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Twistronics

Twistronics is an emerging field in condensed matter physics that explores the manipulation of electronic, optical, and topological properties in two-dimensional (2D) materials by precisely controlling the relative twist angle between stacked atomic layers, leading to the formation of moiré superlattices—periodic interference patterns that act as artificial lattices on the nanoscale.^[1] These moiré patterns, arising from lattice mismatch or angular misalignment, create flat electronic bands with dramatically reduced bandwidths, enhancing electron-electron correlations and enabling exotic quantum states such as unconventional superconductivity and correlated insulating phases.^[2] Originating from studies of graphene, twistronics has expanded to diverse 2D systems, offering a tunable platform for probing strongly correlated phenomena without external magnetic fields.^[3] The field gained prominence in 2018 with the discovery of unconventional superconductivity in twisted bilayer graphene at the so-called "magic angle" of approximately 1.1°, where the twist induces flat bands near the Fermi level, resulting in a critical temperature of up to 1.7 K and tunable zero-resistance states upon doping.^[1] This breakthrough, reported by researchers including Pablo Jarillo-Herrero, demonstrated that the moiré superlattice in twisted graphene mimics high-temperature cuprate superconductors, featuring dome-shaped phase diagrams with competing insulating and superconducting regions.^[1] Prior theoretical work had predicted these flat bands, but experimental realization via mechanical stacking and precise alignment techniques confirmed their role in driving strong correlations, marking a paradigm shift in engineering 2D material properties.^[4] Beyond graphene, twistronics has been extended to transition metal dichalcogenides (TMDs) like MoSe₂, WSe₂, and MoTe₂, where the larger lattice constants and intrinsic spin-valley locking amplify moiré effects, yielding phenomena such as interlayer excitons with binding energies exceeding 300 meV and valley-polarized states.^[5] In twisted TMD bilayers, moiré potentials localize carriers into triangular lattices, fostering topological flat bands with Chern numbers up to ±1 and fractional quantum anomalous Hall effects at zero magnetic field, as observed in twisted MoTe₂ at filling factors like ν = -2/3.^[5] Superconductivity has also emerged in these systems, with critical temperatures around 1.2 K in twisted MoTe₂ at angles near 3.8° and 0.2–0.4 K in twisted WSe₂.^[5] Recent advancements include the development of in situ twisting devices for real-time angle control and the integration of heterostructures with hexagonal boron nitride (hBN) for improved stability, enabling studies of 3D twistronics in multilayer systems and potential applications in quantum computing and spintronics.^[2] These innovations have revealed additional states, such as excitonic insulators and Chern insulators, underscoring twistronics' versatility as a knob for accessing unconventional quantum matter.^[6]

Fundamentals

Definition and Principles

Twistronics is the study of how the relative twist angles between layers of two-dimensional (2D) materials, such as graphene, dramatically alter their electronic, optical, and mechanical properties through precise control of interlayer interactions.^[4] This field emerged from the realization that stacking 2D layers not perfectly aligned introduces tunable periodic potentials that can reshape the material's band structure, enabling the engineering of novel quantum states. The term "twistronics" was coined by the research group of Efthimios Kaxiras at Harvard University in their 2017 theoretical work on graphene superlattices.^[4] At its core, twistronics relies on weak interlayer coupling mediated by van der Waals forces between the atomically thin layers, which allows for mechanical rotation without disrupting the integrity of the individual sheets.^[4] The twist angle θ between layers modulates the overlap of atomic orbitals, thereby tuning the effective potential landscape and the resulting electronic band structure. For small twist angles, this misalignment creates a moiré superlattice with a characteristic wavelength given by

\lambda_m = \frac{a}{2 \sin(\theta/2)},

where a is the lattice constant of the 2D material, such as a \approx 0.246 nm for graphene; this period governs the scale of the emergent superlattice and the strength of interlayer hybridization. A pivotal concept in twistronics is the "magic angle," where the electronic bands flatten dramatically, suppressing kinetic energy and enhancing electron-electron interactions. In twisted bilayer graphene, this occurs at θ ≈ 1.1°, where the Dirac cones—linear dispersions characteristic of pristine graphene—flatten, leading to strongly correlated behavior.^[1] This flattening arises from the resonance between Dirac points of the two layers, amplified by the moiré potential, and marks a regime where collective phenomena dominate over single-particle effects.^[7]

Moiré Superlattices

In twisted two-dimensional (2D) materials, moiré superlattices arise from the interference between the atomic lattices of stacked layers that are rotationally misaligned by a small twist angle. This misalignment causes the periodic structures of the individual layers to beat against each other, producing a larger-scale periodic pattern known as a moiré superlattice, where the superlattice periodicity emerges from the difference in the reciprocal lattice vectors of the two layers.^[8] The moiré pattern can be visualized in momentum space as the beating of wavevectors associated with interlayer hopping processes, leading to a new superlattice with a wavelength much larger than the original atomic lattice constants.^[8] Geometrically, the stacking can be commensurate or incommensurate depending on the twist angle θ. Commensurate stacking occurs at specific discrete angles where the lattices align periodically to form a true 2D crystal, while incommensurate stacking at generic small angles (typically θ ≲ 10°) lacks exact periodicity but still supports a well-defined moiré potential through an effective continuum description.^[8] The twist angle plays a crucial role in determining the superlattice size, which scales inversely with θ, and the resulting potential landscape, where smaller angles yield longer-period moiré cells and stronger interlayer interactions that modulate the local atomic registry.^[8] This periodic moiré potential profoundly affects electron behavior by folding the Brillouin zone of the individual layers into a superlattice Brillouin zone, giving rise to minibands within the electronic structure. In the specific case of twisted bilayer graphene, the misalignment of the honeycomb lattices introduces a long-range potential that splits the Dirac cones into a series of minibands, with bandwidths tunable by the twist angle.^[8] Experimental confirmation of moiré superlattices has been achieved through scanning tunneling microscopy (STM), which directly images the periodic reconstructions on the atomic scale. For instance, STM topographic maps of twisted bilayer graphene reveal triangular moiré lattices with periods matching theoretical predictions, showcasing the superlattice's influence on surface atomic arrangement.

Historical Development

Theoretical Foundations

The theoretical foundations of twistronics trace back to early predictions regarding the electronic properties of misaligned graphene layers. In 2007, A. H. Castro Neto and colleagues hypothesized that rotating one graphene layer relative to another would lead to novel electronic behaviors due to the resulting incommensurate stacking, potentially inducing band gaps or modified Dirac-like dispersions in the low-energy spectrum.^[9] This work laid the groundwork by highlighting how twist angles could tune interlayer coupling beyond simple Bernal stacking, anticipating the emergence of moiré patterns that alter the electronic structure.^[9] A pivotal advancement came in 2011 with the Bistritzer-MacDonald model, which employed a continuum approximation to describe twisted bilayer graphene (TBG) at small twist angles. This model treats each graphene layer as obeying the Dirac equation for massless fermions, with interlayer coupling captured by a periodic potential arising from the moiré superlattice formed by the twist.^[10] It predicts the formation of flat electronic bands near the Fermi level at specific "magic angles," where the Fermi velocity vanishes due to destructive interference between the Dirac cones of the two layers, enhancing electron-electron interactions.^[10] The first magic angle is approximately 1.05°, marking a regime of strongly correlated physics analogous to high-temperature superconductors.^[10] The effective low-energy Hamiltonian in this continuum framework is given by

H_\text{eff} = v_F (\boldsymbol{\sigma} \cdot \mathbf{p}) + V_\text{moiré}(\theta),

where v_F is the Fermi velocity, \boldsymbol{\sigma} are the Pauli matrices acting on the sublattice degree of freedom, \mathbf{p} is the momentum operator, and V_\text{moiré}(\theta) represents the twist-angle-dependent interlayer potential that modulates the Dirac Hamiltonian.^[10] This formulation simplifies the microscopic tight-binding description while capturing the essential moiré-induced band flattening.^[10] Subsequent refinements addressed limitations in the rigid-lattice assumption of the Bistritzer-MacDonald model. In 2017, Efthimios Kaxiras and collaborators performed calculations incorporating lattice relaxation effects, such as atomic rearrangements due to interlayer interactions, which slightly shift the magic angle to approximately 1.08° and further flatten the bands by reducing the effective bandwidth.^[4] These adjustments emphasize the role of structural deformations in stabilizing correlated states, providing a more accurate theoretical baseline for small-angle TBG. This work also introduced the term "twistronics" to describe the manipulation of 2D material properties via twist angles.^[4]

Experimental Milestones

In 2010, Eva Andrei's team at Rutgers University reported the first direct observation of moiré patterns in twisted bilayer graphene using scanning tunneling spectroscopy, revealing sharp van Hove singularities indicative of the altered electronic structure due to interlayer twisting.^[11] Concurrently, a group from the Universidad de Chile identified the significance of small twist angles around 1° in twisted bilayer graphene through tight-binding calculations, predicting the emergence of flat bands that would profoundly influence electron behavior, setting the stage for later experimental validations.^[12] A major experimental breakthrough occurred in 2018 when Pablo Jarillo-Herrero's group at MIT demonstrated unconventional superconductivity in twisted bilayer graphene twisted at approximately 1.1°, the so-called magic angle, with a critical temperature of 1.7 K observed via transport measurements under low magnetic fields.^[1] This discovery confirmed the role of moiré-induced flat bands in enabling strongly correlated electronic states, sparking widespread interest in twistronics. Building on this, in 2019, the same MIT team uncovered correlated insulating states at half-filling in magic-angle twisted bilayer graphene, where resistivity surged dramatically at low temperatures, highlighting the interplay of electron correlations and moiré potentials without invoking magnetism.^[13] In recognition of these foundational contributions, Pablo Jarillo-Herrero, Allan H. MacDonald, and Rafi Bistritzer were awarded the 2020 Wolf Prize in Physics for their pioneering theoretical and experimental work on the electronic properties of twisted bilayer graphene.^[14] Advancing fabrication techniques, a Harvard University team in 2024 developed the MEGA2D micromachine, a fingernail-sized on-chip device enabling precise, in situ control of twist angles in 2D material bilayers, facilitating reproducible studies of moiré superlattices without sample-to-sample variations.^[15]

Materials and Fabrication

Twisted Bilayer Graphene

Twisted bilayer graphene (tBLG) serves as the foundational material in twistronics, built upon the exceptional properties of single-layer graphene, which consists of a two-dimensional honeycomb lattice of carbon atoms exhibiting Dirac-like electronic behavior, massless charge carriers, and ultrahigh electron mobility exceeding 200,000 cm²/V·s at room temperature. As a prerequisite for tBLG, these single-layer sheets are mechanically exfoliated from graphite and then stacked to form bilayers via dry-transfer techniques, enabling the introduction of a tunable twist angle between layers that generates moiré superlattices.^[1] The primary fabrication method for tBLG involves the "tear-and-stack" technique, a modified dry-transfer process where a single graphene flake is torn into two pieces using van der Waals interactions with a hexagonal boron nitride (hBN) stamp at room temperature, followed by precise relative rotation and restacking onto an hBN substrate to minimize substrate-induced effects and charge inhomogeneities.^[16] hBN, with its atomically flat surface and lattice mismatch to graphene, acts as both a protective encapsulation layer (typically 10–30 nm thick) and a substrate to preserve the intrinsic electronic quality of the tBLG.^[17] Twist angle control is achieved through manual rotation of the stamp under an optical microscope, often aided by heating for hBN pickup at approximately 90°C and transfer release at approximately 160°C, with tearing performed at room temperature to facilitate adhesion and release, with the angle verified post-fabrication via transport measurements or scanning tunneling microscopy (STM).^[17] Fabrication challenges in tBLG include minimizing lattice strain, which arises from twist-induced deformations and can be quantified via nano-Raman spectroscopy showing gradients on the nanoscale; managing domain boundaries, where triangular moiré domains meet in soliton-like regions that introduce defects; and ensuring angle homogeneity across the sample, as even small variations (e.g., 0.05°) lead to inhomogeneous electronic properties.^[17] The magic angle, where Dirac velocity vanishes and flat bands emerge, spans a narrow range of approximately 1.05° to 1.15°, demanding sub-degree precision to access correlated states.^[18] In 2018, the first successful tBLG devices achieved twist angle precision of about 0.01°, enabling the observation of unconventional superconductivity with critical temperatures up to 1.7 K.^[16]

Heterostructures with Other 2D Materials

Twistronics has been extended beyond homogeneous graphene bilayers to heterostructures incorporating other two-dimensional (2D) materials, such as hexagonal boron nitride (hBN) and transition metal dichalcogenides (TMDs), enabling tunable moiré potentials and novel electronic interactions through precise angular alignment.^[19] These hybrid systems leverage the weak van der Waals interactions between layers to form moiré superlattices with emergent properties distinct from pure graphene stacks. Fabrication typically involves sequential dry-transfer techniques, where individual 2D flakes are exfoliated onto a substrate and stacked using a polycarbonate/polydimethylsiloxane (PC/PDMS) stamp under an optical microscope, with alignment achieved via markers etched on the substrate to control twist angles to within ~0.1° precision.^[19] A prominent example is twisted graphene aligned to hBN, which introduces a periodic potential from the lattice mismatch and twist, modulating graphene's Dirac bands for applications in tunable superconductivity and correlated states. In such heterostructures, the hBN substrate provides a clean dielectric environment while the moiré pattern imposes a superlattice potential, enhancing electron localization. A specific configuration at a twist angle of approximately 1.17° in graphene/hBN-aligned twisted bilayer graphene has been shown to enable orbital ferromagnetism near three-quarters electron filling, arising from the alignment of the graphene moiré lattice with the hBN substrate.^[20] In TMD-based heterostructures, such as twisted MoSe₂/WSe₂ bilayers, moiré engineering facilitates valleytronics by exploiting valley-dependent spin-orbit coupling and optical selection rules inherent to these materials. At small twist angles (<2°), the moiré potential depth reaches ~27 meV, localizing interlayer excitons (IXs) in quantized traps and enabling their interaction to form interlayer biexcitons with repulsive dipolar forces. These systems exhibit temperature-dependent IX dynamics, with defect-trapped IXs dominating below 30 K and moiré-trapped IXs above, offering pathways for quantum emitters. Recent advances in 2023–2024 have highlighted enhanced spin-orbit effects in twisted TMD moiré superlattices, including chiral superconductivity responses and strain-amplified exciton localization in WSe₂-based stacks, building on foundational valley polarization studies. As of 2025, optimized protocols have enabled high-yield fabrication of bubble-free magic-angle twisted bilayer graphene with twist-angle variations below 0.1°, enhancing device scalability.^[21]^[22]^[23]

Electronic Properties

Flat Bands and Correlations

In twisted bilayer graphene (TBG), flat bands emerge at specific "magic angles," such as approximately 1.1°, where the moiré superlattice causes destructive interference in the electronic wavefunctions, dramatically reducing the bandwidth of the low-energy Dirac cones to around 10 meV. This bandwidth collapse minimizes the kinetic energy of electrons, thereby amplifying the relative strength of electron-electron interactions, which become dominant over hopping processes and drive the system into a strongly correlated regime. These flat bands foster strong correlations, manifesting as Mott-like insulating states at integer fillings of the moiré bands, where charge localization occurs despite the underlying metallic band structure. In theoretical models, this behavior is captured by an effective Hubbard model, in which the on-site Coulomb repulsion U greatly exceeds the hopping parameter t (with U/t \gg 1), promoting localized electron states and insulating phases akin to those in transition metal oxides. The high density of states in the flat bands further enhances this interaction strength, as the reduced bandwidth effectively increases the interaction scale relative to kinetic terms. A key feature of the moiré bands is the divergence in the density of states near van Hove singularities, arising from saddle points in the band structure that logarithmically enhance the available states for electrons. This is expressed as:

\rho(E) \propto \ln \left| \frac{E - E_{\mathrm{vH}}}{\Delta} \right|

where E_{\mathrm{vH}} is the van Hove energy and \Delta is an energy scale set by disorder or interactions, leading to peaked susceptibilities and instability toward ordered phases.^[24] Experimentally, these correlated states are evidenced by the anomalous Hall effect observed at half-filling of the flat bands, signaling spontaneous symmetry breaking and topological order without external magnetism. Additionally, Shubnikov-de Haas oscillations in transport measurements reveal quantized Landau levels and coherent propagation in the correlated insulators, confirming the role of flat-band interactions in reconstructing the electronic structure. Beyond graphene, similar flat bands and enhanced correlations have been observed in twisted transition metal dichalcogenide (TMD) bilayers, such as twisted MoTe₂, where moiré potentials lead to topological flat bands and strongly interacting states at low temperatures.^[5]

Superconductivity and Insulation

In twisted bilayer graphene at the magic angle, unconventional superconducting states emerge upon doping away from charge neutrality. These states are observed near filling factors ν ≈ ±2, where the critical temperature Tc reaches approximately 1.7 K.^[1] The superconductivity is highly tunable via gate voltage, which adjusts the carrier density and enables the system to transition between normal and zero-resistance states.^[1] At half-filling (ν = 0), the material exhibits strongly insulating behavior, attributed to either charge density wave ordering or Mott insulation due to electron correlations within the flat bands. Resistivity in these states shows sharp peaks exceeding 10^{11} Ω/sq, indicating a robust gap opening and suppression of charge transport.^[25] The resulting phase diagram, mapped as a function of doping and twist angle, reveals a rich competition among superconducting domes, insulating phases at integer fillings, and intervening normal metallic regions. This structure closely parallels the phase diagram of high-Tc cuprates, with superconductivity arising near insulating states.^[1] In 2019, transport measurements identified a "strange metal" phase in the region between the ν = 0 insulator and nearby superconductors, marked by linear-in-temperature resistivity and near-Planckian dissipation.^[26]

Exotic Phenomena

Magnetic Effects

In twistronics, the flat bands arising from moiré superlattices can drive Stoner instabilities, where electron-electron interactions overcome the kinetic energy cost, leading to spontaneous spin polarization and ferromagnetism. This mechanism is particularly pronounced near specific fillings, such as three-quarters of the moiré unit cell, where the high density of states enhances susceptibility to magnetic ordering. Experimental evidence for such ferromagnetism has been observed in twisted bilayer graphene encapsulated in hexagonal boron nitride (hBN), manifesting as hysteretic anomalous Hall effects at low temperatures around 30 mK.^[27] Layer-polarized ferromagnetism, where spins align preferentially in one layer due to interlayer interactions, was theoretically proposed in 2020 for ABC-stacked trilayer graphene aligned with hBN. Exact diagonalization studies of narrow moiré bands in this system reveal that Hund's coupling favors full spin polarization, stabilizing the ferromagnetic state.^[28] Orbital magnetism in twistronic systems often involves non-collinear spin textures, such as skyrmion-like configurations, which emerge from the interplay of flat-band topology and interactions. In twisted bilayer graphene structures, these textures arise as low-energy excitations upon doping the correlated insulating states, forming stable skyrmions that carry topological charge and contribute to anomalous Hall conductivity.^[29] Similar orbital magnetic phases have been explored in twisted transition metal dichalcogenide (TMD) heterostructures, where itinerant ferromagnetism at moiré fillings yields estimated Curie temperatures up to 10 K, tunable by twist angle and doping.^[30] In biased twisted bilayers, spatial inhomogeneities in the electrostatic potential create electron-rich puddles, regions of locally enhanced carrier density that amplify interactions. These puddles are proposed to drive local ferromagnetic order through Stoner-like mechanisms, with the bias controlling the transition between antiferromagnetic and ferromagnetic polarization in the inhomogeneous domains.

Topological and Optical States

In twisted bilayer graphene (tBLG), moiré bands exhibit nontrivial topology characterized by nonzero Chern numbers, such as C=±1, leading to the emergence of robust edge modes that propagate without backscattering along sample boundaries.^[31] These edge states arise from the interplay between the moiré superlattice potential and the underlying Dirac fermions, confirming the topological nature of the flat bands through superconducting quantum interferometry measurements.^[32] At fractional fillings of these Chern bands, fractional Chern insulators (FCIs) form, hosting fractionalized excitations analogous to fractional quantum Hall states but in zero external magnetic field. The topological invariants in these systems are quantified by the Chern number, obtained by integrating the Berry curvature Ω(k) over the Brillouin zone:

C = \frac{1}{2\pi} \int_{\text{BZ}} \Omega(\mathbf{k}) \, d^2\mathbf{k},

where Ω(k) captures the geometric phase accumulated by Bloch electrons during adiabatic transport in momentum space.^[33] In tBLG, strain or twist angle variations can tune the Berry curvature distribution, enhancing topological responses like the nonlinear Hall effect.^[34] Experimental observation of FCIs at fractional fillings, such as ν=1/3 and ν=2/5, was reported in magic-angle tBLG in 2021 using local compressibility probes, demonstrating incompressible states with quantized Hall conductance at low magnetic fields.^[35] Zero-field FCIs in tBLG remain theoretically predicted but experimentally unconfirmed as of November 2025. Recent theoretical work in 2025 has predicted extended FCIs near half flux in tBLG above the magic angle.^[36] These FCIs support non-Abelian anyons, proposing applications in topological quantum computing for fault-tolerant qubit operations.^[37] Optical properties in twisted transition metal dichalcogenide (TMD) heterostructures reveal angle-dependent excitons confined by the moiré potential, where twist angles modulate exciton valley polarization up to 90% for intralayer bright spin-singlet states.^[38] In twisted bilayer TMDs like WS₂/WSe₂, the moiré superlattice traps excitons at high-symmetry sites, altering their fine structure and enabling twist-tunable photoluminescence with enhanced binding energies.^[39] Absorption spectra in these systems show tunable features due to twist-controlled bandgaps; for instance, in twisted bilayer graphene, infrared transmission varies dramatically with gate voltage and twist angle, reflecting bandgap opening from ~0 to several meV.^[40] This tunability arises from interlayer hybridization modulated by the moiré pattern, allowing control over light-matter interactions for potential optoelectronic devices.^[41]

Applications and Outlook

Emerging Technologies

Twistronics offers significant potential in quantum devices, where flat-band correlations in moiré superlattices enable tunable qubits with enhanced electron interactions and improved coherence for solid-state quantum computing platforms.^[42] These flat bands suppress kinetic energy, amplifying correlation effects that can be precisely controlled via twist angles to implement low-error quantum gates.^[43] Moiré-based quantum simulators further exploit these structures to model strongly correlated systems, providing tunable platforms for emulating exotic quantum phases without requiring cryogenic temperatures.^[44] In optoelectronics, twisted transition metal dichalcogenide (TMD) heterostructures facilitate ultrasensitive photodetectors by leveraging angle-dependent band alignments that boost exciton binding and light absorption efficiency.^[45] A 2025 advancement introduces biosensor arrays using twisted bilayer graphene superlattices, where angle-tuned dielectric responses enable high-sensitivity, real-time detection of biomolecules through modulated optoelectronic signals.^[46] Electronic applications benefit from twistronics' switchable insulators, derived from correlated states in moiré patterns, which support memristive devices with resistive switching controlled by twist angle and electric fields for energy-efficient neuromorphic circuits.^[47] Strain-twistronics integrates mechanical deformation with interlayer twisting in bilayer graphene, yielding flexible sensors that detect strain variations down to 0.1% with high gauge factors for applications in wearable health monitoring.^[48] Conceptual proposals from 2024 highlight reconfigurable moiré antennas inspired by twistronics, utilizing moiré metasurfaces for dynamic beam steering and polarization manipulation in reconfigurable intelligent surfaces to enhance next-generation wireless networks like 6G.^[49]

Recent Advances and Challenges

In 2025, researchers extended the principles of twistronics beyond electronic systems to elastodynamic metasurfaces, demonstrating broadband topological transitions induced by twisting elastic layers with broken symmetries. This approach enables precise control over phonon fields, opening avenues for tunable mechanical wave manipulation in metamaterials.^[50] Advancements in transition metal dichalcogenide (TMD) moiré superlattices have highlighted their potential for valleytronics, with studies showing twist-angle-dependent valley polarization in heterobilayers like MoS₂/WSe₂, achieving up to 90% polarization at small angles for enhanced light emission efficiency in interlayer excitons.^[38] Fabrication techniques saw significant progress in 2024 with the development of a compact, fingernail-sized automated twisting machine at Harvard University, which allows precise control over twist angles in 2D materials without manual intervention, addressing the limitations of labor-intensive, one-at-a-time device assembly for scalable production.^[51] In September 2025, AI-assisted methods for wafer-scale exfoliation and transfer of 2D materials were reported, enabling high-throughput production and further mitigating scalability challenges in twistronics device fabrication.^[52] A notable application emerged in 2025 with optoelectronic biosensor arrays based on twisted bilayer graphene (tBLG) superlattices integrated with Au nanodisks and CRISPR-Cas12a, demonstrating single-molecule sensitivity for detecting biomolecules like cancer biomarkers at attomolar concentrations.^[46] Despite these breakthroughs, key challenges persist in twistronics. Scalability remains hindered by the difficulty in achieving uniform twist angles across large-area samples, as current methods struggle with consistent alignment in production-scale fabrication.^[51] Strain effects introduce variability, leading to memorized moiré patterns that compromise reproducibility in stacked heterostructures, particularly under thermal or mechanical stress.^[53] Theoretical modeling faces gaps in capturing many-body interactions for non-graphene systems, where relaxation and electron-electron correlations significantly alter electronic properties but are inadequately described by standard density functional theory approaches.^[54] Looking ahead, integration of artificial intelligence for twist angle optimization promises to accelerate material design by predicting optimal configurations through machine learning-driven inverse design, potentially streamlining the discovery of exotic phases. Engineered moiré stacks also hold promise for realizing room-temperature quantum phenomena, such as ultrasensitive sensors and correlated states, by leveraging tunable interactions in hybrid 2D architectures.^[55]^[56]

References

[1]
Unconventional superconductivity in magic-angle graphene ... - Nature
Mar 5, 2018 · Here we report the observation of unconventional superconductivity in a two-dimensional superlattice made from graphene—specifically, 'magic ...
[2]
Magical moiré patterns in twisted bilayer graphene: A review on ...
This review examines recent advances in t-BLG covering aspects of its electronic structure, fabrication, angle-dependent properties and the spectroscopic ...
[3]
Twistronics and moiré superlattice physics in 2D transition metal ...
Aug 3, 2025 · Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides. Authors:Dawei Zhai, Hongyi Yu, Wang Yao.
[4]
Manipulating the electronic properties of two-dimensional layered ...
Feb 17, 2017 · Twistronics is manipulating the electronic properties of 2D materials by controlling the twist angle between layers, which can break ...
[5]
Twistronics and moiré superlattice physics in 2D transition metal ...
Aug 6, 2025 · Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides. Dawei Zhai*, Hongyi Yu* and Wang Yao. Published 6 August ...
[6]
Twistronics and heterolayers - Nature
Twistronics is a field where adjusting the angle between 2D material layers controls electrical properties, producing effects like switching between non- ...Missing: review | Show results with:review
[7]
[1808.05250] Origin of Magic Angles in Twisted Bilayer Graphene
Aug 15, 2018 · Access Paper: View a PDF of the paper titled Origin of Magic Angles in Twisted Bilayer Graphene, by Grigory Tarnopolsky and 2 other authors.
[8]
Moiré bands in twisted double-layer graphene | PNAS
### Summary of Moiré Superlattices in Twisted Bilayer Graphene
[9]
[0709.1163] The electronic properties of graphene - arXiv
Sep 7, 2007 · We discuss the electronic properties of graphene stacks and show that they vary with stacking order and number of layers. Edge (surface) states ...
[10]
Moiré bands in twisted double-layer graphene - PNAS
A moiré pattern is formed when two copies of a periodic pattern are overlaid with a relative twist. We address the electronic structure of a twisted ...<|control11|><|separator|>
[11]
Flat bands in slightly twisted bilayer graphene: Tight-binding ...
In this Rapid Communication, we found nondispersive flat bands no farther than 10 meV of the Fermi energy in slightly twisted bilayer graphene.
[12]
Pablo Jarillo-Herrero wins Wolf Prize for groundbreaking ... - MIT News
Jan 16, 2020 · Professor of physics honored alongside Allan MacDonald and Rafi Bistritzer for pioneering research on twisted bilayer graphene. Carol Breen ...
[13]
https://www.science.org/doi/10.1126/sciadv.aaw9770
[14]
https://news.mit.edu/2020/mit-pablo-jarillo-herrero-wins-wolf-prize-physics-0116
[15]
https://www.nature.com/articles/s41586-024-07826-x
[16]
Origin of Magic Angles in Twisted Bilayer Graphene | Phys. Rev. Lett.
Mar 15, 2019 · Twisted bilayer graphene (TBG) was recently shown to host superconductivity when tuned to special “magic angles” at which isolated and relatively flat bands ...Missing: Chilean | Show results with:Chilean
[17]
New Generation of Moiré Superlattices in Doubly Aligned hBN ...
Feb 25, 2019 · Twisted bilayer graphene (TBLG) is one of the simplest van der Waals heterostructures, yet it yields a complex electronic system with intricate ...Missing: seminal | Show results with:seminal
[18]
Error (ACS Publications)
**Summary:**
[19]
Localization and interaction of interlayer excitons in MoSe 2 /WSe 2 ...
Oct 30, 2023 · Our work elucidates the different excitation and temperature regimes required for the formation of both localized and delocalized IX and biexcitons.
[20]
Progress and prospects of Moiré superlattices in twisted TMD ...
Sep 6, 2024 · This review provides a comprehensive overview of recent progress in moiré superlattices formed from twisted TMD heterostructures.
[21]
Observation of Van Hove singularities in twisted graphene layers
Nov 29, 2009 · Here we report the observation of low-energy Van Hove singularities in twisted graphene layers seen as two pronounced peaks in the density of states.
[22]
Correlated insulator behaviour at half-filling in magic-angle ... - Nature
Mar 5, 2018 · Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018). https://doi.org/10.1038 ...
[23]
https://www.cell.com/newton/fulltext/S2950-6360(24)00007-0
[24]
Emergent ferromagnetism near three-quarters filling in twisted ...
Jul 25, 2019 · They likely result from the lattice alignment of the top graphene sheet with the top hBN layer, with the density 1.15ns corresponding to an ...
[25]
Ferromagnetism in Narrow Bands of Moiré Superlattices
May 7, 2020 · We provide exact diagonalization results for models appropriate for ABC trilayer graphene ... (2020), https://www.nature.com/articles ...
[26]
Skyrmions in Twisted Bilayer Graphene: Stability, Pairing, and ...
Jul 29, 2022 · We study the excitations that emerge upon doping the translationally invariant correlated insulating states in magic-angle twisted bilayer graphene.
[27]
Itinerant ferromagnetism in transition metal dichalcogenide moiré ...
We estimate that Curie temperatures that can reach T ∼ 10 K. Finally, in Sec. IV we summarize and discuss our findings, estimating conditions for which the ...
[28]
Moir\'e edge states in twisted bilayer graphene and their topological ...
Apr 12, 2021 · We show that the twisted bilayer graphene has special edge states associated with the moiré pattern, and the emergence of these moiré edge states is linked ...
[29]
[PDF] Uncovering Topological Edge States in Twisted Bilayer Graphene
Using superconducting quantum interferometry, researchers revealed edge states in twisted bilayer graphene, confirming the unusual moiré band topology.
[30]
Fractional Chern Insulator in Twisted Bilayer | Phys. Rev. Lett.
Indeed, theoretical proposals of FCIs have been put forward in twisted bilayer graphene [16–21] and twisted bilayer transition metal dichalcogenide (TMD) [22–24]Abstract · Article Text · Introduction. · Single-particle electronic...
[31]
[PDF] Moiré Band Topology in Twisted Bilayer Graphene - arXiv
The moiré band topology of t-BLG manifests itself as two pronounced nonlocal responses in the electron and hole superlattice gaps. We further show that the ...
[32]
Tunable large Berry dipole in strained twisted bilayer graphene
May 3, 2021 · In this paper, we show that the large Berry curvature of the narrow bands in strained TBG leads to a strong and tunable nonlinear Hall effect.
[33]
Fractional Chern insulators in magic-angle twisted bilayer graphene
Dec 15, 2021 · Here we report the observation of eight FCI states at low magnetic field in magic-angle twisted BLG enabled by high-resolution local compressibility ...Missing: modes | Show results with:modes
[34]
Contrasting twisted bilayer graphene and transition metal ...
Fractional Chern insulators support anyons that carry fractional units of electric charge and unconventional quantum statistics and are proposed to have ...Article Text · TWISTED BILAYER GRAPHENE · TWISTED TMD HOMOBILAYER
[35]
Twist-Angle-Dependent Valley Polarization of Intralayer Moir\'e ...
Intralayer bright spin-singlet moiré excitons confined in a twisted heterostructure can achieve valley polarization levels as high as 90% at small twist angles.
[36]
Identification of twist-angle-dependent excitons in WS2/WSe2 ...
Our work provides new insight into the steady-state and dynamic properties of twist-angle-dependent excitons in van der Waals heterostructures.Missing: twistronics | Show results with:twistronics
[37]
Gate tunable optical absorption and band structure of twisted bilayer ...
Jun 21, 2019 · We report the infrared transmission measurement on electrically gated twisted bilayer graphene. The optical absorption spectrum clearly manifests dramatic ...
[38]
Twist-angle-dependent optical behaviors of excitons in twisted ...
The moiré potential can serve as a bound potential in space to trap excitons, thus it is more likely to generate bound excitons in twisted bilayer TMDs. The ...Missing: twistronics | Show results with:twistronics
[39]
Twisted Bilayer Materials for Solid-State Qubits
Qubits are the fundamental units in quantum computing, quantum communication, and sensing. In current platforms, such as cold atoms, ...
[40]
Twistronics: Future Scope in Quantum Parallel Computing.
Sep 5, 2025 · Their system utilizes the flat bands that emerge at the magic angle to implement novel quantum gates with reduced error rates. Google's quantum ...
[41]
Moiré straintronics: a universal platform for reconfigurable quantum ...
Apr 18, 2023 · Large-scale two-dimensional (2D) moiré superlattices are driving a revolution in designer quantum materials. The electronic interactions in ...
[42]
Twistronics in two-dimensional transition metal dichalcogenide (TMD)
Jan 17, 2024 · Twist engineering allows the modulation of bandgaps and a phase change from direct to indirect band gap semiconductors as well.
[43]
Ultrasensitive optoelectronic biosensor arrays based on twisted ...
Aug 23, 2025 · Recent advances in twistronics have revealed tunable optoelectronic properties in twisted bilayer graphene (tBLG), including angle-dependent ...
[44]
Exploring Moiré Superlattices and Memristive Switching in Non-van ...
over twist angles that range from 4 to 5.1°. At half-band filling, a correlated insulator appeared that is tunable with both twist angle and displacement field.
[45]
(PDF) Strain Engineering of Twisted Bilayer Graphene - ResearchGate
Apr 15, 2024 · Finally, the conclusion entails prospects for opportunities of strained twisted 2D materials, discussions on existing challenges, and an outlook ...
[46]
Reflective moiré metasurface: Challenges and opportunities
Apr 16, 2024 · Dynamic beamforming is critical in applications such as radar detection, holographic imaging, and reconfigurable intelligent surfaces (RIS).
[47]
Broadband topological transitions in twisted elastodynamic ... - PNAS
Oct 16, 2025 · We predict and experimentally demonstrate topological transitions within twisted elastodynamic metasurfaces, which we harness for broadband, ...
[48]
A smoother way to study 'twistronics' - Harvard Gazette
Sep 16, 2024 · In the paper, the researchers demonstrated the utility of their device with two pieces of hexagonal boron nitride, a close relative of graphene.Missing: review | Show results with:review
[49]
Memorization of Strain-Induced Moiré Patterns in Vertical van der ...
Mar 4, 2025 · We present the mechanistic principles governing the evolution of strain-induced moiré patterns in vertically stacked graphene through atomistic simulations.
[50]
Toward improved property prediction of 2D materials using many ...
Aug 22, 2025 · Modeling spin–orbit in 2D materials can be challenging with standard DFT methods. There have been several computational studies that have shown ...
[51]
[PDF] Chinese Physics Letters 42, 027403 (2025) Review AI-Driven ...
With the advancement of computational power and optimization al- gorithms, materials inverse design is expected to play an increasingly important role in the ...
[52]
Twistronics: Implications for Future Sensor Technologies.
Sep 5, 2025 · The trajectory of twistronics research suggests several promising directions, including room-temperature quantum sensors, ultra-sensitive ...