arXiv subjects

Daniel Kaplan

Publications and source records attributed to Daniel Kaplan.

At least 19 recordsLinked to original sources

arXiv2026

Tunable Skyrmions in a Topological Wigner Crystal

In low density systems with strong interactions electrons are expected to crystallize into a Wigner solid. Recently, advances in two-dimensional systems where electrons carry Berry curvature have added a topological dimension to Wigner crystallization. Using a model for pseudospin interactions in a topological Wigner crystal, here we show that the competition between ferromagnetic Heisenberg exchange $J$ and the chiral interaction $\gamma$ on the triangular lattice stabilizes a zero-field skyrmion crystal whose density is continuously tunable through the ratio $\gamma/J$. The chiral interaction originates from finite Berry curvature in an underlying time-reversal broken Wigner crystal. In the continuum limit, the chiral interaction acts as a chemical potential for skyrmions, while higher-order gradient terms beyond the nonlinear sigma model select the skyrmion density. At large chiral coupling, we uncover a 24-site tetra-skyrmion crystal carrying four units of topological charge per magnetic unit cell, which becomes degenerate with four-sublattice tetrahedral order as $J \to 0$. We characterize the magnon structure for these phases and discuss the transition between the tunable skyrmion crystal to these states at large $\gamma/J$. Our results establish the phase diagram of ferromagnetic topological Wigner crystals.

cond-mat.str-el↗

arXiv2026

Probing the Nature of Interstitial Anionic Electrons in 2D Electride Ca$_2$N via Landau-Level Spectroscopy

We investigate the magnetic-field response of interstitial anionic electrons (IAEs) in two-dimensional electrides, using monolayer Ca$_2$N as a prototypical system. By computing the Landau-level (LL) spectrum of the electride bands forming the Fermi surface, we find a linear LL evolution with magnetic field that closely resembles the behavior of a nearly-free 2D electron gas (2DEG). The extracted cyclotron effective mass and Land\'e g-factor deviate moderately from their free-electron values, indicating that the IAEs retain a remarkably free-electron-like character. Furthermore, the energy dispersion of the electride bands remains insensitive to the choice of exchange-correlation functional (LDA vs.~PBEsol), indicating that local exchange and correlation effects have minimal influence on the IAEs. Overall, our findings provide fundamental insight into the quantum nature of electrides and open new avenues for exploring magnetic confinement, correlation effects, and emergent quantum phenomena in low-dimensional interstitial electronic systems.

cond-mat.mtrl-sci↗

arXiv2026

Relaxation-driven topological domains in moir\'e materials

Spatial control of topology is highly desirable for realizing tunable quantum functionalities in materials. Moir\'e superlattices formed by twisting van der Waals heterostructures provide a natural platform for spatially modulated electronic phases, yet the emergence of tunable topological domains in these systems remains largely unexplored. Here we show that structural relaxation in twisted bilayer BiSb drives the formation of a distinct moir\'e topological phase, characterized by coexisting topologically nontrivial (Z$_2$ = 1) and trivial (Z$_2$ = 0) domains within a single moir\'e unit cell. As the twist angle is reduced, relaxation-induced modulation of the interlayer separation stabilizes an expanding network of topological regions embedded within trivial backgrounds of the moir\'e unit cell. The resulting internal domain boundaries host topologically-protected gapless 1D edge states that are directly visible in our simulated scanning-tunnelling microscopy maps.Furthermore, we demonstrate that the real-space topological domain structure and associated gapless edge states can be reversibly tuned by an out-of-plane electric field. Together, these results establish twisted BiSb as a promising platform for programmable topological domain patterning, where intrinsic networks of edge channels can be continuously tuned and electrically reconfigured in moir\'e materials.

cond-mat.mtrl-sci↗

arXiv2026

Near-degenerate competing magnetic orders in EuAgAs: a tunable route to altermagnetism

Altermagnets (AMs) have recently emerged as a distinct magnetic class bridging central features of ferromagnets (FMs) and antiferromagnets (AFMs), offering new opportunities for spin-based electronics. While they possess zero net magnetization like collinear AFMs, they simultaneously exhibit momentum-dependent spin splitting long thought exclusive to FMs. Despite intense theoretical interest, experimentally accessible materials hosting both altermagnetism and nontrivial band topology remain scarce. EuAgAs, crystallizing in space group $P6_3/mmc$, was previously identified via density functional theory (DFT) as a bulk altermagnetic Dirac semimetal. Contrary to these predictions, our neutron diffraction experiments reveal that the bulk ground state adopts a $\mathbf{q} = (0,0,\tfrac{1}{2})$ AFM structure with an in-plane $\uparrow\uparrow\downarrow\downarrow$ spin sequence. Systematic DFT calculations, however, uncover a remarkable near-degeneracy among competing magnetic orders: the FM and AM configurations lie only $0.11$ and $0.40~\text{meV/f.u.}$ above the AFM ground state, respectively. We further show that while a simple Heisenberg model favors a spin-spiral ground state, the inclusion of non-Heisenberg biquadratic coupling stabilizes the observed commensurate AFM phase. This near-degeneracy renders the magnetic state highly tunable, with DFT predicting a transition to the altermagnetic phase under hydrostatic pressure at approximately $14 \text{ GPa}$, establishing EuAgAs as a controllable platform for accessing topological altermagnetism.

cond-mat.mtrl-sci↗

arXiv2026

Valley polarization of chiral excitonic bound states induced by band geometry

Van der Waals (vdW) materials provide a rich platform for exploring the interplay of interactions, topology, and paired-electron phases. We study how the Berry phase reshapes excitonic pairing in a double-well dispersion representative of layered vdW systems. By computing the temperature-versus-Berry flux phase diagram of the system, we find parameter ranges where finite angular momentum excitons are favored, including chiral states. Strikingly, the condensed angular momentum channel evolves with Berry flux, revealing a pairing problem with no analogue in a hydrogen atom in a uniform magnetic field, where angular momentum states never cross. We then turn to a model of multilayer rhombohedral graphene and examine the effects of trigonal warping. Once continuous rotational symmetry is broken, excitons mix multiple angular momenta, and for a range of parameters we find a variety of linear combination of angular momenta ($s, p, f$ and $g$) in the ground state. Our results point to the possibility of chiral excitonic condensates, and spontaneous symmetry breaking through many-body condensation.

cond-mat.mes-hall↗

arXiv2025

Kuznetsov Categories for Gauged Linear Sigma Models

We define Kuznetsov and anti-Kuznetsov categories for gauged linear sigma models. We show that for complete intersections of ample divisors in smooth projective toric varieties, the Kuznetsov category is left orthogonal to an exceptional collection. We prove that any complete intersection of $r \ge 2$ ample divisors in a Fano GIT quotient is a Fano visitor and the derived category of its Fano host is equivalent to an anti-Kuznetsov category of a gauged linear sigma model.

math.AG↗

arXiv2025

Machine learning assisted high throughput prediction of moir\'e materials

The world of 2D materials is rapidly expanding with new discoveries of stackable and twistable layered systems composed of lattices of different symmetries, orbital character, and structural motifs. Often, however, it is not clear a priori whether a pair of monolayers twisted at a small angle will exhibit correlated or interaction-driven phenomena. The computational cost to make accurate predictions of the single particle states is significant, as small twists require very large unit cells, easily encompassing 10,000 atoms, and therefore implementing a high throughput prediction has been out of reach. Here we show a path to overcome this challenge by introducing a machine learning (ML) based methodology that efficiently estimates the twisted interlayer tunneling at arbitrarily low twist angles through the local-configuration based approach that enables interpolating the local stacking for a range of twist angles using a random forest regression algorithm. We leverage the kernel polynomial method to compute the density of states (DOS) on large real space graphs by reconstructing a lattice model of the twisted bilayer with the ML fitted hoppings. For twisted bilayer graphene (TBG), we show the ability of the method to resolve the magic angle DOS at a substantial improvement in computational time. We use this new technique to scan through the database of stable 2D monolayers (MC2D) and reveal new twistable candidates across the five possible points groups in two-dimensions with a large DOS near the Fermi energy, with potentially exciting interacting physics to be probed in future experiments.

cond-mat.mes-hall↗

arXiv2025

Optically-Induced Faraday-Goldstone Waves

Faraday waves, typically observed in driven fluids, result from the confluence of nonlinearity and parametric amplification. Here we show that optical pulses can generate analogous phenomena that persist much longer than the pump time-scales in ordered quantum solids. We present a theory of ultrafast light-matter interactions within a symmetry-broken state; dynamical nonlinear coupling between the Higgs (amplitude) and the Goldstone (phase) modes drives an emergent phason texture that oscillates in space and in time: Faraday-Goldstone waves. Calculated signatures of this spatiotemporal order compare well with measurements on K$_{0.3}$MnO$_{3}$; Higgs-Goldstone beating, associated with coherent energy exchange between these two modes, is also predicted. We show this light-generated crystalline state is robust to thermal noise, even when the original Goldstone mode is not. Our results offer a new pathway for the design of periodic structures in quantum materials with ultrafast light pulses.

cond-mat.mes-hall↗

arXiv2025

Anomalous Hall effect in rhombohedral graphene

Motivated by recent experiments on rhombohedral stacked multilayer graphene and the observation of the anomalous Hall effect in a spontaneous spin-valley polarized quarter metal state, we calculate the anomalous Hall conductivity for this system in the presence of two types of impurities: weak and dense as well as sparse and strong. Our calculation of $\sigma_{xy}$ is based on the Kubo-Streda diagrammatic approach. In a model with Gaussian disorder applicable to weak dense impurities, this involves all non-crossing diagrams (intrinsic, side-jump and Gaussian skew-scattering contributions) and additionally diagrams with two intersecting impurities, X and $\Psi$, representing diffractive skew-scattering processes. A "Mercedes star" diagram (non-Gaussian skew scattering) is furthermore included to treat in the case of strong, sparse impurities. We supplement our asymptotically exact analytical solutions for an isotropic model without warping effects by semi-numerical calculations accounting perturbatively for warping, which plays a crucial role in the low-energy band structure.

cond-mat.mes-hall↗

arXiv2025

Spatiotemporal Order and Parametric Instabilities from First-Principles

Shaping crystal structure with light is an enduring goal of physics and materials engineering. Here we present calculations in candidate materials selected by symmetry that allow light-induced spatiotemporal parametric instabilities. We demonstrate a theoretical framework that includes a complete symmetry analysis of phonon modes that contribute to parametric instabilities across all non-centrosymmetric point groups, a detailed survey of the materials landscape and finally the computation of nonlinear couplings from first principles. We then showcase detailed results for chiral crystals, ferroelectrics, and layered van der Waals materials. Our results pave the way towards realizing designer time-crystalline order in quantum materials, detectable with time-resolved diffractive probes.

cond-mat.mtrl-sci↗

arXiv2025

Nonprojective crepant resolutions of quiver varieties

In this paper, we construct a large class of examples of proper, nonprojective crepant resolutions of singularities for Nakajima quiver varieties. These include four and six dimensional examples and examples with $Q$ containing only three vertices. There are two main techniques: by taking a locally projective resolution of a projective partial resolution as in our previous work arXiv:2311.07539, and more generally by taking quotients of open subsets of representation space which are not stable loci, related to Arzhantsev--Derental--Hausen--Laface's construction in the setting of Cox rings. By the latter method we exhibit a proper crepant resolution that does not factor through a projective partial resolution. Most of our quiver settings involve one-dimensional vector spaces, hence the resolutions are toric hyperk\"ahler, which were studied from a different point of view in Arbo and Proudfoot arXiv:1511.09138. This builds on the classification of projective crepant resolutions of a large class of quiver varieties in arXiv:2212.09623 and the classification of proper crepant resolutions for the hyperpolygon quiver varieties in arXiv:2406.04117.

math.AG↗

arXiv2025

Engineering stacking-induced topological phase transitions in bilayer heterostructures

Nonmagnetic topological insulators (TIs) are known for their robust metallic surface/edge states that are protected by time-reversal symmetry, making them promising candidates for next-generation spintronic and nanoelectronic devices. Traditional approaches to realizing TIs have focused on inducing band inversion via strong spin-orbit coupling (SOC), yet many materials with substantial SOC often remain topologically trivial. In this work, we present a materials-design strategy for engineering topologically non-trivial phases, e.g., quantum spin Hall phases, by vertically stacking topologically trivial Rashba monolayers in an inverted fashion. Using BiSb as a prototype system, we demonstrate that while the BiSb monolayer is topologically trivial (despite having significant SOC), an inverted BiSb-SbBi bilayer configuration realizes a non-trivial topological phase with enhanced spin Hall conductivity. We further reveal a delicate interplay between the SOC strength and the interlayer electron tunneling that governs the emergence of a nontrivial topological phase in the bilayer heterostructure. This phase can be systematically tuned using an external electric field, providing an experimentally accessible means of controlling the system's topology. Our magnetotransport studies further validate this interplay, by revealing $g$-factor suppression and the emergence a zeroth Landau level. Notably, the inverted bilayer heterostructure exhibits a robust and tunable spin Hall effect, with performance comparable to that of state-of-the-art materials. Thus, our findings unveil an alternative pathway for designing and engineering functional properties in 2D topological systems using topologically trivial constituent monolayers.

cond-mat.mes-hall↗

arXiv2025

Ultrafast switchable polar and magnetic orders by nonlinear light-matter interaction

An outstanding challenge in materials science and physics is the harnessing of light for switching charge order in e.g., ferroelectrics. Here we propose a mechanism through which electrons in ferroelectric bilayers excited with light cause ionic structural transitions. Using perturbation theory within a many-body formalism, we show that the ionic coupling is mediated by a resonant change in electronic occupation functions, ultimately governed by the quantum geometric tensor (QGT) of the ground state. Furthermore, we show that such transitions are generally accompanied by multiferroic order switching. We demonstrate two examples of light-induced structural and polarization switching under this mechanism using first-principle calculations on bilayer CrI$_{3}$ and MoTe$_{2}$. We show that the two materials can switch between atomic stackings with a light intensity threshold of only 10-100 GW/cm$^2$, a value 1-3 orders of magnitude lower than that required by direct light-ion coupling thanks to the superior efficiency of resonant light-electron coupling. Since such switching is fast, highly controllable, contactless, and reversible, it is promising for use in optically controlled nonvolatile memory, nanophotonics and polar electronics.

cond-mat.mtrl-sci↗

arXiv2025

Oscillate and Renormalize: Fast Phonons Reshape the Kondo Effect in Flat Band Systems

We examine the interplay between electron correlations and phonons in an Anderson-Holstein impurity model with an Einstein phonon. When the phonons are slow compared to charge fluctuations (frequency $\omega_0 \ll U/2$, the onsite Coulomb scale $U/2$), we demonstrate analytically that the expected phonon-mediated reduction of interactions is completely suppressed, even in the strong coupling regime. This suppression arises from the oscillator's inability to respond to rapid charge fluctuations, manifested as a compensation effect between the polaronic cloud and the excited-state phonons associated with valence fluctuations. We identify a novel frozen mixed valence phase, above a threshold dimensionless electron-phonon coupling $\alpha^*$ when the phonons are slow, where the static phonon cloud locks the impurity into specific valence configurations, potentially explaining the puzzling coexistence of mixed valence behavior and insulating properties in materials like rust. Conversely, when the phonon is fast ($\omega_0 \gtrsim U/2$), the system exhibits conventional polaronic behavior with renormalized onsite interactions effectively $U_{\text{eff}}$ due to phonon mediated attraction, with additional satellite features in the local spectral function due to phonon excitations. Using numerical renormalization group (NRG) calculations, a fully dynamic renormalization technique, we confirm these behaviors in both regimes. These findings have important implications for strongly correlated systems where phonon energy scales may be comparable to the Coulomb scale, such as in twisted bilayer graphene, necessitating careful consideration of interaction renormalizations in theoretical models.

cond-mat.str-el↗

arXiv2025

Band Renormalization, Quarter Metals, and Chiral Superconductivity in Rhombohedral Tetralayer Graphene

Recently, exotic superconductivity emerging from a spin-and-valley-polarized metallic phase has been discovered in rhombohedral tetralayer graphene. To explain this observation, we study the role of electron-electron interactions in driving flavor symmetry breaking, using the Hartree-Fock (HF) approximation, and in stabilizing superconductivity mediated by repulsive interactions. Though mean-field HF correctly predicts the isospin flavors and reproduces the experimental phase diagram, it overestimates the band renormalization near the Fermi energy and suppresses superconducting instabilities. To address this, we introduce a physically motivated scheme that includes internal screening in the HF calculation. Using this formalism, we find superconductivity arising from the spin-valley polarized phase for a range of electric fields and electron dopings. Our findings reproduce the experimental observations and reveal a p-wave, finite-momentum, time-reversal-symmetry-broken superconducting state, encouraging further investigation into exotic phases in graphene multilayers.

cond-mat.str-el↗

arXiv2025

Quantum geometric photocurrents of quasiparticles in superconductors

Nonlinear optical response is a sensitive probe of the geometry and symmetry of electronic Bloch states in solids. Here, we extend this notion to the Bogoliubiov-de-Gennes (BdG) quasiparticles in superconductors. We present a theory of photocurrents in superconductors and show that they sensitively depend on the quantum geometry of the BdG excitation spectrum. For all light polarizations, the photocurrent is proportional to the quantum geometric tensor: for linear polarized light it is related to the quantum metric and for circular polarization -- the Berry curvature dipole of the associated BdG bands. We further relate the photocurrent to the ground state symmetries, providing a symmetry dictionary for the allowed photocurrent responses. For light not at normal incidence to the sample, photocurrent probes time-reversal symmetry breaking in systems with chiral point groups (such as twisted bilayers). We demonstrate that photocurrents allow to probe topology and TRS breaking in twisted $d$-wave superconductors and test the nature of superconductivity in twisted WSe$_2$ and multilayer stacks of rhombohedral graphene. Our results pave the way to contactless measurement of the quantum geometric properties and symmetry of superconductivity in materials and heterostructures.

cond-mat.supr-con↗

arXiv2024

Deep Learning Based Superconductivity: Prediction and Experimental Tests

The discovery of novel superconducting materials is a longstanding challenge in materials science, with a wealth of potential for applications in energy, transportation, and computing. Recent advances in artificial intelligence (AI) have enabled expediting the search for new materials by efficiently utilizing vast materials databases. In this study, we developed an approach based on deep learning (DL) to predict new superconducting materials. We have synthesized a compound derived from our DL network and confirmed its superconducting properties in agreement with our prediction. Our approach is also compared to previous work based on random forests (RFs). In particular, RFs require knowledge of the chemical properties of the compound, while our neural net inputs depend solely on the chemical composition. With the help of hints from our network, we discover a new ternary compound $\textrm{Mo}_{20} \textrm{Re}_{6} \textrm{Si}_{4}$, which becomes superconducting below 5.4 K. We further discuss the existing limitations and challenges associated with using AI to predict and, along with potential future research directions.

cs.LG↗

arXiv2024

Real-Space Imaging of the Band Topology of Transition Metal Dichalcogenides

The topological properties of Bloch bands are intimately tied to the structure of their electronic wavefunctions within the unit cell of a crystal. Here, we show that scanning tunneling microscopy (STM) measurements on the prototypical transition metal dichalcogenide (TMD) semiconductor WSe$_2$ can be used to unambiguously fix the location of the Wannier center of the valence band. Using site-specific substitutional doping, we first determine the position of the atomic sites within STM images, establishing that the maximum electronic density of states at the $K$-point lies between the atoms. In contrast, the maximum density of states at the $\Gamma$ point is at the atomic sites. This signifies that WSe$_2$ is a topologically obstructed atomic insulator, which cannot be adiabatically transformed to the trivial atomic insulator limit.

cond-mat.mtrl-sci↗