much larger than conventional theories of superconductivity predicted. They thought the excess was related to the quantum geometry of MATBG—how the quantum states of electrons are related to each other.
” We observed a tenfold increase in the stiffness of the superfluid compared to conventional expectations, with a temperature dependence consistent with what quantum geometry theory predicts,” says Tanaka. This was a “smoking gun” that pointed to the role of quantum geometry in controlling the stiffness of the superfluid in this two-dimensional material.
“This work is an excellent example of how sophisticated quantum technology, currently used in quantum circuits, can be used to investigate dense matter systems composed of strongly interacting particles,” adds Jarillo-Herrero.
This research was funded in part by the U.S. Army Research Office, the National Science Foundation, the U.S. Air Force Office of Scientific Research, and the U.S. Assistant Secretary of Defense for Research and Engineering.
A complementary study on magic-angle twisted trilayer graphene (MATTG), conducted in collaboration with Philip Kim’s group at Harvard University and the Jarillo-Herrero group at MIT, appears in the same issue of Nature.
