arXiv subjects

Luiz H. Santos

Publications and source records attributed to Luiz H. Santos.

At least 19 recordsLinked to original sources

arXiv2026

Exciton-Anyon Binding in Fractional Chern Insulators: Spectral Fingerprints

Transition--metal dichalcogenides (TMDs) uniquely combine topological electronic states realized without external magnetic fields with a strong optical response arising from long--lived excitons. Motivated by this confluence, we investigate an interacting fermion--boson system formed by coupling an exciton to a quasihole of a fractional Chern insulator (FCI) at filling fraction $1/3$. We introduce a kagome--lattice fermion--boson model hosting an electronic FCI and a mobile exciton whose dispersion is tunable from a parabolic band to a flatband. Using exact diagonalization, we demonstrate the emergence of exciton--quasihole bound states controlled by the repulsive electron--exciton interaction $V_{\mathrm{FB}}$ and the exciton kinetic energy $t_{\mathrm{B}}$. These states appear as low--lying levels in the fermion--boson spectrum, well separated from the scattering continuum, and arise despite repulsive interactions due to a residual attraction to the local charge depletion associated with a quasihole. Reducing $t_{\mathrm{B}}$ enhances this effect by favoring interaction--dominated binding. Our results provide a model description of moiré TMD heterostructures, including fractional Chern insulating twisted bilayer MoTe$_2$ proximitized by excitonic TMD heterobilayers, where we estimate exciton--quasihole binding energy scales of $0.8$--$1.2$~meV, placing these effects within reach of photoluminescence spectroscopy.

cond-mat.str-el↗

arXiv2026

Logarithmic Entanglement and Emergent Dipole Symmetry from a Strongly Coupled Light-Matter Quantum Circuit

Hybrid systems where a quantum material strongly couples to a nonlocal cavity photon mode have emerged as a new frontier for controlling and probing quantum correlations, yet the structure and scaling of light-matter entanglement produced by the nonlocal coupling remains poorly understood. We address this problem through an exactly solvable framework based on reinterpreting the Power--Zienau--Woolley (PZW) transformation as a \textit{light-matter quantum circuit} that couples the photonic position quadrature $X \sim a + a^\dagger$ to the many-body dipole $\mathcal{P}$ of a one-dimensional quantum chain. We derive a closed-form expression for the reduced density matrix valid at all coupling strengths, in which off-diagonal elements between matter states of unequal dipole are suppressed by a Gaussian factor encoding the full weak-to-ultrastrong coupling crossover. At weak coupling, the reduced density matrix takes a Lindbladian form with $\mathcal{P}$ as the jump operator, and the entanglement entropy is controlled by the dipole variance. At ultrastrong coupling, the density matrix becomes exactly block-diagonal in dipole sectors, reflecting an \textit{emergent dipole symmetry} dynamically imposed by the photon field, with entanglement entropy given exactly by the Shannon entropy of the dipole-sector weight distribution. Applying this framework to a half-filled Su--Schrieffer--Heeger chain, we show that, at strong coupling, both the light-matter entanglement and the spatial entanglement of the photon-dressed matter state scale logarithmically with system size, $S_\infty \sim \fracα{2}\log L$, robust across the SSH phase diagram. The logarithm originates from the photon resolving a single collective coordinate $\mathcal{P}$ whose fluctuations grow as $L^{α/2}$, a distinct mechanism from the logarithmic entanglement of critical one-dimensional systems.

cond-mat.str-el↗

arXiv2025

Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe$_2$ bilayers

Twisted bilayer transition metal dichalcogenides, such as MoTe$_2$, provide a versatile platform for exploring correlated topological phases. This work investigates the interplay of perpendicular magnetic and electric fields in tuning the electronic structure and emergent topological orders of twisted bilayer MoTe$_2$ (t-MoTe$_2$) across two distinct regimes: a low-twist-angle phase ($θ\approx2.1^\circ$) hosting multiple Chern bands of identical Chern numbers per valley, and a higher-angle phase ($θ\approx 3.89^\circ$) featuring Haldane-like bands with opposite Chern numbers. Using a continuum model incorporating moiré potentials up to second harmonics, we compute the Hofstadter fractal spectra under applied fields, revealing Landau fan structures and magnetic-flux-dependent band topology. These fractal spectra are useful in studying emergent topological orders in terms of the composite fermion picture, where the statistical Chern-Simons flux is approximated as a uniform gauge field. We demonstrate that the system hosts both Jain-sequence fractional Chern insulators (FCIs) and non-Jain "fractal FCIs" with higher Chern numbers. The electric field suppresses composite fermion gaps and induces topological quantum phase transitions. Furthermore, our analysis extends to valley-contrasting flux attachment, proposing pathways to describe fractional quantum spin Hall states.

cond-mat.str-el↗

arXiv2025

Higher-Order Van Hove Singularities in Kagome Topological Bands

Motivated by the growing interest in band structures featuring higher-order Van Hove singularities (HOVHS), we investigate a spinless fermion kagome system characterized by nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping amplitudes. While NN hopping preserves time-reversal symmetry, NNN hopping, akin to chiral hopping on the Haldane lattice, breaks time-reversal symmetry and leads to the formation of topological bands with Chern numbers ranging from $C = \pm 1$ to $ \pm 4$. We perform analytical and numerical analysis of the energy bands near the high-symmetry points $\boldsymbolΓ$, $\pm \boldsymbol{K}$, and $\boldsymbol{M_i}$ ($i=1,2,$ and $3$), which uncover a rich and complex landscape of HOVHS, controlled by the magnitude and phase of the NNN hopping. We observe power-law divergences in the density of states (DOS), $ρ(ε) \sim |ε|^{-ν}$, with exponents $ν= 1/2, 1/3, 1/4$, which can significantly affect the anomalous Hall response at low temperatures when the Fermi level crosses the HOVHS. Additionally, the NNN hopping induces the formation of higher Chern number bands $C = \pm 2, \pm 4$ in the middle of the spectrum obeying a sublattice interference whereupon electronic states are maximally localized in each of the sublattices when the momentum approaches the three high-symmetry points $\boldsymbol{M_i}$ ($i=1,2,$ and $3$) on the Brillouin zone boundary. This classification of HOVHS in kagome systems provides a platform to explore unconventional electronic orders induced by electronic correlations.

cond-mat.mes-hall↗

arXiv2024

Fractional Chern Insulators in Twisted Bilayer MoTe$_2$: A Composite Fermion Perspective

The discovery of Fractional Chern Insulators (FCIs) in twisted bilayer MoTe$_2$ has sparked significant interest in fractional topological matter without external magnetic fields. Unlike the flat dispersion of Landau levels, moiré electronic states are influenced by lattice effects within a nanometer-scale superlattice. This study examines the impact of these lattice effects on the topological phases in twisted bilayer MoTe$_2$, uncovering a family of FCIs with Abelian anyonic quasiparticles. Using a composite fermion approach, we identify a sequence of FCIs with fractional Hall conductivities $σ_{xy} = \frac{C}{2C + 1} \frac{e^2}{h}$ linked to partial filling $ν_{\,\text{h}}$ of holes of the topmost moiré valence band. These states emerge from incompressible composite fermion bands of Chern number $C$ within a complex Hofstadter spectrum. This approach explains FCIs with Hall conductivities $σ_{xy} = (2/3) e^2/h$ and $σ_{xy} = (3/5) e^2/h$ at fractional fillings $ν_{\,\text{h}} = 2/3$ and $ν_{\,\text{h}} = 3/5$ observed in experiments, and uncovers other fractal FCI states. The Hofstadter spectrum reveals new phenomena, distinct from Landau levels, including a higher-order Van Hove singularity (HOVHS) at half-filling, leading to novel quantum phase transitions. This work offers a comprehensive framework for understanding FCIs in transition metal dichalcogenide moiré systems and highlights mechanisms for topological quantum criticality.

cond-mat.str-el↗

arXiv2024

Chern Bands with Higher-Order Van Hove Singularities on Topological Moiré Surface States

In two-dimensional electronic lattices, changes in the topology of the Fermi surface (Lifshitz transitions) lead to Van Hove singularities characterized by a divergence in the electronic density of states. Van Hove singularities can enhance the effect of electronic interactions, providing a platform to explore novel correlated electronic states. In this work, we investigate the emergence of topological Chern bands on the surface of three-dimensional topological insulators, which host higher-order Van Hove singularities that are characterized by the power-law diverging density of states. These singularities can arise from the interplay between a time-reversal breaking Zeeman field induced by proximity to a ferromagnetic insulator and a time-reversal invariant moiré potential on the surface electrons, created by quintuple layer misalignment in a family of topological insulators such as Bi$_2$Se$_3$ and Bi$_2$Te$_3$, which host a single surface Dirac fermion. We establish the onset of Chern bands near charge neutrality with Chern numbers $C = \pm 1$ that also possess a manifold of higher-order Van Hove singularities on the moiré Brillouin zone valleys controlled by the Zeeman and moiré potential energy scales, unveiling a new platform to realize exotic Lifshitz transitions in topological bands. Furthermore, we show that the strong peaks in the density of states in the vicinity of Lifshitz transitions give rise to characteristic features in the low-temperature intrinsic anomalous Hall conductivity, yielding a path to probe Van Hove singularities in Chern bands through anomalous transport measurements.

cond-mat.mes-hall↗

arXiv2023

Quantum Fractality on the Surface of Topological Insulators

Three-dimensional topological insulators support gapless Dirac fermion surface states whose rich topological properties result from the interplay of symmetries and dimensionality. Their topological properties have been extensively studied in systems of integer spatial dimension but the prospect of these surface electrons arranging into structures of non-integer dimension like fractals remains unexplored. In this work, we investigate a new class of states arising from the coupling of surface Dirac fermions to a time-reversal symmetric fractal potential, which breaks translation symmetry while retaining self-similarity. Employing large-scale exact diagonalization, scaling analysis of the inverse participation ratio, and the box-counting method, we establish the onset of self-similar Dirac fermions with fractal dimension for a symmetry-preserving surface potential with the geometry of a Sierpinski carpet fractal with fractal dimension $D \approx 1.89$. Dirac fractal surface states open a fruitful avenue to explore exotic regimes of transport and quantum information storage in topological systems with fractal dimensionality.

cond-mat.mes-hall↗

arXiv2023

Time-Reversal Invariant Topological Moiré Flatband: A Platform for the Fractional Quantum Spin Hall Effect

Motivated by recent observation of the quantum spin Hall effect in monolayer germanene and twisted bilayer transition-metal-dichalcogenides (TMDs), we study the topological phases of moiré twisted bilayers with time-reversal symmetry and spin $s_z$ conservation. By using a continuum model description which can be applied to both germanene and TMD bilayers, we show that at small twist angles, the emergent moiré flatbands can be topologically nontrivial due to inversion symmetry breaking. Each of these flatbands for each spin projection admits a lowest-Landau-level description in the chiral limit and at magic twist angle. This allows for the construction of a many-body Laughlin state with time-reversal symmetry which can be stabilized by a short-range pseudopotential, and therefore serves as an ideal platform for realizing the so-far elusive fractional quantum spin Hall effect with emergent spin-1/2 U(1) symmetry.

cond-mat.mes-hall↗

arXiv2023

Entanglement and Topology in Su-Schrieffer-Heeger Cavity Quantum Electrodynamics

Cavity materials are a frontier to investigate the role of light-matter interactions on the properties of electronic phases of matter. In this work, we raise a fundamental question: can non-local interactions mediated by cavity photons destabilize a topological electronic phase? We investigate this question by characterizing entanglement, energy spectrum and correlation functions of the topological Su-Schrieffer-Heeger (SSH) chain interacting with an optical cavity mode. Employing density-matrix renormalization group (DMRG) and exact diagonalization (ED), we demonstrate the stability of the edge state and establish an area law scaling for the ground state entanglement entropy, despite long-range correlations induced by light-matter interactions. These features are linked to gauge invariance and the scaling of virtual photon excitations entangled with matter, effectively computed in a low-dimensional Krylov subspace of the full Hilbert space. This work provides a framework for characterizing novel equilibrium phenomena in topological cavity materials.

cond-mat.str-el↗

arXiv2023

Emergence of Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model

While advances in electronic band theory have brought to light new topological systems, understanding the interplay of band topology and electronic interactions remains a frontier question. In this work, we predict new interacting electronic orders emerging near higher-order Van Hove singularities present in the Chern bands of the Haldane model. We classify the nature of such singularities and employ unbiased renormalization group methods that unveil a complex landscape of electronic orders, which include ferromagnetism, density-waves and superconductivity. Importantly, we show that repulsive interactions can stabilize long-sought pair-density wave state and an exotic Chern supermetal, which is a new class of non-Fermi liquid with anomalous quantum Hall response. This framework opens a new path to explore unconventional electronic phases in two-dimensional chiral bands through the interplay of band topology and higher-order Van Hove singularities.

cond-mat.str-el↗

arXiv2022

Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions

Fractal Hofstadter bands have become widely accessible with the advent of moiré superlattices, opening the door to studies of the effect of interactions in these systems. In this work we employ a renormalization group (RG) analysis to demonstrate that the combination of repulsive interactions with the presence of a tunable manifold of Van Hove singularities provides a new mechanism for driving unconventional superconductivity in Hofstadter bands. Specifically, the number of Van Hove singularities at the Fermi energy can be controlled by varying the flux per unit cell and the electronic filling, leading to instabilities toward nodal superconductivity and chiral topological superconductivity with Chern number $\mathcal{C} = \pm 6$. The latter is characterized by a self-similar fixed trajectory of the RG flow and an emerging self-similarity symmetry of the order parameter. Our results establish Hofstadter quantum materials such as moiré heterostructures as promising platforms for realizing novel reentrant Hofstadter superconductors.

cond-mat.supr-con↗

arXiv2022

Triplet Pair-Density Wave Superconductivity on the $π$-flux Square Lattice

Pair-density waves (PDW) are superconducting states that spontaneously break translation symmetry in systems with time-reversal symmetry (TRS). Evidence for PDW has been seen in several recent experiments, as well as in the pseudogap regime in cuprates. Theoretical understanding of PDW has been largely restricted to phenomenological and numerical studies, while microscopic theories typically require strong-coupling or fine-tuning. In this work, we provide a novel symmetry-based mechanism under which PDW emerges as a weak coupling instability of a 2D TRS metal. Combining mean-field and renormalization group analyses, we identify a weak-coupling instability towards a triplet PDW realized in the $π$-flux square lattice model with on-site repulsion and moderate nearest-neighbor attraction when the Fermi level crosses Van Hove singularities at 1/4 and 3/4 fillings. This PDW is protected by the magnetic translation symmetries characteristic of Hofstadter systems, of which the $π$-flux lattice is a special time-reversal symmetric case.

cond-mat.supr-con↗

arXiv2021

Theory of Hofstadter Superconductors

We study mean-field states resulting from the pairing of electrons in time-reversal broken fractal Hofstadter bands, which arise in two-dimensional lattices where the unit cell traps magnetic flux $Φ= (p/q)Φ_0$ comparable to the flux quantum $Φ_0 = h/e$. It is established that the dimension and degeneracy of the irreducible representations of the magnetic translation group (MTG) furnished by the charge 2e pairing fields have different properties from those furnished by single particle Bloch states, and in particular are shown to depend on the parity of the denominator $q$. We explore this symmetry analysis to formulate a Ginzburg-Landau theory describing the thermodynamic properties of Hofstadter superconductors at arbitrary rational flux $Φ= (p/q)Φ_0$ in terms of a multicomponent order parameter that describes the finite momentum pairing of electrons across different Fermi surface patches. This phenomenological theory leads to a rich phase diagram characterized by different symmetry breaking patterns of the MTG, which can be interpreted as distinct classes of vortex lattices. A class of $\mathbb{Z}_q$-symmetric Hofstadter SCs is identified, in which the MTG breaks down to a $\mathbb{Z}_q$ subgroup. We study the topological properties of such $\mathbb{Z}_q$-symmetric Hofstadter SCs and show that the parity of the Chern numbers is fixed by the parity of $q$. We identify the conditions for the realization of Bogoliubov Fermi surfaces in the presence of parity and MTG symmetries, establishing a novel topological invariant capturing the existence of such charge-neutral gapless excitations. Our findings, which could bear relevance to the description of re-entrant superconductivity in moiré systems in the Hofstadter regime, establish Hofstadter SC as a fertile setting to explore symmetry broken and topological orders.

cond-mat.supr-con↗

arXiv2020

Classification of Topological Phase Transitions and van Hove Singularity Steering Mechanism in Graphene Superlattices

We study quantum phase transitions in graphene superlattices in external magnetic fields, where a framework is presented to classify multiflavor Dirac fermion critical points describing hopping tuned topological phase transitions of integer and fractional Hofstadter-Chern insulators. We argue and provide numerical support for the existence of transitions that can be explained by a nontrivial interplay of Chern bands and van Hove singularities near charge neutrality. This work provides a route to critical phenomena beyond conventional quantum Hall plateau transitions.

cond-mat.str-el↗

arXiv2020

Entanglement Entropy of Generalized Moore-Read Fractional Quantum Hall State Interfaces

Topologically ordered phases of matter can be characterized by the presence of a universal, constant contribution to the entanglement entropy known as the topological entanglement entropy (TEE). The TEE can been calculated for Abelian phases via a "cut-and-glue" approach by treating the entanglement cut as a physical cut, coupling the resulting gapless edges with explicit tunneling terms, and computing the entanglement between the two edges. We provide a first step towards extending this methodology to non-Abelian topological phases, focusing on the generalized Moore-Read (MR) fractional quantum Hall states at filling fractions $ν=1/n$. We consider interfaces between different MR states, write down explicit gapping interactions, which we motivate using an anyon condensation picture, and compute the entanglement entropy for an entanglement cut lying along the interface. Our work provides new insight towards understanding the connections between anyon condensation, gapped interfaces of non-Abelian phases, and TEE.

cond-mat.str-el↗

arXiv2020

Classification of Strongly Disordered Topological Wires Using Machine Learning

In this article we apply the random forest machine learning model to classify 1D topological phases when strong disorder is present. We show that using the entanglement spectrum as training features the model gives high classification accuracy. The trained model can be extended to other regions in phase space, and even to other symmetry classes on which it was not trained and still provides accurate results. After performing a detailed analysis of the trained model we find that its dominant classification criteria captures degeneracy in the entanglement spectrum.

cond-mat.dis-nn↗

arXiv2019

Electron-phonon Coupling and Kohn Anomaly due to the Floating 2D Electronic Bands on the Surface of ZrSiS

ZrSiS, an intriguing candidate of topological nodal line semimetals, was discovered to have exotic surface floating two-dimensional (2D) electrons [Phys. Rev. X 7, 041073 (2017)], which are likely to interact with surface phonons. Here, we reveal a prominent Kohn anomaly in a surface phonon branch by mapping out the surface phonon dispersions of ZrSiS using high-resolution electron energy loss spectroscopy. Theoretical analysis via an electron-phonon coupling (EPC) model attributes the strong renormalization of the surface phonon branch to the interactions with the surface floating 2D electrons. With the random phase approximation, we calculate the phonon self-energy and evaluate the mode-specific EPC constant by fitting the experimental data. The EPC picture provided here may be important for potential applications of topological nodal line semimetals.

cond-mat.mtrl-sci↗

arXiv2019

Parafermions in Hierarchical Fractional Quantum Hall States

Motivated by recent theoretical progress demonstrating the existence of non-Abelian parafermion zero modes in domain walls on interfaces between two dimensional Abelian topological phases of matter, we investigate the properties of gapped interfaces of hierarchical fractional quantum Hall states, in the lowest Landau level, characterized by the Hall conductance $σ_{xy}(m,p) = \frac{p}{2mp+1} \frac{e^{2}}{h}$, for integer numbers $(m,p)$ with $m,p \geq 1$. The case $m=1$ corresponds to the experimentally well established sequence of fractional quantum Hall states with $σ_{xy} = \frac{1}{3}\frac{e^{2}}{h}, \frac{2}{5}\frac{e^{2}}{h}, \frac{3}{7}\frac{e^{2}}{h}, ...\, $, which has been observed in many two dimensional electron gases. Exploring the mechanism by which the $(m,p+1)$ hierarchical state is generated from the condensation of quasiparticles of the ``parent" state $(m,p)$, we uncover a remarkably rich sequence of parafermions in hierarchical interfaces whose quantum dimension $d_{m,p}$ depends both upon the total quantum dimension $\mathcal{D}_{m,p} = \sqrt{2mp+1}$ of the bulk Abelian phase, as well as on the parity of the ``hierarchy level" $p$, which we associate with the $\mathbb{Z}_2$ stability of Majorana zero modes in one dimensional topological superconductors. We show that these parafermions reside on domain walls separating segments of the interface where the low energy modes are gapped by two distinct mechanisms: (1) a charge neutral backscattering process or (2) an interaction that breaks $U(1)$ charge conservation symmetry and stabilizes a condensate whose charge depends on $p$. Remarkably, this charge condensate corresponds to a clustering of quasiparticles of fractional charge $\frac{p}{2mp+1}\,e$, allowing us to draw a correspondence between these fractionalized condensates and Read-Rezayi non-Abelian fractional quantum Hall cluster states.

cond-mat.str-el↗