arXiv subjects

Mohammed M. Al Ezzi

Publications and source records attributed to Mohammed M. Al Ezzi.

14 recordsLinked to original sources

arXiv2026

Theory for Lattice Relaxation in Marginal Twist Moirés

Atomically thin moiré materials behave like elastic membranes where at very small twist angles, the van der Waals adhesion energy much exceeds the strain energy. In this ``marginal twist" regime, regions with low adhesion energy expand, covering most of the moiré unit cell, while all the unfavorable energy configurations shrink to form topological defects linked by a periodic network of domain walls. We find analytical expressions that successfully capture this strong-coupling regime for both the triangular soliton network and the honeycomb soliton network matching predictions from LAMMPS molecular dynamics simulations, and numerical solutions of continuum elasticity theory. There is an emergent universality where the theory is characterized by a single twist-angle dependent parameter. Our formalism is essential to understand experiments on a wide-range of materials of current interest including twisted bilayer graphene, both parallel and antiparallel stacked tWSe2 and tMoTe2, and any other twisted homobilayer with the same stacking symmetry.

cond-mat.mes-hall↗

arXiv2026

Twisted bilayer graphene from first-principles: structural and electronic properties

We present a comprehensive first-principles study of twisted bilayer graphene (tBLG) for a wide range of twist angles, with a focus on structural and electronic properties. By employing density functional theory (DFT) with an optimized local basis set, we simulate tBLG, obtaining fully relaxed commensurate structures for twist angles down to 0.987°. For all angles the lattice relaxation agrees well with continuum elastic models. For angles accessible to plane-wave DFT (VASP), we provide a detailed comparison with our local basis DFT (SIESTA) calculations, demonstrating excellent agreement in both the atomic and electronic structure. The dependence of the Fermi velocity and band width on the twist angle shows qualitative agreement with results from an `exact' $\mathbf{k \cdot p}$ continuum model, but reveals a small twist angle offset. Additionally, we provide details of the low-energy wavefunction character, band inversion and symmetries. Our results provide an ab initio reference point for the microscopic structure and electronic properties of tBLG which will serve as the foundation for future studies incorporating many-body effects.

cond-mat.mes-hall↗

arXiv2026

Continuous correlated states and dual-flatness in a moiré heterostructure

Many-body effects in condensed matter yield novel quantum states when the electronic density of states is enhanced. A vivid example is flat bands, which suppress kinetic energy and let interactions dominate, when they are filled with an integer number of electrons in moire systems. Yet flat bands and commensurate fillings are not the only conditions for correlated phenomena. Situations may occur where the band structure develops locally enhanced density of states, leading to strong correlations even at non-integer fillings, although such cases often yield pseudogaps that make detection elusive. Here we demonstrate that small-angle twisted monolayer-bilayer graphene combines moire-induced global flat band and additional local band flattening. Their coexistence allows direct comparison of correlated effects. The global route stabilizes commensurate states, while the local mechanism produces nearly flat bands, lifting degeneracy and generating symmetry breaking at non-integer fillings, yet without opening a global gap. Because there is no global gapped signature, the system remains metallic, but the effect reveals itself in anomalous Hall responses, signaling time-reversal symmetry breaking and valley polarization. Our results demonstrate dual-flatness as a guiding principle, extending moire physics beyond commensurate fillings and identifying topological transport as a probe of gapless correlated metals.

cond-mat.str-el↗

arXiv2026

Wavefunction textures in twisted bilayer graphene from first principles

Motivated by recent experiments probing the wavefunctions of magic-angle twisted bilayer graphene (tBLG), we perform large-scale first-principles calculations of tBLG with full atomic relaxation across a wide range of twist angles down to $0.99^\circ$. Focusing on the magic angle, we compute wavefunctions of the low energy bands, resolving atomic-scale details and moiré-scale patterns that form triangular, honeycomb, and Kagome lattices. By tuning the interlayer interactions, we illustrate the formation of the flat bands from isolated monolayers and the emergence of the band inversion and fragile topology at a sufficiently large interaction strength. We identify strong indicators of a new phase transition with increasing interlayer interaction strength, achievable with external pressure or a decrease in the twist angle. When this transition occurs, the upper and lower flat bands exchange their wavefunction character and symmetry eigenvalues, which may be correlated with the appearance of superconductivity with electron doping below the magic angle. Our study demonstrates the feasibility of using first-principles wavefunctions to help interpret experimental signatures of topological and correlated phases in tBLG.

cond-mat.mes-hall↗

arXiv2025

Squeezing Quantum States in Three-Dimensional Twisted Crystals

A fundamental idea in wave mechanics is that propagation in a periodic medium can be described by Bloch waves whose conserved crystal momenta define their transformations when displaced by the set of discrete lattice translations. In ordered materials where incommensurate spatial periods compete, this general principle is rendered ineffective, often with dramatic consequences. Examples are crystals with broken symmetries from charge or spin density waves, quasiperiodic lattices that produce diffraction patterns with crystallographically forbidden point symmetries, and stacks of two-dimensional lattices with a relative rotation (twist) between layers. In special cases when there is a small difference between the competing periods, a useful work-around is a continuum description where a periodic long-wavelength field produces Bragg scattering that coherently mixes short-wavelength carrier waves. In this work, we advocate an alternative approach to study three-dimensional twisted crystals that replaces their spectrally congested momentum-space Bloch band structures with a representation using squeezed coherent states in a Fock space of free-particle vortex states. This reorganization of the Hilbert space highlights the crucial role of the Coriolis force in the equations of motion that leads to unconventional phase space dynamics and edge state structure generic to a family of complex crystals.

cond-mat.mes-hall↗

arXiv2025

Universal Symmetries in Twisted Moiré Materials

Two-dimensional multi-layer materials with an induced moiré pattern, either due to strain or relative twist between layers, provide a versatile platform for exploring strongly correlated and topological electronic phenomena. While these systems offer unprecedented tunability, their theoretical description remains challenging due to their complex atomic structures and large unit cells. A notable example is twisted bilayer graphene, where even the relevant symmetry group remains unsettled despite its critical role in constructing effective theories. Here, we focus on twisted bilayer graphene and use a combination of analytical methods, molecular dynamics simulations, and first-principles calculations to show that twisted atomic configurations with distinct microscopic symmetries converge to a universal interlayer structure that governs the low-energy physics. This emergent universality provides a robust foundation for symmetry-respecting models and offers insight into the role of commensurability in real twisted moiré systems.

cond-mat.str-el↗

arXiv2024

Analytical Model for Atomic Relaxation in Twisted Moiré Materials

By virtue of being atomically thin, the electronic properties of heterostructures built from two-dimensional materials are strongly influenced by atomic relaxation. The atomic layers behave as flexible membranes rather than rigid crystals. Here we develop an analytical theory of lattice relaxation in twisted moiré materials. We obtain analytical results for the lattice displacements and corresponding pseudo gauge fields, as a function of twist angle. We benchmark our results for twisted bilayer graphene and twisted WSe$_2$ bilayers using large-scale molecular dynamics simulations. Our \textit{single-parameter} theory is valid in graphene bilayers for twist angles $θ~\gtrsim 0.7^\circ$, and in twisted WSe$_2$ for $θ~\gtrsim 1.6^\circ$. We also investigate how relaxation alters the electronic structure in twisted bilayer graphene, providing a simple extension to the continuum model to account for lattice relaxation.

cond-mat.str-el↗

arXiv2024

Imaging the Sub-Moiré Potential Landscape using an Atomic Single Electron Transistor

Electrons in solids owe their properties to the periodic potential landscapes they experience. The advent of moiré lattices has revolutionized our ability to engineer such landscapes on nanometer scales, leading to numerous groundbreaking discoveries. Despite this progress, direct imaging of these electrostatic potential landscapes remains elusive. In this work, we introduce the Atomic Single Electron Transistor (SET), a novel scanning probe utilizing a single atomic defect in a van der Waals (vdW) material, which serves as an ultrasensitive, high-resolution potential imaging sensor. Built upon the quantum twisting microscope (QTM) platform, this probe leverages the QTM's distinctive capability to form a pristine, scannable 2D interface between vdW heterostructures. Using the Atomic SET, we present the first direct images of the electrostatic potential in one of the most canonical moiré interfaces: graphene aligned to hexagonal boron nitride. Our results reveal that this potential exhibits an approximate C6 symmetry, has minimal dependence on the carrier density, and has a substantial magnitude of ~60 mV even in the absence of carriers. Theoretically, the observed symmetry can only be explained by a delicate interplay of physical mechanisms with competing symmetries. Intriguingly, the magnitude of the measured potential significantly exceeds theoretical predictions, suggesting that current understanding may be incomplete. With a spatial resolution of 1 nm and a sensitivity to detect the potential of even a few millionths of an electron charge, the Atomic SET opens the door for ultrasensitive imaging of charge order and thermodynamic properties for a range of quantum phenomena, including various symmetry-broken phases, quantum crystals, vortex charges, and fractionalized quasiparticles.

cond-mat.mes-hall↗

arXiv2024

A self-consistent Hartree theory for lattice-relaxed magic-angle twisted bilayer graphene

For twisted bilayer graphene close to magic angle, we show that the effects of lattice relaxation and the Hartree interaction both become simultaneously important. Including both effects in a continuum theory reveals a Lifshitz transition to a Fermi surface topology that supports both a ``heavy fermion" pocket and an ultraflat band ($\approx 8~{\rm meV}$) that is pinned to the Fermi energy for a large range of fillings. We provide analytical and numerical results to understand the narrow ``magic angle range" that supports this pinned ultraflat band and make predictions for its experimental observation. We believe that the bands presented here are accurate at high temperature and provide a good starting point to understand the myriad of complex behaviour observed in this system.

cond-mat.str-el↗

arXiv2023

Controlled alignment of supermoiré lattice in double-aligned graphene heterostructures

The supermoiré lattice, built by stacking two moiré patterns, provides a platform for creating flat mini-bands and studying electron correlations. An ultimate challenge in assembling a graphene supermoiré lattice is in the deterministic control of its rotational alignment, which is made highly aleatory due to the random nature of the edge chirality and crystal symmetry of each component layer. Employing the so-called golden rule of three, here we present an experimental strategy to overcome this challenge and realize the controlled alignment of double-aligned hBN/graphene/hBN supermoiré lattice, where graphene is precisely aligned with both top hBN and bottom hBN. Remarkably, we find that the crystallographic edge of neighboring graphite can be used to better guide the stacking alignment, as demonstrated by the controlled production of 20 moiré samples with an accuracy better than 0.2 degree. Finally, we extend our technique to other strongly correlated electron systems, such as low-angle twisted bilayer graphene and ABC-stacked trilayer graphene, providing a strategy for flat-band engineering in these moiré materials.

cond-mat.mes-hall↗

arXiv2023

Topological Flat Bands in Graphene Super-moiré Lattices

Moiré-pattern based potential engineering has become an important way to explore exotic physics in a variety of two-dimensional condensed matter systems. While these potentials have induced correlated phenomena in almost all commonly studied 2D materials, monolayer graphene has remained an exception. We demonstrate theoretically that a single layer of graphene, when placed between two bulk boron nitride crystal substrates with the appropriate twist angles can support a robust topological ultra-flat band emerging from the second hole band. This is one of the simplest platforms to design and exploit topological flat bands.

cond-mat.mes-hall↗

arXiv2023

Extended magic phase in twisted graphene multilayers

Theoretical and experimental studies have verified the existence of ``magic angles'' in twisted bilayer graphene, where the twist between layers gives rise to flat bands and consequently highly correlated phases. Narrow bands can also exist in multilayers with alternating twist angles, and recent theoretical work suggests that they can also be found in trilayers with twist angles between neighboring layers in the same direction. We show here that flat bands exist in a variety of multilayers where the ratio between twist angles is close to coprime integers. We generalize previous analyses, and, using the chiral limit for interlayer coupling, give examples of many combinations of twist angles in stacks made up of three and four layers which lead to flat bands. The technique we use can be extended to systems with many layers. Our results suggest that flat bands can exist in graphene multilayers with angle disorder, that is, narrow samples of turbostatic graphite.

cond-mat.str-el↗

arXiv2020

Moiré patterns in graphene -- rhenium disulfide vertical heterostructures

Vertical stacking of atomically thin materials offers a large platform for realizing novel properties enabled by proximity effects and moiré patterns. Here we focus on mechanically assembled heterostructures of graphene and ReS$_2$, a van der Waals layered semiconductor. Using scanning tunneling microscopy and spectroscopy (STM/STS) we image the sharp edge between the two materials as well as areas of overlap. Locally resolved topographic images revealed the presence of a striped superpattern originating in the interlayer interactions between graphene's hexagonal structure and the triclinic, low in-plane symmetry of ReS$_2$. We compare the results with a theoretical model that estimates the shape and angle dependence of the moiré pattern between graphene and ReS$_2$. These results shed light on the complex interface phenomena between van der Waals materials with different lattice symmetries.

cond-mat.mtrl-sci↗

arXiv2020

Tunable van Hove Singularities and Correlated States in Twisted Trilayer Graphene

Understanding and tuning correlated states is of great interest and significance to modern condensed matter physics. The recent discovery of unconventional superconductivity and Mott-like insulating states in magic-angle twisted bilayer graphene (tBLG) presents a unique platform to study correlation phenomena, in which the Coulomb energy dominates over the quenched kinetic energy as a result of hybridized flat bands. Extending this approach to the case of twisted multilayer graphene would allow even higher control over the band structure because of the reduced symmetry of the system. Here, we study electronic transport properties in twisted trilayer graphene (tTLG, bilayer on top of monolayer graphene heterostructure). We observed the formation of van Hove singularities which are highly tunable by twist angle and displacement field and can cause strong correlation effects under optimum conditions, including superconducting states. We provide basic theoretical interpretation of the observed electronic structure.

cond-mat.mes-hall↗