arXiv subjects

Pu Yu

Publications and source records attributed to Pu Yu.

At least 19 recordsLinked to original sources

arXiv2026

Observation of light-induced Haldane gap in graphene

Symmetry and topology, encoded in electronic wavefunctions, play a central role in the electronic properties and emergent phenomena of quantum materials. While these properties are conventionally determined by the equilibrium Hamiltonian, strong optical fields offer a fundamentally different route by reshaping the Hamiltonian on ultrafast timescales, turning symmetry and topology into dynamically controllable degrees of freedom. Graphene provides a paradigmatic platform for realizing this concept, where circularly polarized light has long been predicted to dynamically break time-reversal symmetry (TRS) and open a topologically nontrivial gap at the Dirac point. Despite extensive experimental efforts, direct observation of this Dirac gap-the defining spectroscopic signature of the dynamical TRS-breaking induced topological phase-has remained missing. Here we directly observe this light-induced Dirac gap in monolayer graphene. Time- and angle-resolved photoemission spectroscopy reveals that the gap emerges simultaneously with the optical field and exclusively under circularly polarized driving, directly linking its opening to dynamical TRS breaking. Together with Floquet theory, we identify the gap with a light-induced Haldane mass and reveal the associated nontrivial Floquet Berry curvature and Chern topology. By demonstrating dynamical TRS breaking in a prototypical non-magnetic material, our results establish optical driving as a route to ultrafast engineering of symmetry and topology, opening opportunities for dynamically tunable quantum matter beyond equilibrium.

cond-mat.mes-hall↗

arXiv2026

The circle packing and Riemann uniformization embedding of the mated-CRT map converges to Liouville quantum gravity

We prove that the mated-CRT map converges to Liouville quantum gravity under circle packing and the Riemann uniformization embedding. The proof is based on our recent work on circle packing and the Riemann uniformization embedding for random planar maps in ergodic-scale free environments, comparison of circle packing in different domains and several existing and new estimates for the mated-CRT map. As an intermediate step, we prove an extension of He and Schramm's result (1996) on convergence of circle packing maps to conformal maps to global uniform topology in several settings. The latter results are of independent interest and will be applied in our subsequent work on the convergence of spanning tree weighted planar maps to $\sqrt{2}$-LQG under circle packing and Riemann uniformization embedding.

math.PR↗

arXiv2026

The circle packing and Riemann uniformization embedding of the tree-weighted planar maps converges to Liouville quantum gravity

We prove that in the disk, sphere, whole-plane topology, spanning tree weighted planar maps converge to $\sqrt{2}$-Liouville quantum gravity disk, sphere or cone under circle packing and Riemann uniformization embedding as the number of faces of the map goes to infinity. As a byproduct, we also prove that the natural path on faces of the embedded tree-weighted planar maps converge to SLE$_8$. The proof is based on our earlier work on circle packing and Riemann uniformization embedding for random planar maps in ergodic scale-free environments, comparisons of circle packings in different domains in a companion paper, and the convergence of tree-weighted planar maps to $\sqrt{2}$-LQG by the first author.

math.PR↗

arXiv2026

Ferroelectric switching of odd-parity magnon spin splitting

Magnetic symmetry can lift spin degeneracy in momentum space without producing net magnetization, generating spin textures classified by their parity under momentum reversal. Even-parity textures have well established in altermagnets. Odd-parity spin textures have recently emerged in electronic bands of compensated magnets, but their counterpart in collective bosonic excitations remains experimentally unresolved. Magnons provide a natural setting for this extension because they carry spin angular momentum through insulating magnets without accompanying charge flow. Beyond realizing this missing state, a broader challenge is to program spin splitting with voltage at room temperature. Here we report room-temperature transport evidence for ferroelectric switching odd-parity magnon spin splitting in multiferroic BiFeO3. Symmetry analysis and spin-wave calculations reveal that the cycloidal chirality splits opposite-spin magnon branches with an odd-in-momentum dependence and sets the sign. Experimentally, an injected in-plane-polarized spin current generates an out-of-plane magnon spin component during propagation. This component exhibits the crystalline angular dependence predicted by theory and reverses upon ferroelectric switching, providing a transport fingerprint of the spin-split magnon state. We use the programmed magnon spin to drive deterministic field-free switching of a perpendicular ferromagnet and demonstrate XNOR logic-in-memory. Our results extend odd-parity spin splitting from fermionic electronic states to bosonic collective modes and establish nonvolatile electrical control at room temperature.

cond-mat.mtrl-sci↗

arXiv2026

The $p$-$θ$ relation in mating of trees and its application to skew Brownian permutons

In the mating-of-trees approach to Schramm-Loewner evolution (SLE) and Liouville quantum gravity (LQG), it is natural to consider two pairs of correlated Brownian motions coupled together. This arises in the scaling limit of bipolar-orientation-decorated planar maps (Gwynne-Holden-Sun, 2016) and in the related skew Brownian permuton studied by Borga et al. There are two parameters that can be used to index the coupling between the two pairs of Brownian motions, denoted as $p$ and $θ$ in the literature: $p$ describes the Brownian motions, whereas $θ$ describes the SLE curves on LQG surfaces. In this paper, we derive an exact relation between the two parameters and demonstrate its application to computing statistics of the skew Brownian permuton. Our derivation relies on the synergy between mating-of-trees and Liouville conformal field theory (LCFT), where the boundary three-point function in LCFT provide the exact solvable inputs.

math.PR↗

arXiv2026

Oriented planar maps and annular mating of trees

We study a class of oriented annular planar maps which are closely related to bipolar-oriented maps. We prove that such maps can be encoded by a 2D lattice walk which converges to a 2D Brownian path in the scaling limit. We further prove a mating-of-trees result for the annulus, where the aforementioned Brownian path and a generalization encodes an LQG annulus decorated by a counterclockwise space-filling SLE loop with parameter $γ=16κ^{-1/2}\in(0,2)$.

math.PR↗

arXiv2026

The bulk one-arm exponent for the CLE$_{κ'}$ percolations

The conformal loop ensemble (CLE) is a conformally invariant random collection of loops. In the non-simple regime $κ'\in (4,8)$, it describes the scaling limit of the critical Fortuin-Kasteleyn (FK) percolations. CLE percolations were introduced by Miller-Sheffield-Werner (2017). The CLE$_{κ'}$ percolations describe the scaling limit of a natural variant of the FK percolation called the fuzzy Potts model, which has an additional percolation parameter $r$. Based on CLE percolations and assuming that the convergence of the FK percolation to CLE, K{ö}hler-Schindler and Lehmkuehler (2022) derived all the arm exponents for the fuzzy Potts model except the bulk one-arm exponent. In this paper, we exactly solve this exponent, which prescribes the dimension of the clusters in CLE$_{κ'}$ percolations. As a special case, the bichromatic one-arm exponent for the critical 3-state Potts model should be $4/135$. To the best of our knowledge, this natural exponent was not predicted in physics. Our derivation relies on the iterative construction of CLE percolations from the boundary conformal loop ensemble (BCLE), and the coupling between Liouville quantum gravity and SLE curves. The source of the exact solvability comes from the structure constants of boundary Liouville conformal field theory. A key technical step is to prove a conformal welding result for the target-invariant radial SLE curves. As intermediate steps in our derivation, we obtain several exact results for BCLE in both the simple and non-simple regimes, which extend results of Ang-Sun-Yu-Zhuang (2024) on the touching probability of non-simple CLE. This also provides an alternative derivation of the relation between the BCLE parameter $ρ$ and the additional percolation parameter $r$ in CLE percolations, which was originally due to Miller-Sheffield-Werner (2021, 2022).

math.PR↗

arXiv2026

Nanoscale Polar Landscapes in Quantum Paraelectric SrTiO3

SrTiO3 is a textbook quantum paraelectric, with ferroelectricity purportedly suppressed by quantum fluctuations of ionic positions down to the lowest temperatures. The precise real space structure of SrTiO3 at low temperature, however, has remained undefined despite decades of study. Here we directly image the low-temperature polar structure of quantum parelectric SrTiO3, using cryogenic scanning transmission electron microscopy down to 20 K. High resolution imaging reveals a spatially fluctuating landscape of nanoscale domains of finite polarization. The short-range polar domains first grow and self-organize into a periodic structure over tens of nanometers. However, the process reverses when entering the quantum paraelectric regime below 40 K and the periodically ordered polar nanodomains fragment into small clusters.

cond-mat.mtrl-sci↗

arXiv2026

Occupation Dynamics of Floquet-Volkov States and Spectral Sum Rule

Time-periodic light fields can dress electronic states in quantum materials, forming Floquet states whose dynamic occupation determines transient material properties. Here by using time- and angle-resolved photoemission spectroscopy (TrARPES), we reveal the transient occupation of Floquet-Volkov states in two semiconductors, black phosphorus and MoSe$_2$. While the occupation of the light-induced sidebands, directly reflected by TrARPES spectral weight, strongly depends on the driving field, we find that the total spectral weight obtained by summing up all sidebands is conserved upon below-gap driving. Our work provides critical insights into the Floquet population dynamics, which are essential for light-field tailoring of transient material properties.

cond-mat.mtrl-sci↗

arXiv2026

Circle packing and Riemann uniformization of random planar maps in an ergodic scale-free environment

We prove that embedded infinite planar maps in ergodic scale-free environments are close to their circle packing and Riemann uniformization embedding on a large scale, as long as suitable moment and connectivity conditions are satisfied. Ergodic scale-free environments were earlier considered by Gwynne, Miller and Sheffield (2018) in the context of the invariance principles for random walk, and they arise naturally in the study of random planar maps and Liouville quantum gravity.

math.PR↗

arXiv2026

Field-induced asymmetric band flattening and ideal quantum geometry in rhombohedral graphene

Rhombohedral graphene exhibits an exceptionally diverse array of correlated phases that depend sensitively on the displacement field. Compiling reported phases into a unified phase diagram reveals a pronounced field-dependent electron-hole asymmetry: correlated states on the hole-doped side emerge at small displacement fields, whereas the fractional quantum anomalous Hall effect (FQAHE) is observed exclusively on the electron-doped side under large displacement fields. This stark asymmetry highlights the need to understand how flat bands evolve with displacement fields. Here, we directly visualize the field-induced electron-hole asymmetric band flattening in rhombohedral pentalayer graphene (R5G) using nanospot angle-resolved photoemission spectroscopy with electrostatic gating. Beyond gap opening and spectral weight redistribution indicative of layer polarization, the gating field drives a strongly asymmetric modification of the flat bands: the flat valence band (FVB) evolves into an M-shaped dispersion at high field, whereas the flat conduction band (FCB) progressively flattens with increasing field. Comparison with calculations identifies critical parameters governing the band curvature of R5G, from which the resulting finite Berry curvature and near-ideal quantum geometry support the emergence of topological phases under electron doping at large fields. These results establish a direct link between the asymmetric phase diagram, band structure evolution, and quantum geometry, providing a microscopic framework for understanding correlated and topological phases in rhombohedral graphene.

cond-mat.mes-hall↗

arXiv2026

Radial conformal welding in Liouville quantum gravity

The seminal work of Sheffield showed that when random surfaces called Liouville quantum gravity (LQG) are conformally welded, the resulting interface is Schramm-Loewner evolution (SLE). This has been proved for a variety of configurations, and has applications to the scaling limits of random planar maps and the solvability of SLE and Liouville conformal field theory. We extend the theory to the setting where two sides of a canonical three-pointed LQG surface are conformally welded together, resulting in a radial SLE curve which can be described by imaginary geometry.

math.PR↗

arXiv2026

Observation of Floquet-induced gap in graphene

Floquet engineering provides a powerful pathway for creating non-equilibrium phases of matter with tailored electronic structures and properties through time-periodic driving. As the original theoretical prototype, graphene established the framework in which the Floquet topological insulator with light-induced anomalous Hall effect was proposed. However, the defining spectroscopic signature of Floquet engineering in graphene--light-induced hybridization (avoided-crossing) gap at Floquet band crossings, has remained experimentally elusive. Here, we report direct observation of Floquet-induced hybridization gap in monolayer graphene under resonant driving by a strong light field. Time- and angle-resolved photoemission spectroscopy reveals gap opening at Floquet band crossings, accompanied by coherent Floquet sidebands. The gap exhibits pronounced momentum anisotropy, featuring two Dirac nodes protected by the spatiotemporal symmetry and tunable by light polarization. These results provide long-sought experimental demonstration of Floquet band engineering in graphene, opening up opportunities for light-field engineered quantum phases in graphene and related materials.

cond-mat.mes-hall↗

arXiv2026

Charge disproportionation as a possible mechanism towards polar antiferromagnetic metal in molecular orbital crystal

Polar antiferromagnetic metals have recently garnered increasing interests due to their combined traits of both ferromagnets and antiferromagnets for spintronic applications. However, the inherently incompatible nature of antiferromagnet, metallicity and polarity pose a significant challenge. We propose that charge disproportionation can lead to this novel state in negative charge transfer gap regime in molecular orbital crystal by molecular orbital analyses of first-principles DFT+$U$ electronic band structure for representative Ruddlesden-Popper bilayer perovskite oxides Sr$_3$Co$_2$O$_7$, corroborated by Density Matrix Renormalization Group calculation. Due to the negative charge transfer nature of Co$^{4+}$ and imposed by strong interlayer coupling, localized molecular orbitals stemming from the hybridization of Co $d_{z^2}$ and $d_{xz/yz}$ orbitals through the apical oxygen $p$ orbitals are preferably emergent within each bilayer unit, which develop antiferromagnetic ordering by invoking Hubbard repulsion. Charge disproportionation driven by Hund's physics, makes an occupation imbalance with broken inversion symmetry in the remaining $d_{xy}$ and $d_{x^2-y^2}$ orbitals from distinct Co atoms within the bilayer unit, resulting in the polar metallicity. Meanwhile, this charge disproportionation scenario allows consequent conducting carriers to couple with interlayer local spins via Hund's coupling, giving rise to in-plane double-exchange ferromagnetism. Our molecular orbital formulation further provides a guide towards an effective Hamiltonian for modelling the unconventional synergy of metallicity, polarity and antiferromagnetism in Sr$_3$Co$_2$O$_7$, which may be a unified framework widely applicable to double-layer Ruddlesden-Popper perovskite oxides.

cond-mat.mtrl-sci↗

arXiv2025

Moiré-modulated $Γ$ valley in twisted bilayer and twisted double-bilayer MoTe$_2$

Twisted MoTe$_2$ hosts intriguing correlated quantum phenomena including the fractional quantum anomalous Hall effect in twisted bilayer (t-BL) MoTe$_2$ near 3.7$^\circ$, which is sensitive to the twist angle and moiré superlattices. Here, we directly visualize the twist-angle-modulated electronic structure of t-BL and twisted double-bilayer (t-DBL) near this critical angle. We find that the moiré superlattice not only modifies the relative energy between $Γ$ and K valleys in t-BL MoTe$_2$, but also strongly reconstructs the $Γ$ valley for both t-BL and t-DBL. Specifically, the deep $p_z$-derived band at $Γ$ exhibits a distinct splitting that systematically varies with increasing twist angle. Theoretical analysis suggests that this modulation arises from the twist-angle-dependent lattice relaxation, especially interfacial corrugations. Our work directly visualizes the moiré-modulated electronic structure and provides key spectroscopic information of lattice relaxation and interlayer interactions underlying the physics of twisted MoTe$_2$.

cond-mat.str-el↗

arXiv2025

Strongly confined Mid-infrared to Terahertz Phonon Polaritons in Ultra-thin SrTiO3

Phonon polaritons (PhPs) enable subwavelength light control for infrared sensing, imaging, and optoelectronics, but conventional polar materials have narrow Reststrahlen bands, limiting applications. Materials that support PhPs with broad spectral range, strong field confinement, slow group velocity, and high quality factor are therefore needed. Here, using monochromatic electron energy loss spectroscopy in a scanning transmission electron microscope, we demonstrate that ultra-thin SrTiO3 membranes possess the desired properties. Systematic measurements across varying thicknesses reveal two PhP branches with wide spectral dispersion, strong confinement, and anomalously slow group velocities spanning from the mid-infrared to terahertz range. Notably, in 3-nm-thick membranes, these polaritons exhibit unprecedented confinement factors exceeding 500 and group velocities as low as ~ 7 x 10-5c, rivaling the best-performing van der Waals materials. These findings establish perovskite oxide such as SrTiO3 as versatile platforms for tailoring light-matter interactions at the nanoscale, providing critical insights for the design of next-generation photonic devices requiring broadband operation and enhanced optical confinement.

physics.optics↗

arXiv2025

Floquet engineering enabled by charge density wave transition

Floquet engineering has emerged as a powerful approach for dynamically tailoring the electronic structures of quantum materials through time-periodic light fields generated by ultrafast laser pulses. The light fields can transiently dress Bloch electrons, creating novel electronic states inaccessible in equilibrium. While such temporal modulation provides dynamic control, spatially periodic modulations, such as those arising from charge density wave (CDW) order, can also dramatically reconstruct the band structure through real-space symmetry breaking. The interplay between these two distinct forms of modulation-temporal and spatial-opens a new frontier in electronic-phase-dependent Floquet engineering. Here we demonstrate this concept experimentally in the prototypical CDW material 1T-TiSe$_2$. Using time- and angle-resolved photoemission spectroscopy (TrARPES) with mid-infrared pumping, we observe a striking pump-induced instantaneous downshift of the valence band maximum (VBM), which is in sharp contrast to the subsequent upward shift on picosecond timescale associated with CDW melting. Most remarkably, the light-induced VBM downshift is observed exclusively in the CDW phase and only when the pump pulse is present, reaching maximum when pumping near resonance with the CDW gap. These observations unequivocally reveal the critical role of CDW in the Floquet engineering of TiSe$_2$. Our work demonstrates how time-periodic drives can synergistically couple to spatially periodic modulations to create non-equilibrium electronic states, establishing a new paradigm for Floquet engineering enabled by spontaneous symmetry breaking.

cond-mat.mtrl-sci↗

arXiv2025

Conformal welding of quantum disks and multiple SLE: the non-simple case

Two-pointed quantum disks with a weight parameter $W>0$ is a canonical family of finite-volume random surfaces in Liouville quantum gravity. We extend the conformal welding of quantum disks in [AHS23] to the non-simple regime, and give a construction of the multiple SLE associated with any given link pattern for $κ\in(4,8)$. Our proof is based on connections between SLE and Liouville conformal field theory (LCFT), where we show that in the conformal welding of multiple forested quantum disks, the surface after welding can be described in terms of LCFT, and the random conformal moduli contains the SLE partition function for the interfaces as a multiplicative factor. As a corollary, for $κ\in(4,8)$, we prove the existence of the multiple SLE partition functions, which are smooth functions satisfying a system of PDEs and conformal covariance.

math.PR↗