arXiv subjects

Eduardo V. Castro

Publications and source records attributed to Eduardo V. Castro.

At least 19 recordsLinked to original sources

arXiv2026

Quasiperiodicity-induced enhancement of superconductivity in one-dimensional critical systems

We show that quasiperiodicity can enhance superconductivity in one-dimensional narrow-band systems with s-wave pairing. Using a generalized Aubry-André-Harper model featuring quasiperiodic modulations in both the on-site potential and the hoppings, we study superconductivity across the extended, critical, and localized phases present in the noninteracting limit. Our results show that within the critical and localized phases, the superconducting critical temperature exhibits an algebraic scaling with the interaction strength, in contrast to the conventional BCS scaling observed in periodic approximants with a similar density of states. This direct comparison establishes that the enhancement originates from the nature of the single-particle eigenstates, rather than from band flattening alone. Furthermore, we find that the superfluid weight remains finite across all phases, including the localized regime, highlighting that superconducting phase coherence is retained throughout. The effects of quasiperiodicity on the superfluid weight are most pronounced in the weak-coupling regime, indicating the nontrivial role of the localization properties of the parent eigenstates in shaping the superconducting phases.

cond-mat.supr-con↗

arXiv2026

Temperature-induced optical enhancement near a localization transition

Quasiperiodic systems are an intermediate class of systems between periodic crystals and disordered systems, famously exhibiting metal-insulator transitions (MITs) even in one dimension. While their transport properties have been studied extensively, a systematic analysis of the finite-frequency optical conductivity near the critical point has been lacking. In this work, we carry out a detailed study of the optical conductivity in the paradigmatic Aubry-André model. We find that the zero-temperature low-frequency optical signal is strongly restructured by the quasiperiodic potential, exhibiting an optical gap that closes discontinuously as the system approaches the MIT. Most strikingly, we uncover a mechanism for a strong enhancement of the low-frequency finite temperature optical conductivity at certain resonant frequencies. This enhancement stems from the thermal activation of Pauli-blocked transitions between strongly resonant van Hove singularities. This mechanism provides new insight into finite-frequency transport in quasiperiodic systems and a new pathway for manipulating optical properties near a localization transition. Furthermore, our findings establish the optical response as a powerful, experimentally accessible tool for probing non-trivial quasiperiodicity effects.

cond-mat.dis-nn↗

arXiv2026

Effective band-projected description of interacting quasiperiodic systems

We study the interplay between electronic interactions and quasiperiodicity in a one-dimensional narrow-band system, focusing on ground-state and low-energy excitation properties. Using band projection as low-energy effective approach, we show that a projection restricted to first order in the interaction strength fails to reproduce the correlated phase diagram. This contrasts with the standard success of first-order band projection in translationally invariant flatband systems and highlights the essential role of virtual processes involving remote bands in quasiperiodic settings. By incorporating second-order interband contributions perturbatively, we obtain an effective Hamiltonian that quantitatively reproduces the exact phase iagram previously obtained using density matrix renormalization group calculations, including the transition between a Luttinger liquid and a charge-density-wave phase and the crossover to a quasifractal charge-density-wave regime at strong quasiperiodicity. We further use this controlled framework to investigate low-energy neutral excitations and the optical conductivity, identifying clear dynamical signatures distinguishing the different phases. Our results establish second-order band projection as a reliable tool for correlated quasiperiodic narrow-band systems and suggest a promising route for studying interacting quasiperiodic and moiré materials beyond one dimension.

cond-mat.str-el↗

arXiv2025

Local Density of States as a Probe of Multifractality in Quasiperiodic Moiré Materials

Quasiperiodic moiré materials provide a new platform for realizing critical electronic states, yet a direct and experimentally practical method to characterize this criticality has been lacking. We show that a multifractal analysis of the local density of states (LDOS), accessible via scanning tunneling microscopy, offers an unambiguous signature of criticality from a single experimental sample. Applying this approach to a one-dimensional quasiperiodic model, a stringent test case due to its fractal energy spectrum, we find a clear distinction between the broad singularity spectra $f\left(α\right)$ of critical states and the point-like spectra of extended states. We further demonstrate that these multifractal signatures remain robust over a wide range of energy broadenings relevant to experiments. Our results establish a model-independent, experimentally feasible framework for identifying and probing multifractality in the growing family of quasiperiodic and moiré materials.

cond-mat.dis-nn↗

arXiv2025

Ground state and excitations of quasiperiodic 1D narrow-band moiré systems: a mean field approach

We demonstrate that a mean field approximation can be confidently employed in quasiperiodic moiré systems to treat interactions and quasiperiodicity on equal footing. We obtain the mean field phase diagram for an illustrative one-dimensional moiré system that exhibits narrow bands and a regime with non-interacting multifractal critical states. By systematically comparing our findings with existing exact results, we identify the regimes where the mean field approximation provides an accurate description. Interestingly, in the critical regime, we obtain a quasifractal charge density wave, consistent with the exact results. To complement this study, we employ a real-space implementation of the time-dependent Hartree-Fock, enabling the computation of the excitation spectrum and response functions at the RPA level. These findings indicate that a mean field approximation to treat systems hosting multifractal critical states, as found in two-dimensional quasiperiodic moiré systems, is an appropriate methodology.

cond-mat.str-el↗

arXiv2025

Quasiperiodic Quadrupole Insulators

Higher-order topological insulators are an intriguing new family of topological states that host lower-dimensional boundary states. Concurrently, quasiperiodic systems have garnered significant interest due to their complex localization and topological properties. In this work we study the impact of chiral symmetry preserving quasiperiodic modulations on the paradigmatic Benalcazar-Bernevig-Hughes model, which hosts topological insulating phases with zero-energy sublattice-polarized modes. We find that the topological properties are not only robust to the quasiperiodic modulation, but can even be enriched. In particular, we unveil the first instance of a quasiperiodic induced second-order topological insulating phase. Furthermore, in contrast with disorder, we find that quasiperiodic modulations can induce multiple reentrant topological transitions, showing an intricate sequence of localization properties. Our results open a promising avenue for exploring the rich interplay between higher-order topology and quasiperiodicity.

cond-mat.mes-hall↗

arXiv2025

Disorder-induced instability of a Weyl nodal loop semimetal towards a diffusive topological metal with protected multifractal surface states

Weyl nodal loop semimetals are gapless topological phases that, unlike their insulator counterparts, may be unstable to small perturbations that respect their topology-protecting symmetries. Here, we analyze a clean system perturbed by chiral off-diagonal disorder using numerically exact methods. We establish that the ballistic semimetallic phase is unstable towards the formation of an unconventional topological diffusive metal hosting topological multifractal surface states. Although, as in the clean case, surface states are exponentially localized along the direction perpendicular to the nodal loop, disorder induces a multifractal structure in the remaining directions. Surprisingly, the number of these states also increases with a small amount of disorder. Eventually, as disorder is further increased, the number of surface states starts decreasing.

cond-mat.dis-nn↗

arXiv2024

Fractal Quasicondensation in One Dimension

We unveil a novel mechanism for quasicondensation of hard-core bosons in the presence of quasiperiodicity-induced multifractal single-particle states. The new critical state, here dubbed fractal quasicondensate, is characterized by natural orbitals with multifractal properties and by an occupancy of the lowest natural orbital, λ0 ~ Lγ, which grows with system size but with a nonuniversal scaling exponent, γ < 1/2. In contrast to fractal quasicondensates obtained when the chemical potential lies in a region of multifractal single-particle states, placing the chemical potential in regions of localized or delocalized states yields, respectively, no condensation or the usual 1D quasicondensation with γ = 1/2. Our findings are established by studying one-dimensional hardcore bosons subjected to various quasiperiodic potentials, including the well-known Aubry-Andre model, employing a mapping to non-interacting fermionics that allows for numerically exact results. We discuss how to test our findings in state-of-the-art ultracold atom experiments.

cond-mat.quant-gas↗

arXiv2024

Topological Anderson insulating phases in the interacting Haldane model

We analyze the influence of disorder and strong correlations on the topology in two dimensional Chern insulators. A mean field calculation in the half-filled Haldane model with extended Hubbard interactions and Anderson disorder shows that disorder favors topology in the interacting case and extends the topological phase to a larger region of the Hubbard parameters. In the absence of a staggered potential, we find a novel disorder-driven topological phase with Chern number C=1, with co-existence of topology with long range spin and charge orders. More conventional topological Anderson insulating phases are also found in the presence of a finite staggered potential.

cond-mat.str-el↗

arXiv2024

Fate of Quadratic Band Crossing under quasiperiodic modulation

We study the fate of two-dimensional quadratic band crossing topological phases under a one-dimensional quasiperiodic modulation. By employing numerically exact methods, we fully characterize the phase diagram of the model in terms of spectral, localization and topological properties. Unlike in the presence of regular disorder, the quadratic band crossing is stable towards the application of the quasiperiodic potential and most of the topological phase transitions occur through a gap closing and reopening mechanism, as in the homogeneous case. With a sufficiently strong quasiperiodic potential, the quadratic band crossing point splits into Dirac cones which enables transitions into gapped phases with Chern numbers $C=\pm1$, absent in the homogeneous limit. This is in sharp contrast with the disordered case, where gapless $C=\pm1$ phases can arise by perturbing the band crossing with any amount of disorder. In the quasiperiodic case, we find that the $C=\pm1$ phases can only become gapless for a very strong potential. Only in this regime, the subsequent quasiperiodic-induced topological transitions into the trivial phase mirror the well-known ``levitation and annihilation'' mechanism in the disordered case.

cond-mat.dis-nn↗

arXiv2024

Instability of QBC systems to Topological Anderson Insulating phases

Here we study the instabilities of a quadratic band crossing system to Chern insulating states and uncorrelated disorder. We determined the phase diagram in the plane of topological mass versus disorder strength, characterizing the system with respect to spectral, localization and topological properties. In the clean limit, the system has two gapped Chern insulating phases with Chern numbers C=\pm2, and a trivial phase with C=0. For finite disorder, the quadratic band crossing points are unstable to emergent gapless Chern insulating phases with C=\pm1, not present in the clean limit. These phases occupy a considerable region of the phase diagram for intermediate disorder and show features of topological Anderson insulators: it is possible to reach them through disorder-driven transitions from trivial phases.

cond-mat.dis-nn↗

arXiv2023

Fragility of the antichiral edge states under disorder

Chiral edge states are the fingerprint of the bulk-edge correspondence in a Chern insulator. Co-propagating edge modes, known as antichiral edge states, have been predicted to occur in the so-called modified Haldane model describing a two-dimensional semi-metal with broken time reversal symmetry. These counterintuitive edge modes are argued to be immune to backscattering and extremely robust against disorder. Here, we investigate the robustness of the antichiral edge states in the presence of Anderson disorder. By analysing different localization parameters, we show that, contrary to the general belief, these edge modes are fragile against disorder, and can be easily localized. Our work provides insights to improve the transport efficiency in the burgeoning fields of antichiral topological photonics and acoustics.

cond-mat.mes-hall↗

arXiv2023

Effects of dilution in a 2D topological magnon insulator

We study the effect of diluting a two-dimensional ferromagnetic insulator hosting a topological phase in the clean limit. By considering the ferromagnetic Heisenberg model in the honeycomb lattice with second nearest-neighbor Dzyanshikii-Moriya interaction, and working in the linear spin-wave approximation, we establish the topological phase diagram as a function of the fraction $p$ of diluted magnetic atoms. The topological phase with Chern number $C=1$ is robust up to a moderate dilution $p_{1}^{*}$, while above a higher dilution $p_{2}^{*}>p_{1}^{*}$ the system becomes trivial. Interestingly, both $p_{1}^{*}$ and $p_{2}^{*}$ are below the classical percolation threshold $p_{c}$ for the honeycomb lattice, which gives physical significance to the obtained phases. In the topological phase for $p p_{2}^{*}$, when all states become localized, the system shows $C=0$ as expected for a trivial phase. Replacing magnetic with non-magnetic atoms in a systems hosting a magnon Chern insulator in the clean limit puts all the three phases within experimental reach.

cond-mat.dis-nn↗

arXiv2023

Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants

We develop a renormalization group (RG) description of the localization properties of onedimensional (1D) quasiperiodic lattice models. The RG flow is induced by increasing the unit cell of subsequent commensurate approximants. Phases of quasiperiodic systems are characterized by RG fixed points associated with renormalized single-band models. We identify fixed-points that include many previously reported exactly solvable quasiperiodic models. By classifying relevant and irrelevant perturbations, we show that phase boundaries of more generic models can be determined with exponential accuracy in the approximant's unit cell size, and in some cases analytically. Our findings provide a unified understanding of widely different classes of 1D quasiperiodic systems.

cond-mat.dis-nn↗

arXiv2023

Third-order topological insulator induced by disorder

We have found the first instance of a third-order topological Anderson insulator (TOTAI). This disorder-induced topological phase is gapped and characterized by a quantized octupole moment and topologically protected corner states, as revealed by a detailed numerically exact analysis. We also find that the disorder-induced transition into the TOTAI phase can be analytically captured with remarkable accuracy using the self-consistent Born approximation. For a larger disorder strength, the TOTAI undergoes a transition to a trivial diffusive metal, that in turn becomes an Anderson insulator at even larger disorder. Our findings show that disorder can induce third-order topological phases in 3D, therefore extending the class of known higher-order topological Anderson insulators.

cond-mat.dis-nn↗

arXiv2023

Incommensurability enabled quasi-fractal order in 1D narrow-band moiré systems

We demonstrate that quasiperiodicity can radically change the ground state properties of 1D moiré systems with respect to their periodic counterparts. By studying an illustrative example we show that while narrow bands play a significant role in enhancing interactions both for commensurate and incommensurate structures, only quasiperiodicity is able to extend the ordered phase down to an infinitesimal interaction strength. In this regime, the quasiperiodic-enabled state has contributions from infinitely many wave vectors. This quasi-factal regime cannot be stabilized in the commensurate case even in the presence of a narrow band. These findings suggest that quasiperiodicity may be a critical factor in stabilizing non-trivial ordered phases in interacting moiré structures and signal out multifractal non-interacting phases, recently found in 2D incommensurate moiré systems, as particularly promising parent states.

cond-mat.str-el↗

arXiv2023

Critical phase dualities in 1D exactly-solvable quasiperiodic models

We propose a solvable class of 1D quasiperiodic tight-binding models encompassing extended, localized, and critical phases, separated by nontrivial mobility edges. Limiting cases include the Aubry-André model and the models of PRL 114, 146601 and PRL 104, 070601. The analytical treatment follows from recognizing these models as a novel type of fixed-points of the renormalization group procedure recently proposed in arXiv:2206.13549 for characterizing phases of quasiperiodic structures. Beyond known limits, the proposed class of models extends previously encountered localized-delocalized duality transformations to points within multifractal critical phases. Besides an experimental confirmation of multifractal duality, realizing the proposed class of models in optical lattices allows stabilizing multifractal critical phases and non-trivial mobility edges without the need for the unbounded potentials required by previous proposals.

cond-mat.dis-nn↗

arXiv2023

Short-range interactions are irrelevant at the quasiperiodic-driven Luttinger Liquid to Anderson Glass transition

We show that short-range interactions are irrelevant around gapless ground-state delocalization-localization transitions driven by quasiperiodicity in interacting fermionic chains. In the presence of interactions, these transitions separate Luttinger Liquid and Anderson glass phases. Remarkably, close to criticality, we find that excitations become effectively non-interacting. By formulating a many-body generalization of a recently developed method to obtain single-particle localization phase diagrams, we carry out precise calculations of critical points between Luttinger Liquid and Anderson glass phases and find that the correlation length critical exponent takes the value $ν= 1.001 \pm 0.007$, compatible with $ν=1$ known exactly at the non-interacting critical point. We also show that other critical exponents, such as the dynamical exponent $z$ and a many-body analog of the fractal dimension are compatible with the exponents obtained at the non-interacting critical point. Noteworthy, we find that the transitions are accompanied by the emergence of a many-body generalization of previously found single-particle hidden dualities. Finally, we show that in the limit of vanishing interaction strength, all finite range interactions are irrelevant at the non-interacting critical point.

cond-mat.dis-nn↗