arXiv subjects

Juan Felipe Mendez-Valderrama

Publications and source records attributed to Juan Felipe Mendez-Valderrama.

8 recordsLinked to original sources

arXiv2026

Symmetric Mode Ansatz: Theory of Magnon Collective Modes in Chern Insulators

Moiré materials host integer and fractional Chern insulators (FCIs) where time-reversal is broken spontaneously by flat band ferromagnetism. In twisted MoTe2, unlike in quantum Hall, opposite spins carry opposite Chern numbers and realize Ising ferromagnetism with gapped magnon excitations. Clarifying the nature of these collective modes and the origin of the magnon gap is key to understanding the stability of the Chern magnets in these materials. To do so, we develop a generalized single-mode approximation, which we call the symmetric mode ansatz (SyMA), to describe the low-energy magnon spectrum. We find it to be in exceptional agreement with numerical calculations at integer filling, and qualitatively accurate across fractional fillings including FCIs. To explain the accuracy of the SyMA, we present two families of Hubbard models (including the Haldane model and continuum ideal bands) whose collective modes are analytically solvable and for which the SyMA is either exact or an accurate approximation. For a class of these models where SyMA is exact, we prove two-sided bounds on the zero-momentum magnon gap in terms of the Chern number, Berry curvature, and quantum metric, revealing that uniform quantum geometry is sufficient for stabilizing magnetism in Chern bands.

cond-mat.str-el↗

arXiv2026

Distinguishing Mott and strain-induced anisotropic semimetals in magic-angle twisted bilayer graphene using Landau level spectroscopy

Recent quantum twisting microscopy experiments [1] have provided unprecedented momentum- and energy-resolved imaging of magic-angle twisted bilayer graphene, revealing a stark dichotomy between the heavy and light electronic characters of its narrow bands. In this work, we provide a sharp distinguishing criterion between the two most likely candidate states that exhibit spectroscopic features consistent with the experimental results. Focusing on charge neutrality, these states are 1) the 'Mott semimetal', governed by strong dynamical correlations, and 2) the 'strain-induced anisotropic semimetal', characterized by weak Hartree-Fock effects. We demonstrate that an out-of- plane magnetic field serves as a sharp discriminating probe based on the expected Landau level gap size hierarchy. We find that the strain-induced anisotropic semimetal has a robust gap hierarchy where the Chern C gaps, Δ_C , decrease in order Δ_{\pm 4} > Δ_{\pm 8} > Δ_{\pm 12}. In contrast, for the Mott semimetal, Δ_{\pm 4} remains the largest gap, while the relative magnitude of the C = \pm 8, \pm 12 gaps depends sensitively on the applied magnetic field. We test the robustness of these results against strain orientation and lattice relaxation finding consistency between the gap hierarchy of the strained semimetal and previous incompressibility measurements at finite magnetic field [2].

cond-mat.str-el↗

arXiv2025

Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry

Inspired by the discovery of a variety of correlated insulators in the moiré universe, controlled by interactions projected to a set of isolated bands with a narrow bandwidth, we examine here a partial sum-rule associated with the inverse frequency-weighted optical conductivity restricted to low-energies. Unlike standard sum-rules that extend out to $infinite$ frequencies, which include contributions from $all$ inter-band transitions, we focus here on transitions associated $only$ with the $projected$ degrees of freedom. We analyze the partial sum-rule in a non-perturbative but "solvable" limit for a variety of correlation-induced insulators. This includes (i) magic-angle twisted bilayer graphene at integer-filling with projected Coulomb interactions, starting from the chiral flat-band limit and including realistic perturbations, (ii) fractional fillings of Chern-bands which support generalized Laughlin-like states, starting from a Landau-level and including a periodic potential and magnetic-field, respectively, drawing connections to twisted MoTe$_2$, and (iii) integer filling in toy-models of non-topological flat-bands with a tunable quantum geometry in the presence of repulsive interactions. The partial sum-rule in all of these examples is implicitly constrained by the form of the band quantum geometry via the low-lying excitation spectrum, but is not related to it explicitly. For interacting Slater-determinant insulators, the partial sum-rule is related to a new quantity -- "many-body projected quantum geometry" -- obtained from the interaction-renormalized electronic bands. We also point out an intriguing connection between the partial sum-rule and the quantum Fisher information associated with the projected many-body position operator.

cond-mat.str-el↗

arXiv2025

Spinless and spinful charge excitations in moiré Fractional Chern Insulators

Fractionally charged elementary excitations, the quasi-electron and quasi-hole, are one of the hallmarks of the fractional Chern insulator (FCI). In this work, we observe that spontaneous spin polarization in twisted MoTe$_2$ leads to multiple species of low-energy quasi-particles distinguished by their spin quantum numbers. We perform large-scale exact diagonalization (ED) calculations to investigate the nature of these excitations and develop a method to extract their fundamental energetic properties. Focusing on $θ= 3.7^{\circ}$ and filling factor $ν= -2/3$ relevant to recent experiments, we show that spin-preserving (spinless) charge excitations have smaller gap than spin-flipping (spinful) excitations both with and without band mixing. This result is in qualitative agreement with the measured magnetic field dependence of the transport gaps. Beyond the spinless and spinful quasi-particle gaps, we extract the full quasi-electron and quasi-hole ``band structure'' and find significant dispersion with emergent magnetic translation symmetry -- a fundamental departure from the immobile excitations of the quantum Hall fluid. Our results establish a framework for computing the properties of novel elementary excitations in FCIs.

cond-mat.str-el↗

arXiv2025

Observation of High-Temperature Dissipationless Fractional Chern Insulator

The fractional quantum anomalous Hall effect has recently been experimentally observed in zero-field fractional Chern insulators (FCI). However, an outstanding challenge is the presence of a substantial longitudinal resistance $R_{xx}$ (a few k$Ω$), even though the anomalous Hall resistance $R_{xy}$ is quantized. This dissipative behavior is likely linked to imperfect sample quality. Here, we report transport measurements of a drastically improved twisted $\text{MoTe}_2$ bilayer device, which exhibits quantized $R_{xy}$ and vanishing $R_{xx}$ for the $-2/3$ state, marking a dissipationless FCI. Contrary to fractional quantum Hall states where the energy gap increases with magnetic field, we find that the thermal activation gap of the observed FCI states decreases rapidly as the magnetic field rises from zero, then plateaus above a few teslas. This observation is attributed to the interplay between spin and charge gaps. Due to the spontaneous ferromagnetism, the spin gap dominates at low field, while the charge gap becomes appreciable once the magnetic field freezes spin fluctuations. For the $-2/3$ state, we estimate the spin and FCI gap of about 55 and 20 K, respectively. Our results provide insights into the energy scale of FCI and offer a pathway for quantum engineering of exotic correlated topological states.

cond-mat.mes-hall↗

arXiv2025

Theory of Correlated Insulators and Superconductor at $ν=1$ in Twisted WSe$_2$

The observation of a superconducting phase, an intertwined insulating phase, and a continuous transition between the two at a commensurate filling of $ν=1$ in bilayers of twisted WSe$_2$ at $θ=3.65^0$ raises a number of intriguing questions about the origin of this phenomenology. Here we report the possibility of a displacement-field induced continuous transition between a superconductor and a quantum spin-liquid Mott insulator at $ν=1$, starting with a simplified three-orbital model of twisted WSe$_2$, including on-site, nearest-neighbor density-density interactions, and a chiral-exchange interaction, respectively. By employing parton mean-field theory, we discuss the nature of these correlated insulators, their expected evolution with the displacement-field, and their phenomenological properties.

cond-mat.str-el↗

arXiv2024

Correlated Topological Mixed-Valence Insulators in Moiré Hetero-Bilayers

Moiré transition metal dichalcogenide (TMD) materials provide an ideal playground for studying the combined interplay of strong interactions and band-topology over a range of electronic fillings. Here we investigate the panoply of interaction-induced electronic phases that arise at a total commensurate filling of $ν_T=2$ in moiré TMD heterobilayers, focusing specifically on their renormalized band-topology. We carry out a comprehensive self-consistent parton mean-field analysis on an interacting mixed-valence Hamiltonian describing AB-stacked MoTe$_2$/WSe$_2$ to highlight different ingredients that arise due to "Mottness", band-flattening, an enhanced excitonic tendency, and band-inversion, leading to correlated topological semi-metals and insulators. We also propose a possible route towards realizing fractionalized insulators with emergent neutral fermionic excitations in this and other closely related platforms.

cond-mat.str-el↗

arXiv2023

Investigation of Planckian behavior in a high-conductivity oxide: PdCrO$_2$

The layered delafossite metal PdCrO$_2$ is a natural heterostructure of highly conductive Pd layers Kondo coupled to localized spins in the adjacent Mott insulating CrO$_2$ layers. At high temperatures $T$ it has a $T$-linear resistivity which is not seen in the isostructural but non-magnetic PdCoO$_2$. The strength of the Kondo coupling is known, as-grown crystals are extremely high purity and the Fermi surface is both very simple and experimentally known. It is therefore an ideal material platform in which to investigate 'Planckian metal' physics. We do this by means of controlled introduction of point disorder, measurement of the thermal conductivity and Lorenz ratio and studying the sources of its high temperature entropy. The $T$-linear resistivity is seen to be due mainly to elastic scattering and to arise from a sum of several scattering mechanisms. Remarkably, this sum leads to a scattering rate within 10$\%$ of the Planckian value of $k_BT/$$\hbar$.

cond-mat.str-el↗