arXiv subjects

Gerardo G. Naumis

Publications and source records attributed to Gerardo G. Naumis.

At least 19 recordsLinked to original sources

arXiv2026

The First Magic Angle Beyond the Chiral Limit in Twisted Bilayer Graphene

We develop a squared-Hamiltonian description of twisted bilayer graphene beyond the chiral limit to explain why the first magic angle remains robust under lattice relaxation, while higher-order magic angles are strongly destabilized. Starting from the non-chiral Bistritzer--MacDonald model with finite same-sublattice tunneling, we show that lattice relaxation reshapes the effective confinement landscape rather than acting as a simple perturbation of the chiral theory. A central result is that the realistic relaxation-renormalized tunneling ratio lies close to a special confinement point where the oscillatory part of the symmetric confinement potential nearly cancels. This places realistic twisted bilayer graphene near a nearly uniform confinement regime. At the same time, finite same-sublattice tunneling activates an additional inter-sublattice current-like channel that competes with the chiral orbital channel. The first magic angle survives because these confinement and current-like contributions remain balanced, whereas higher-order magic angles lose this balance through stronger remote-band hybridization and enhanced real-space localization around AA regions. Our results provide a single-particle mechanism for the breakdown of the chiral magic-angle hierarchy and clarify why the experimentally relevant first magic angle remains the most stable remnant of the chiral flat-band structure.

cond-mat.mes-hall↗

arXiv2026

Gap-controlled thermalization in a SSH model version of the Fermi-Pasta-Ulam-Tsingou chain

In classical anharmonic lattices, the resonance structure driving nonlinear mode mixing is reshaped by band gaps. However, it remains unclear whether a spectral gap hinders or promotes long-time thermalization. Here we study a dimerized Fermi-Pasta-Ulam-Tsingou chain - a classical SSH model analogue with alternating spring constants - and quantify how the acoustic-optical gap controls relaxation under alpha-type (cubic) nonlinearity. Tracking modal energies and spectral entropy via long-time symplectic simulations, we find a sharp isolation threshold when the dimerization strength reaches half its maximum value, set by the onset of the first umklapp process that allows two zone-boundary acoustic phonons to fuse into a zone-center optical phonon; below this threshold, three-wave acoustic-acoustic-optical scattering activates the optical branch on timescales of order 1e4 oscillation periods, while above it the bands remain dynamically isolated. We further show that boundary conditions reshape this picture, producing long-lived sticky states for specific mode excitations. These results establish the phononic gap as a tunable, momentum-selective filter for nonlinear energy transport, suggesting a general route to controlling thermalization in dimerized or topologically gapped nonlinear lattices.

cond-mat.stat-mech↗

arXiv2026

Interaction-driven charge textures and unconventional superconductivity in strained monolayer graphene

Two-dimensional systems with flat bands support correlated phases such as superconductivity. While twisted moiré systems, like twisted bilayer graphene, have revealed such states, they remain complex to control. Here, we study monolayer graphene under uniaxial periodic strain, which forms a quasi-one-dimensional moiré lattice that hosts two flat sublattice-polarized bands. When electron-electron interactions are included at the self-consistent Hartree level, we find features familiar from moiré flat-band systems, such as Fermi-level pinning to the Van Hove singularity and a Kohn-Luttinger-like pairing instability. In addition, we find strong interband enhancement of the pairing scale and higher-energy metastable electrostatic textures in enlarged supercells, with charge localized in selected regions of multiple unit cells.

cond-mat.mes-hall↗

arXiv2025

Magnetic phase transitions protected by topological quantum geometry transitions: effects of electron-electron interactions in the Creutz ladder system

The interplay between electronic correlations and band topology is a central theme in modern condensed matter physics. In this work, we investigate the effects of on-site Hubbard interactions on the topological, magnetic, and quantum geometric properties of the Creutz ladder, a paradigmatic model of a one-dimensional topological insulator. Using a self-consistent mean-field approach, we uncover a first-order, interaction-driven phase transition that is simultaneously magnetic and topological. We demonstrate that as the Hubbard interaction $U$ is increased, the system's ground state abruptly switches from an anti-ferromagnetic (AF) configuration to a ferromagnetic (F) one. This magnetic transition coincides with a topological transition, marked by a quantized jump in the Zak phase from $\pmπ$ to $0$. We systematically compute the phase diagrams in the parameter space of on-site energy staggering ($ε$) and inter-chain hopping asymmetry ($λ$), revealing the critical interaction strength $U_c$. Furthermore, we analyze the quantum geometry of the Bloch states by calculating the Fubini-Study metric, demonstrating that its components exhibit divergences that precisely signal the topological phase transition. By analyzing the full energy spectrum, we distinguish the true ground state from metastable excited states that emerge past the critical point. Our results establish the Creutz-Hubbard ladder as a minimal model for studying interaction-induced topological phenomena and suggest a potential route for controlling magnetic, topological, and geometric properties via electronic correlations.

cond-mat.str-el↗

arXiv2025

Electronic structure and optical signatures of highly-doped graphene

Heavily doping graphene by intercalation can raise its Fermi level near an extended van Hove singularity, potentially inducing correlated electronic phases. Intercalation also modifies the band structure: dopants may hybridize with carbon orbitals and order into $\sqrt{3}\times\sqrt{3}$ or $2\times2$ superstructures, introducing periodic potentials that fold the graphene $π$ bands. Angle-resolved photoemission spectroscopy further shows a pronounced flattening of the conduction band near the M points, producing higher-order van Hove singularities. These effects depend strongly on the dopant species and substrate, with implications for both many-body physics and transport. We construct effective tight-binding models that incorporate dopant ordering, carbon-dopant hybridization, and $π$-band renormalization. Model parameters are obtained from density functional theory and reproduce dispersions observed in photoemission experiments. Using these models, we compute the optical conductivity and identify characteristic signatures associated with dopant ordering and hybridization. Our results provide a framework to interpret experimental spectra and to probe the superlattice symmetry of highly doped monolayer graphene.

cond-mat.mes-hall↗

arXiv2025

Hyperbolic Plasmon dispersion and Optical Conductivity of Holey Graphene: signatures of flat-bands

Holey graphene (HG) is a novel two-dimensional (2D) material that has attracted considerable attention due to its remarkable electrical, thermal, and mechanical properties. The recent discovery of flat bands in HG has garnered significant interest. In this work, we systematically investigate the tunable plasmonic modes and optical conductivity of HG at or near the flat band condition by changing the holes radii and periodic configuration. It is found that HG presents nearly flat plasmonic bands in configurations with larger hole radii. Hyperbolic plasmons are found due to the breaking of the graphene's bipartite sublattice symmetry induced by the holes. Such an effect is also confirmed by looking at the optical conductivity, that also presents a marked anisotropy. The material's marked optical anisotropy leads to hyperbolic plasmons, making it a promising platform for nanophotonic applications.

physics.optics↗

arXiv2025

Topological phase diagram of twisted bilayer graphene as a function of the twist angle

Twisted bilayer graphene (TBG) hosts a rich landscape of electronic phases arising from the interplay between strong electron-electron interactions and nontrivial band topology. While the flat bands near zero energy are central to many correlated phenomena, their interaction with higher-energy remote bands remains less understood. Here, we investigate these hybridization processes as a function of the twist angle and analyze their impact on the charge distribution, topological properties such as Chern number, quantum metric, and orbital magnetic energy. We identify multiple topological phase transitions between magic angles, driven by band inversions at high-symmetry points in momentum space. Notably, the central bands can exhibit phases with Chern numbers C = 2, revealing previously unreported topological states in TBG.

cond-mat.mes-hall↗

arXiv2025

Designing Flat Bands and Pseudo-Landau Levels in GaAs with Patterned Gates

We investigate the electronic properties of two-dimensional electron gases (2DEGs) subjected to a periodic patterned gate. By incorporating the superlattice (SL) potential induced by patterning into the Schrodinger equation, we develop a methodology for obtaining exact analytical solutions. These solutions enable us to construct a comprehensive phase diagram illustrating the emergence of narrow bands and pseudo-Landau levels driven by the SL potential. To complement the analytical approach, we employ a standard plane-wave formalism to track the evolution of the band structure as the SL strength increases. By breaking the inversion symmetry of the SL potential, we found a nontrivial Berry curvature. Furthermore, we introduce a self-consistent Hartree screening to account for the interplay between the SL potential and electronic interactions. Our findings not only reveal the emergence of a non-trivial quantum geometry and a competition between SL strength and electron-electron interactions, but also highlight the value of exact analytical solutions for understanding and engineering electronic phases in patterned 2DEG systems.

cond-mat.mes-hall↗

arXiv2025

When Adiabaticity Is Not Enough to Study Topological Phases in Solid-State Physics: Comparing the Berry and Aharonov-Anandan Phases in 2D Materials

Topological phases emerge as the parameters of a quantum system vary with time. Under the adiabatic approximation, the time dependence can be eliminated, allowing the Berry topological phase to be obtained from a closed trajectory in parameter space. In solid-state physics, this approach is commonly applied by taking a reciprocal space wavevector as the parameter, which is assumed to be varied by electromagnetic fields.The Berry curvature is then obtained by computing the derivatives of Bloch wavefunctions in reciprocal space. However, in many systems-especially gapless ones-the adiabatic approximation is never satisfied. This is particularly true in Dirac and Weyl materials, where the Berry curvature is often calculated without considering the breakdown of the adiabatic condition. In this work, we demonstrate how other time-dependent topological quantities, specifically the Aharonov-Anandan phase, can be used to extract information not only about topology but also about band transitions in 2D materials. In particular, a relationship between the current and the Aharonov-Anandan phase is proved, showing that photon-induced transitions produce current vortices. To illustrate this, we analyze graphene under electromagnetic radiation from a time-driven perspective, showing how the Aharonov-Anandan and Berry phases provide complementary insights into topology, interband transitions, and currents. This is achieved by using the Dirac-Bloch formalism and by solving the time-dependent equations within Floquet theory.

cond-mat.mes-hall↗

arXiv2024

Electronic Structure and Kohn-Luttinger Superconductivity of Heavily-Doped Single-Layer Graphene

The existence of superconductivity (SC) in graphene appears to be established in both twisted and non-twisted multilayers. However, whether their building block, single-layer graphene (SLG), can also host SC remains an open question. Earlier theoretical works predicted that SLG could become a chiral d-wave superconductor driven by electronic interactions when doped to its van Hove singularity, but questions such as whether the d-wave SC survives the strong band renormalizations seen in experiments, its robustness against the source of doping, or if it will occur at any reasonable critical temperature (Tc) have remained difficult to answer, in part due to uncertainties in model parameters. In this study, we adopt a random-phase approximation framework based on a Kohn-Luttinger-like mechanism to investigate SC in heavily-doped SLG. We predict that robust d+id topological SC could arise in SLG doped by Tb, with a Tc up to 600 mK. We also investigate the possibility of realizing d-wave SC by employing other dopants, such as Li or Cs. The structural models have been derived from angle-resolved photoemission spectroscopy measurements on Tb-doped graphene and first-principles calculations for Cs and Li doping. We find that dopants that change the lattice symmetry of SLG are detrimental to the d-wave state. The stability of the d-wave SC predicted here in Tb-doped SLG could provide a valuable insight for guiding future experimental efforts aimed at exploring topological superconductivity in monolayer graphene.

cond-mat.mes-hall↗

arXiv2024

Curved graphene: a possible answer to the problem of graphene's diverging magnetic susceptibility

A study of strongly curved graphene magnetization and magnetic susceptibility is carried out. Through a Dirac model complemented with a tight-binding model analysis, we are able to show that mechanical deformations solve the long-standing problem of graphene's theoretically calculated diamagnetic divergence at low temperatures. This suggests that corrugations and mechanical defects in graphene are the cause of finite experimentally measurable magnetic susceptibility. Furthermore, a mechanical effect is also found due to an electronic contribution, which produces a pseudo-de Haas van Alphen (dHvA) effect. This effect is related to oscillating (electronic) forces that oppose deformations; these forces are divergent in flat graphene, indicating that graphene (without substrate) achieves mechanical equilibrium by corrugations. In addition, paramagnetism is predicted for graphene with negative curvature under strong magnetic fields.

cond-mat.mes-hall↗

arXiv2023

Flat bands without twists: periodic holey graphene

\textit{Holey Graphene} (HG) is a widely used graphene material for the synthesis of high-purity and highly crystalline materials. In this work, we explore the electronic properties of a periodic distribution of lattice holes, demonstrating the emergence of flat bands with compact localized states. It is shown that the holes break the bipartite sublattice and inversion symmetries, inducing gaps and a nonzero Berry curvature. Moreover, the folding of the Dirac cones from the hexagonal Brillouin zone (BZ) to the holey superlattice rectangular BZ of HG with sizes proportional to an integer $n$ times the graphene's lattice parameter leads to a periodicity in the gap formation such that $n \equiv 0$ (mod $3$). Meanwhile, it is shown that if $n \equiv \pm 1$ (mod $3$), a gap emerges where Dirac points are folded along the $Γ-X$ path. The low-energy hamiltonian for the three central bands is also obtained, revealing that the system behaves as an effective $α-\mathcal{T}_{3}$ graphene material. Therefore, a simple protocol is presented here that allows obtaining flat bands at will. Such bands are known to increase electron-electron correlated effects. This work provides an alternative system, much easier to build than twisted systems, to obtain highly correlated quantum phases.

cond-mat.mes-hall↗

arXiv2023

Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals

The topological properties of the flat band states of a one-electron Hamiltonian that describes a chain of atoms with $s-p$ orbitals are explored. This model is mapped onto a Kitaev-Creutz type model, providing a useful framework to understand the topology through a nontrivial winding number and the geometry introduced by the \textit{Fubini-Study (FS)} metric. This metric allows us to distinguish between pure states of systems with the same topology and thus provides a suitable tool for obtaining the fingerprint of flat bands. Moreover, it provides an appealing geometrical picture for describing flat bands as it can be associated with a local conformal transformation over circles in a complex plane. In addition, the presented model allows us to relate the topology with the formation of Compact Localized States (CLS) and pseudo-Bogoliubov modes. Also, the properties of the squared Hamiltonian are investigated in order to provide a better understanding of the localization properties and the spectrum. The presented model is equivalent to two coupled SSH chains under a change of basis.

cond-mat.str-el↗

arXiv2023

Self-duality properties and localization centers of the electronic wave functions at high magic angles in twisted bilayer graphene

Twisted bilayer graphene (TBG) is known for exhibiting highly correlated phases at magic angles due to the emergence of flat bands that enhance electron-electron interactions. In the TBG chiral model, electronic wave function properties depend on a single parameter ($α$), inversely proportional to the relative twist angle between the two graphene layers. In previous studies, as the twist angles approached small values, strong confinement, and convergence to coherent Landau states were observed. This work explores flat-band electronic modes, revealing that flat band states exhibit self-duality; they are coherent Landau states in reciprocal space and exhibit minimal dispersion, with standard deviation $σ_k=\sqrt{3α/2π}$ as $α$ approaches infinity. Subsequently, by symmetrizing the wave functions and considering the squared TBG Hamiltonian, the strong confinement observed in the $α\rightarrow\infty$ limit is explained. This confinement arises from the combination of the symmetrized squared norm of the moiré potential and the quantized orbital motion of electrons, effectively creating a quantum well. The ground state of this well, located at defined spots, corresponds to Landau levels with energy determined by the magic angle. Furthermore, we demonstrate that the problem is physically analogous to an electron attached to a non-Abelian $SU(2)$ gauge field with an underlying $C_3$ symmetry. In regions of strong confinement, the system can be considered as Abelian. This allows to define a magnetic energy in which the important role of the wave function parity and gap closing at non-magic angles is revealed. Finally, we investigate the transition from the original non-Abelian nature to an Abelian state by artificially changing the pseudo-magnetic vector components from an $SU(2)$ to a $U(1)$ field, which alters the sequence of magic angles.

cond-mat.mes-hall↗

arXiv2023

Flat band localization in twisted bilayer graphene nanoribbons

We analyze the electronic structure of twisted bilayer graphene (TBG) nanoribbons close to the magic angle. We describe a transition from an incomplete to a complete moiré structure. By considering zigzag and armchair edge terminations, the low-energy bands are strongly modified, and thus, the edge flat band localization is sensitive to the type of boundary. By means of a scaled tight-binding model, we calculate the band structure and find that, for an armchair configuration, an incomplete moiré edge suppresses the edge localization, while for a zigzag configuration, we find a strong interference of the edge states with the moiré bands. In particular, for the armchair termination, we observe a competition between the ribbon periodicity and the graphene monolayers, which we describe with a potential well toy model. Furthermore, for ribbons with widths of multiple moiré cells, the flat bands of the moirés in the bulk are unperturbed as we change the borders. These results are explained in terms of the strong electronic localization, nearly Gaussian, in the AA stacking regions, as confirmed by an inverse participation ratio analysis. Our results demonstrate that the electronic structure of TBG nanoribbons is sensitive to the edge termination, offering an explanation for recent experimental results.

cond-mat.mes-hall↗

arXiv2023

Reduction of the Twisted Bilayer Graphene Chiral Hamiltonian into a $2\times2$ matrix operator and physical origin of flat-bands at magic angles

The chiral Hamiltonian for twisted graphene bilayers is written as a $2\times2$ matrix operator by a renormalization of the Hamiltonian that takes into account the particle-hole symmetry. This results in an effective Hamiltonian with an average field plus and effective non-Abelian gauge potential. The action of the proposed renormalization maps the zero-mode region into the ground state. Modes near zero energy have an antibonding nature in a triangular lattice. This leads to a phase-frustration effect associated with massive degeneration, and makes flat-bands modes similar to confined modes observed in other bipartite lattices. Suprisingly, the proposed Hamiltonian renormalization suggests that flat-bands at magic angles are akin to floppy-mode bands in flexible crystals or glasses, making an unexpected connection between rigidity topological theory and magic angle twisted two-dimensional heterostructures physics.

cond-mat.mes-hall↗

arXiv2023

Multifractal wave functions of charge carriers in graphene with folded deformations, ripples or uniaxial flexural modes: analogies to the quantum Hall effect under random pseudomagnetic fields

The electronic behavior in graphene under arbitrary uniaxial deformations, such as foldings or flexural fields is studied by including in the Dirac equation pseudoelectromagnetic fields. General foldings are thus studied by showing that uniaxial deformations can be considered pseudomagnetic fields in the Coulomb gauge norm. This allows to give an expression for the Fermi (zero) energy modes wavefunctions. For random deformations, contact is made with previous works on the quantum Hall effect under random magnetic fields, showing that the density of states has a power law behavior and that the zero energy modes wavefunctions are multifractal. This hints at an unusual electron velocity distribution. Also, it is shown that a strong Aharonov-Bohm pseudo-effect is produced. For more general non-uniaxial general flexural strain, it is not possible to use the Coulomb gauge. The results presented here helps to tailor-made graphene uniaxial deformations to achieve specific wavefunctions.

cond-mat.mes-hall↗

arXiv2023

Topological origin of flat-bands as pseudo-Landau levels in uniaxial strained graphene nanoribbons and induced magnetic ordering due to electron-electron interactions

Flat-bands play a central role in the presence of correlated phases in Moiré and other modulated two dimensional systems. In this work, flat-bands are shown to exist in uniaxially periodic strained graphene. Such strain should be produced for example by a substrate. The model is thus mapped into a one-dimensional effective Hamiltonian and this allows to find the conditions for having flat-bands, i.e., a long-wavelength modulation only on each one of the bipartite graphene sublattices, while having a tagged strain field between neighboring carbon atoms. The origin of such flat-bands is thus tracked down to the existence of topological localized wavefunctions at domain walls separating different regions, each with a non-uniform Su-Schriffer-Hegger model (SSH) type of coupling. Thereafter, the system is mapped into a continuum model allowing to explain the numerical results in terms of the Jackiw-Rebbi model and of pseudo-Landau levels. Finally, the interplay between the obtained flat-bands and electron-electron interaction is explored through the Hubbard model. The numerical results within the mean-field approximation indicate that the flat-bands induce Néel antiferromagnetic and ferromagnetic domains even for a very weak Hubbard interaction. The present model thus provides a simple platform to understand the physical origin of flat-bands, pseudo-Landau levels and the effects of the electron-electron interaction.

cond-mat.mes-hall↗