During his time as king of England, Scotland and Ireland, William III must have thoroughly enjoyed his bedtime views. His state bedroom at Hampton Court Palace is awash with sumptuously decorated moiré patterned fabric (pronounced “mwa ray”) giving an almost psychedelic optical illusion of flowing water. When two different fabrics, each exhibiting the same repeating patterns, are interwoven, the results are remarkable: an entirely new pattern, magical and worthy of a king’s bedroom, emerges. Depending on the way the two initial fabrics are sewn together, new moiré patterns of very different appearance can arise, a versatility that made this fabric the centerpiece of 17th- and 18th-century royal houses and clothing.

But this is not a story about wealthy monarchs and their exquisite fabric. Moiré patterns are also used by engineers to direct ships into harbors with arrows that appear to change direction, depending on the ship’s location. And last year, physicists demonstrated that such patterns made from two atom-thin sheets of carbon, known as graphene, have surprising and unexpected properties, blowing a new field of quantum research wide-open and profoundly impacting our understanding of how to engineer new wonder materials.

Electrons flow through everything we make and touch. But fundamentally new properties of matter appear when we restrict the flow of electrons to two dimensions—by, for example, isolating a sheet of carbon atoms to make graphene. The discovery of this carbon flatland earned flatland earned researchers Konstantin Novoselov and Andre Geim the 2010 Nobel Prize in physics.

The electrons in a single sheet of graphene behave in a self-centered manner: two (or more) electrons do not care about one each other’s presence and go about just as they would if they were alone. Physicists call this phenomenon noninteracting behavior, and in graphene, it unfortunately preempts the appearance of more fundamental quantum effects such as superconductivity. Superconductivity, the state where electrons flow without resistance through a material, is a purely “interacting” effect, where two or more electrons decide it is quantum mechanically favorable to join forces and coordinate their motion.

At present, superconductivity only appears in materials that have been cooled to temperatures far below freezing. Creating a high-temperature superconductor would completely revolutionize daily life—for example, it would reduce the world’s carbon footprint by nearly 15 percent by allowing the long-distance transmission of electricity with perfect efficiency. Wonderful though single-layer graphene is, its electrons are not social enough to interact and permit superconductivity.

Enter the moiré effect. In 2018 Pablo Jarillo-Herrero of the Massachusetts Institute of Technology and his colleagues stacked two graphene layers on top of each other and twisted one of them by a certain “magic angle,” producing a superconducting state of matter with zero electrical resistance! They suddenly had a material that behaves completely differently from its individual constituents. This finding opened the door of discovery to other quantum states of matter that could be created and optimized in materials.

Compared with previously discovered superconductors known as cuprates, which were the subject of intense research over the past 30 years because they work at relatively high temperatures, this moiré graphene is infinitely more simple and controllable. If the electrons in twisted graphene are as interacting and entangled as those in cuprates, then this much simpler material, in which the concentrated electrons can be adjusted by simply applying a voltage to a nearby electrode, offers a versatile platform to solve the 30-year-old mystery of high-temperature superconductivity and to guide us toward finding materials for an energy-sustainable future.

To find out how much the electrons that reside in the moiré layers are interacting, one must somehow probe them. In a new paper just published in Nature, our laboratory groups at Princeton University have now accomplished this goal using a scanning tunneling microscope (STM) which is capable of capturing images of materials with atomic resolution. STM is a sort of a quantum version of a drilling rig that travels back and forth across the material, trying to investigate interesting and fertile places, but that, crucially, does not pollute the sample.

This noninvasive machine probes the entanglement, or interaction, of the wave functions of electrons in twisted bilayer graphene. At the same time, the concentration of electrons can be varied during the measurement to analyze how the electron wave functions are modified by these interactions. It’s the quantum equivalent of measuring the waves spread by a small boat on Lake Erie while, at the same time, changing the water level in the lake.

In simple metals and insulators, electrons occupy well-defined energy levels. They know where to sit and what to do. When we examined the twisted bilayer graphene at the magic angle, we found this type of electron behavior at very high or low electron concentrations, where the system acts like a simple a metal or an insulator, respectively. But near the electron concentration where superconductivity emerges, we found that the electron energy levels of twisted bilayer graphene suddenly become unexpectedly broad, which is a telltale sign of strong interactions.

A future extension of this experimental study aims to tease out the nature of electron-electron interactions in the system more precisely and to establish the mechanism of superconductivity. The possibility of doing so is helped by the fact that fine-tuning electron concentrations in the same sample while performing STM measurements will allow scientists to obtain unprecedented information. The new moiré superconducting platform may be the playground in which the 30-year-old mystery of how strongly interacting electrons superconduct can be solved.

Moreover, scientists are now racing to build many other moiré patterns using rotated single layers of other materials, with encouraging early results. As with the patterns adorning royal palaces, the quantum world of electron moiré patterns combines beauty and novelty with breathtaking results.