2026 Kavli
Prize in
Nanoscience

Citation from The Kavli Prize Committee in Nanoscience

Twistronics is a field of condensed matter physics that studies how the electronic properties ofatomically thin materials change when two or more layers are stacked with a slight rotationaltwist between them. The use of geometric alignment as a tuning knob for engineering the bandstructure introduced a new paradigm in nanoscience. This has led to a wealth of new phases ofmatter and new quantum behaviour such as unconventional superconductivity and correlatedinsulating states.

In 2009, using scanning tunnelling microscopy and spectroscopy on suspended twisted bilayergraphene, Eva Y. Andrei and her group demonstrated that small variations in twist angleprofoundly modified the electronic structure [1]. She showed that interlayertwist generatestwist-dependent van Hove singularities in the electronic density of states and identified aspecial twist angle, later known as the “magic” angle, at which these singularities merge to forman unusually flat electronic band. At this angle,she observed a gap at the Fermi level, providingwhat appears to be the first evidence of an emergent correlated electronic state, identified as acharge density wave. The demonstration that flat bands can be engineered through geometriccontrol rather than chemical composition represented a fundamental advance in materialsdesign and arguably launched the field now known as Twistronics.

This experimental discovery was placed on a firm theoretical foundation in 2011 by Allan H.MacDonald, who developed a continuum model describing how interlayer twist reshapes theelectronic band structure of twisted bilayer graphene [2]. His group’s workquantitativelyaccounted for the experimentally observed van Hove singularities and explained the emergenceof flat bands at discrete magic angles. This framework has since become the theoreticalfoundation of moiré materials and has guided subsequent experimental and theoreticaldevelopments across a wide range of twisted and layered systems. To establish the nature ofthe correlated states and to probe superconductivity, however, it was necessary to achieveprecise control of twist angle, carrier density,and dielectric environment. These stringentrequirements were met through subsequent technical advances by others, including theidentification of hexagonal boron nitride as an ideal non-invasive substrate and thedevelopment of techniques for deterministic control of the twist angle, completing theexperimental toolbox of Twistronics.

The broader significance of twist-engineered flat bands was demonstrated in 2018, when PabloJarillo-Herrero’s group, who observed correlated insulating phases and superconductivity inmagic-angle twisted bilayer graphene devices [3]. These results showedthat superconductivitycan emerge in a system composed of two weakly coupled graphene layers when tuned by twistangle and electrostatic gating. Moreover, it led to an expansion of our understanding ofsuperconductivity and related physical phenomena. Theresulting platform, combining atomic-scale structural simplicity with electronic tunability, has enabled systematic investigations of interaction-driven quantum phases and has had broad and lasting impact across nanoscienceand quantum material research.

Key references:
1.Observation of Van Hove singularities in twisted graphene layers, Guohong Li, A. Luican, J. M. B. Lopes dos Santos, A. H.Castro Neto, A. Reina, J. Kong, E. Y. Andrei, Nature Physics 6, 109 (2010) Published: 29 November 2009
2.Moiré bands in twisted double-layer graphene, Rafi Bistritzer and Allan H. MacDonald, PNAS 108,1223 (2011)
3.Unconventional superconductivity in magic-angle graphene superlattices, Yuan Cao, Valla Fatemi, Shiang Fang, KenjiWatanabe, Takashi Taniguchi, Efthimios Kaxiras, Pablo Jarillo-Herrero, Nature volume 556, 43 (2018)

Electronics with a Twist

By Fabio Pulizzi, science writer

In making their award, the Kavli Prize in Committee in Nanoscience has selected three scientists for their pioneering work on the ability to control the electronic properties of stacks of two-dimensional materials by merely varying the rotation between layers.

A toy that has fascinated children and adults for generations is the kaleidoscope: a simple cylinder lined with mirrors and filled with loose beads or coloured glass. Peer inside and you see intricate patterns formed by repeated reflections. Rotate the tube and the scene transforms, the pieces shift, and new, hypnotic, rotationally symmetric designs appear. The physics behind the breakthroughs of Eva Andrei, Allan MacDonald and Pablo Jarillo Herrero could not be more different, yet they share one essential idea with the kaleidoscope, that is using rotation as a tool for creating entirely new phenomena.

Virtually every electronic device we use today works because of the way electrons move through a material. The atomic nuclei in the lattice create an energy landscape that dictates how fast electrons can travel, which energies they are allowed to occupy, and even how many electrons can share the same combination of speed and energy, a quantity known as the density of states. Because this landscape is ultimately set by the spatial arrangement and charges of the atoms, the traditional way to change a material’s electronic behaviour is to alter its chemical composition. That is how an insulator can be turned into a conductor, or even into a superconductor, a material that, below a certain temperature, carries electrical current with no energy loss.

When graphene was first isolated in 2004 and used to build electronic devices, it quickly became clear that this single layer of carbon atoms arranged in a honeycomb lattice could host remarkable physical behaviour. Its electrons move as if they were massless particles, giving graphene an electronic structure unlike that of any conventional material and opening the door to an entirely new class of phenomena. Drawing on her extensive expertise in solid state physics, particularly in artificial two-dimensional semiconductors, Eva Andrei at Rutgers University moved into graphene research almost immediately after the material’s discovery. Her group produced some of the earliest and most striking insights into graphene’s electronic behaviour. In 2010, they examined two graphene layers rotated relative to each other. Using a scanning tunnelling microscope in spectroscopy mode, they found that at certain twist angles the density of states spikes dramatically, signalling the presence of Van Hove singularities. [1]

The presence of Van Hove singularities in a bilayer is especially intriguing because when a large number of electrons accumulate under the same conditions, they can no longer be treated as independent particles. Instead, they begin to behave collectively, forming a strongly interacting electronic state that can give rise to entirely new phenomena.

The work of Eva Andrei and her group was placed into a broader theoretical framework in 2011 by Allan MacDonald and Rafi Bistritzer at the University of Texas at Austin. They explored how the electronic properties of two graphene layers change as the twist angle between them varies [2].

When two identical lattices are slightly misaligned, for example, by rotating one sheet relative to the other, they produce a moiré pattern, a new superlattice with a much larger periodicity than that of graphene itself. In their model, the two layers were treated as largely independent, with the interaction between them captured through a moiré band potential. This simple but powerful approach revealed two key insights.

First, the electronic structure of the bilayer can be tuned continuously by adjusting the twist angle. Second, and most importantly, at certain special, “magic” angles, the lowest energy electronic states become flat, meaning the electrons have effectively zero velocity. In this regime, the density of states diverges, allowing an enormous number of electrons to occupy the same energy level. Such an accumulation is profound: it creates precisely the conditions under which strong correlations and superconductivity can emerge.

The work of MacDonald and Bistritzer sparked an explosion of interest in the electronic behaviour of stacked two-dimensional crystals. By 2017, a new field had taken shape, “twistronics,” a term introduced by Efthimios Kaxiras and collaborators to capture the idea that simply rotating one atomic layer relative to another could fundamentally reshape its electronic properties [3].

Yet for all the theoretical excitement, compelling experimental confirmation remained elusive. One serious problem was that despite their exceptional mobility, electrons in graphene tend to suffer from scattering from dangling bonds and from corrugations. Furthermore, controlling the angle between two layers with high precision was a hugely difficult task. In 2018 however, Pablo Jarillo-Herrero and his team at MIT succeeded in fabricating electronic devices with exceptionally high mobility, made of two graphene sheets rotated by 1.1 degrees, the magic angle predicted to produce an enormous density of electronic states. To achieve this, they first adopted the technique developed by Cory R. Dean and James Hone at Columbia University and their colleagues, who showed that using hexagonal boron nitride as an atomically flat and chemically inert supporting layer suppresses disorder in graphene and allows the electrons to move with their highest possible mobility [4].

To obtain precise control over the rotation between the two graphene layers, they then used a method introduced by Emanuel Tutuc at the University of Texas at Austin and colleagues. This tear‑and‑stack approach relies on the natural attraction between hexagonal boron nitride and graphene to lift and separate half of a graphene sheet, rotate it by a defined angle using a mechanical stage, and place it back on top of the remaining half to create a bilayer with a controlled relative orientation [5].

Lo and behold, when Jarillo-Herrero and colleagues measured the electrical resistance as the temperature dropped, they saw a dramatic result: below 1.7 Kelvin, the resistance fell to zero, unmistakable evidence of superconductivity [6]. Further measurements revealed that this was no ordinary superconducting state. The temperature at which it appeared, combined with the extremely low density of charge carriers, pointed to unconventional superconductivity driven by exceptionally strong electron–electron interactions, stronger, in fact, than in any previously known superconducting system.

Twistronics is, of course, far more than superconductivity. The idea of rotating atom thin layers has been extended to semiconductors such as MoS₂ and WS₂, where researchers have uncovered entirely new optical behaviours. “Twistronics introduced a new paradigm in nanoscience and opened a powerful new platform for exploring interaction-driven quantum materials. The field of Twistronics may also form the basis of future electronic and optoelectronic technologies.” says Mari-Ann Einarsrud, Chair of the Nanoscience Committee.