arXiv subjects

Leonardo A. Navarro-Labastida

Publications and source records attributed to Leonardo A. Navarro-Labastida.

9 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↗

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

Thermal quantum information capacity in a topological insulator

Thermal effects in a one-dimensional Su-Schrieffer-Hegger (SSH) topological insulator are studied. Particularly, we focus on quantum information processing (QIP) capacity for thermal ensembles. To evaluate QIP an optimized quantum Fisher information (OQFI) is introduced as a quantifier of entanglement and topological phases are calculated by a definition in real space for the electric polarization of mixture states. For the thermal ensemble, there is a relationship between the Fisher metric and the electric polarization in such a way that in the topological region, there is more entanglement, therefore, these generate more robustness and protection in the quantum information due to thermal effects. Also, long-range hopping effects are studied and it is found that in this case, the OQFI captures these topological phase transitions in the limit of low temperature by this formalism in real space.

quant-ph↗

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

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

3/2 magic-angle quantization rule of flat bands in twisted bilayer graphene and relationship with the Quantum Hall effect

Flat band electronic modes in twisted graphene bilayers are responsible for superconducting and other highly correlated electron-electron phases. Although some hints were known of a possible connection between the quantum Hall effect and zero flat band modes, it was not clear how such connection appears. Here the electronic behavior in twisted bilayer graphene is studied using the chiral model Hamiltonian. As a result, it is proved that for high-order magic angles, the zero flat band modes converge into coherent Landau states with a dispersion $σ^2=1/3α$, where $α$ is a coupling parameter that incorporates the twist angle and energetic scales. Then it is proved that the square of the hamiltonian, which is a $2\times 2$ matrix operator, turns out to be equivalent to a two-dimensional quantum harmonic oscillator. The interlayer currents between graphene's bipartite lattices are identified with the angular momentum term while the confinement potential is an effective quadratic potential. From there it is proved a limiting quantization rule for high-order magic angles, i.e., $α_{m+1}-α_{m}=3/2$ where $m$ is the order of the angle. All these results are in very good agreement with numerical calculations.

cond-mat.mes-hall↗

arXiv2022

Topological phases and entanglement in real space for 1D SSH topological insulator: effects of first and second neighbor-hoppings

The hybrid atoms-cell site entanglement in a one-dimensional Su-Schrieffer-Heeger (SSH) topological insulator with first and second neighbor hopping interaction in space representation of finite chains is analyzed. The geometric phase is calculated by the Resta electric polarization and the entanglement in the atomic basis by the Schmidt number. A relation between entanglement and the topological phase transitions (TPT) is given since the Schmidt number has critical points of maximal entangled (ME) states in the singularities of the geometrical phase. States with second-neighbors have higher entanglement than first-order hopping. The general conditions to produce ME hybrid Bell states and the localization-entanglement relation are given.

quant-ph↗

arXiv2022

Flat bands, quantum Hall effect and superconductivity in twisted bilayer graphene at magic angles

Flat band electronic modes are responsible for superconductivity in twisted bilayer graphene (TBG) rotated at magic angles. From there other magic angles can be found for any multilayered twisted graphene systems. Eventually, this lead to the discovery of the highest ever known electron-electron correlated material. Moreover, the quantum phase diagram of TBG is akin to those observed among high-$T_{c}$ superconductors and thus there is a huge research effort to understand TBG in the hope of clarifying the physics behind such strong correlations. A particularity of the TBG is the coexistence of superconductivity and the fractional Quantum Hall effect, yet this relationship is not understood. In this work, a simple $2\times 2$ matrix model for TBG is introduced. It contains the magic angles and due to the intrinsic chiral symmetry in TBG, a lowest energy level related to the quantum Hall effect. The non-Abelian properties of this Hamiltonian play a central role in the electronic localization to produce the flat bands and here it is proved that the squared Hamiltonian of the chiral TBG model is equivalent to a single electron Hamiltonian inside of a non-Abelian pseudo-magnetic field produced by electrons in other layers. Therefore, the basic and fundamental elements in the physics of magic angles are determined. In particular, a study is made on these fundamental energy contributions at the $Γ$-point due to its relation to the recurrence of magic angles and its relationship with the Quantum Hall effect.

cond-mat.mes-hall↗

arXiv2022

Why the first magic-angle is different from others in twisted graphene bilayers: interlayer currents, kinetic and confinement energy and wavefunction localization

The chiral Hamiltonian for twisted graphene bilayers is analyzed in terms of its squared Hamiltonian which removes the particle-hole symmetry and thus one bipartite lattice, allowing to write the Hamiltonian in terms of a $2\times 2$ matrix. This brings to the front the three main physical actors of twisted systems: kinetic energy, confinement potential and an interlayer interaction operator which is divided in two parts: a non-Abelian interlayer operator and an operator which contains an interaction energy between layers. Here, each of these components is analyzed as a function of the angle of rotation, as well as in terms of the wave-function localization properties. In particular, it is proved that the non-Abelian operator represents interlayer currents between each layer triangular sublattices, i.e., a second-neighbor interlayer current between bipartite sublattices. A crossover is seen between such contributions and thus the first magic angle is different from other higher order magic angles. Such angles are determined by a balance between the negative energy contribution from interlayer currents and the positive contributions from the kinetic and confinement energies. A perturbative analysis performed around the first magic angle allows to explore analytically the details of such energy balance.

cond-mat.mes-hall↗