arXiv subjects

Filippo Gaggioli

Publications and source records attributed to Filippo Gaggioli.

14 recordsLinked to original sources

arXiv2026

Rhombohedral Graphene: A Tale of Many Crystals

Experiments on rhombohedral graphene have uncovered an extraordinary wealth of correlated quantum phases - from chiral superconductors to electronic crystals - all within a single family of atomically thin materials. Here, we introduce a simple indicator, derived from the noninteracting band dispersion, that identifies strongly correlated regions in the phase diagram of rhombohedral graphene as a function of carrier density and displacement field. We develop a neural-network variational Monte Carlo method, combined with Hartree-Fock theory, to solve the interacting ground states. Our calculation reveals a variety of electron crystals with no classical analog. These include, at increasing density: Wigner crystal, self-doped Wiger crystal, as well as ''anticrystal'', a lattice of holes in an electron liquid. We discuss their experimental manifestations and possible connection to superconductivity.

cond-mat.str-el↗

arXiv2026

Accurate Self-Attention Wavefunctions at Large Scale

Self-attention neural networks provide powerful variational wavefunctions that surpass the expressivity of traditional variational ansatze. This expressivity, however, comes with increased computational complexity, raising a pressing question about scalability -- can such wavefunctions retain their accuracy at large system sizes? We apply self-attention wavefunctions to the two-dimensional homogeneous electron gas for up to N=169 particles, obtaining energies systematically lower than state-of-the-art DMC. Direct access to the ground state wavefunction further lets us recover the full collective-mode dispersion of the liquid phase, from the small-q plasmon branch to a roton-like minimum near q=2k_F. Observables at N=91 and N=169 are in near-perfect agreement, indicating convergence to the thermodynamic limit.

cond-mat.str-el↗

arXiv2026

Quantum Electron Quasicrystal

The strongly correlated phases of the homogeneous electron gas constitute the vocabulary of many-body condensed matter physics and find a natural realization in semiconductors. In this setting, recent neural-network variational Monte Carlo calculations discovered an unexpected quantum phase of matter in wide quantum wells: an electronic quasicrystal formed by a bilayer Wigner crystals with a 30-degrees twist. This state defies classical expectations and emerges in a regime dominated by quantum fluctuations. Here, we develop an analytical framework to reveal its origin. By computing zero-point energy corrections to bilayer Wigner crystal configurations, we show that quantum fluctuations qualitatively reshape the energetic landscape, destabilizing the classical honeycomb state and selecting the 30-degrees quasicrystalline ground state over a broad parameter range. Our results identify zero-point motion as the mechanism stabilizing the electronic quasicrystal and establish a route to spontaneous moir\'e physics driven by many-body quantum effects.

cond-mat.str-el↗

arXiv2025

Electronic crystals and quasicrystals in semiconductor quantum wells: an AI-powered discovery

The homogeneous electron gas is a cornerstone of quantum condensed matter physics, providing the foundation for developing density functional theory and understanding electronic phases in semiconductors. However, theoretical understanding of strongly-correlated electrons in realistic semiconductor systems remains limited. In this work, we develop a neural network based variational approach to study quantum wells in three dimensional geometry for a variety of electron densities and well thicknesses. Starting from first principles, our unbiased AI-powered method reveals metallic and crystalline phases with both monolayer and bilayer charge distributions. In the emergent bilayer, we discover a new quantum phase of matter: the electronic quasicrystal.

cond-mat.str-el↗

arXiv2025

Higher-dimensional Fermiology in bulk moir\'e metals

In the past decade, moir\'e materials have revolutionized how we engineer and control quantum phases of matter. Among incommensurate materials, moir\'e materials are aperiodic composite crystals whose long-wavelength moir\'e superlattices enable tunable properties without chemically modifying their layers. To date, nearly all reports of moir\'e materials have investigated van der Waals heterostructures assembled far from thermodynamic equilibrium. Here we introduce a conceptually new approach to synthesizing high-mobility moir\'e materials in thermodynamic equilibrium. We report a new family of foliated superlattice materials (Sr$_6$TaS$_8$)$_{1+\delta}$(TaS$_2$)$_8$ that are exfoliatable van der Waals crystals with atomically incommensurate lattices. Lattice mismatches between alternating layers generate moir\'e superlattices, analogous to those of 2D moir\'e heterobilayers, that are coherent throughout these crystals and are tunable through their synthesis conditions without altering their chemical composition. High-field quantum oscillation measurements map the complex Fermiology of these moir\'e metals, which can be tuned via the moir\'e superlattice structure. We find that the Fermi surface of the structurally simplest moir\'e metal is comprised of over 40 distinct cross-sectional areas, the most observed in any material to our knowledge. This can be naturally understood by postulating that bulk moir\'e materials can encode electronic properties of higher-dimensional superspace crystals in ways that parallel well-established crystallographic methods used for incommensurate lattices. More broadly, our work demonstrates a scalable synthesis approach potentially capable of producing moir\'e materials for electronics applications and evidences a novel material design concept for accessing a broad range of physical phenomena proposed in higher dimensions.

cond-mat.mtrl-sci↗

arXiv2025

Magic continuum in multi-moir\'e twisted trilayer graphene

Moir\'e lattices provide a highly tunable platform for exploring the interplay between electronic correlations and band topology. Introducing a second moir\'e pattern extends this paradigm: interference between the two moir\'e patterns produces a supermoir\'e modulation, opening a route to further tailor electronic properties. Twisted trilayer graphene generally exemplifies such a system: two distinct moir\'e patterns arise from the relative twists between adjacent graphene layers. Here, we report the observation of correlated phenomena across a wide range of twisted trilayer graphene devices whose twist angles lie along two continuous lines in the twist-angle parameter space. Depending on the degree of lattice relaxation, twisted trilayer graphene falls into two classes: moir\'e polycrystals, composed of periodic domains with locally commensurate moir\'e order, and moir\'e quasicrystals, characterized by smoothly varying local moir\'e configurations. In helically twisted moir\'e polycrystals, we observe an anomalous Hall effect, consistent with topological bands arising from domains with broken $xy$-inversion symmetry. In contrast, superconductivity appears generically in our moir\'e quasicrystals. A subset of these systems exhibits signatures of spatially modulated superconductivity, which we attribute to the supermoir\'e structure. Our findings uncover the organizing principles of the observed correlated phases in twisted trilayer graphene, highlight the critical roles of the supermoir\'e modulation and lattice relaxation, and suggest a broader framework in which magic conditions arise not as isolated points but as extended manifolds within the multi-dimensional twist-angle space of complex moir\'e materials.

cond-mat.mes-hall↗

arXiv2025

Artificial Intelligence for Quantum Matter: Finding a Needle in a Haystack

Neural networks (NNs) have great potential in solving the ground state of various many-body problems. However, several key challenges remain to be overcome before NNs can tackle problems and system sizes inaccessible with more established tools. Here, we present a general and efficient method for learning the NN representation of an arbitrary many-body complex wave function from its N-particle probability density and probability current density and successfully test on (non-Abelian) fractional quantum Hall states and chiral BCS wavefunction. Having reached overlaps as large as 99.9%, we employ our neural wave function for pre-training to effortlessly solve the fractional quantum Hall problem with Coulomb interactions and realistic Landau-level mixing for as many as 25 particles and uncover distinctive features of the edge. Our work demonstrates efficient, scalable and accurate simulation of highly-entangled quantum matter using general-purpose deep NNs enhanced with physics-informed initialization.

cond-mat.str-el↗

arXiv2025

Spontaneous vortex-antivortex lattice and Majorana fermions in rhombohedral graphene

The discovery of superconducting states in multilayer rhombohedral graphene with spin and valley polarization has raised an interesting question: how does superconductivity cope with time-reversal symmetry breaking? In this work, using Ginzburg-Landau theory and microscopic calculation, we predict the existence of a new superconducting state at low electron density, which exhibits a spontaneously formed lattice of vortices and antivortices hosting Majorana zero-modes in their cores. We further identify this vortex-antivortex lattice (VAL) state in the experimental phase diagram and describe its experimental manifestations.

cond-mat.supr-con↗

arXiv2024

Experimental detection of vortices in magic-angle graphene

The tunability of superconducting magic-angle twisted-layer graphene films elevates this material system to a promising candidate for superconducting electronics. We implement a gate-tuned Josephson junction in a magic-angle twisted four-layer graphene film. Field-dependent measurements of the critical current show a Fraunhofer-like pattern that differs from the standard pattern with characteristics typical for a weak transverse screener. We observe sudden shifts associated with vortices jumping into and out of the leads. By tuning the leads to the edge of the superconducting dome, we observe fast switching between superconducting and normal states, an effect associated with vortex dynamics. Time-dependent measurements provide us with the vortex energy scale and an estimate for the London penetration depth, in agreement with recent kinetic inductance measurements on twisted graphene films. Our results prove the utility of our junction as a sensor for vortex detection, allowing us to extract fundamental properties of the 2D superconductor.

cond-mat.mes-hall↗

arXiv2024

Nonreciprocity of supercurrent along applied magnetic field

Nonreciprocal current responses arise in a broad range of systems, from magnons and phonons to supercurrents, due to an interplay between spatial and temporal symmetry breakings. These find applications in devices, such as circulators and rectifiers, as well as in probing the interactions and states that underlie the nonreciprocity. An established symmetry argument anticipates emergence of nonreciprocal currents along a direction perpendicular to the applied magnetic field that breaks the time-reversal symmetry. Here, motivated by recent experiments, we examine the emergence of nonreciprocity in vortex-limited superconducting critical currents along an applied magnetic field. Employing London's equations for describing the Meissner response of a superconducting film, we find that an additional symmetry breaking due to a preferred vortex axis enables nonreciprocal critical currents along the applied magnetic field, consistent with the so far unexplained experimental observation. Building on our concrete theoretical model for supercurrents, we discuss a possible generalization of the prevailing symmetry consideration to encompass nonreciprocal currents along the time-reversal symmetry breaking direction.

cond-mat.supr-con↗

arXiv2024

Creep-enhanced vortex pinning revealed through nonmonotonic relaxation of the Campbell length

We study the effects of flux creep on the linear AC response of the vortex lattice in single crystals Ca$_3$Ir$_4$Sn$_{13}$ by measuring the Campbell penetration depth, $\lambda_{\rm \scriptscriptstyle C}(T,H,t)$. Thermal fluctuations release vortices from shallow pinning sites, only for them to become re-trapped by deeper potential wells, causing an initial increase of the effective Labusch parameter, which is proportional to the pinning well curvature. This effect cannot be detected in conventional magnetic relaxation measurements but is revealed by our observation of a nonmonotonic time evolution of $\lambda_{\rm \scriptscriptstyle C}(T,H,t)$, which directly probes the average curvature of the occupied pinning centers. The time evolution of $\lambda_{\rm \scriptscriptstyle C}(T,H,t)$ was measured at different temperatures in samples with different densities of pinning centers produced by electron irradiation. The curves can be collapsed together when plotted on a logarithmic time scale $t \to T\ln{(t/t_0)}$ confirming that the time evolution is driven by flux creep. The $\lambda_{\rm \scriptscriptstyle C}(T,H,t)$ is hysteretic with a noticeable nonmonotonic relaxation in the presence of a vortex density gradient (after zero-field cooling), but is monotonic after field cooling, where the vortex density is uniform. This result quantitatively corroborates the novel picture of vortex creep based on the strong pinning theory.

cond-mat.supr-con↗

arXiv2024

Superconductivity in atomically thin films: 2D critical state model

The comprehensive understanding of superconductivity is a multi-scale task that involves several levels, starting from the electronic scale determining the microscopic mechanism, going to the phenomenological scale describing vortices and the continuum-elastic scale describing vortex matter, to the macroscopic scale relevant in technological applications. The prime example for such a macro-phenomenological description is the Bean model that is hugely successful in describing the magnetic and transport properties of bulk superconducting devices. Motivated by the development of novel devices based on superconductivity in atomically thin films, such as twisted-layer graphene, here, we present a simple macro-phenomenological description of the critical state in such two-dimensional (2D) thin films. While transverse screening and demagnetization can be neglected in these systems, thereby simplifying the task in comparison with usual film- and platelet shaped samples, surface and bulk pinning are important elements to be included. We use our 2D critical state model to describe the transport and magnetic properties of 2D thin-film devices, including the phenomenon of non-reciprocal transport in devices with asymmetric boundaries and the superconducting diode effect.

cond-mat.supr-con↗

arXiv2023

Strong pinning transition with arbitrary defect potentials

Dissipation-free current transport in type II superconductors requires vortices to be pinned by defects in the underlying material. The pinning capacity of a defect is quantified by the Labusch parameter $κ\sim f_p/ξ\bar{C}$, measuring the pinning force $f_p$ relative to the elasticity $\bar{C}$ of the vortex lattice, with $ξ$ denoting the coherence length (or vortex core size) of the superconductor. The critical value $κ= 1$ separates weak from strong pinning, with a strong defect at $κ> 1$ able to pin a vortex on its own. So far, this weak-to-strong pinning transition has been studied for isotropic defect potentials, resulting in a critical exponent $μ= 2$ for the onset of the strong pinning force density $F_\mathrm{pin} \sim n_p f_p (ξ/a_0)^2(κ-1)^μ$, with $n_ p$ denoting the density of defects and $a_0$ the intervortex distance. The behavior changes dramatically when studying anisotropic defects with no special symmetries: the strong pinning then originates out of isolated points with length scales growing as $ξ(κ- 1)^{1/2}$, resulting in a different force exponent $μ= 5/2$. Our analysis of the strong pinning onset for arbitrary defect potentials $e_p(\mathbf{R})$, with $\mathbf{R}$ a planar coordinate, makes heavy use of the Hessian matrix describing its curvature and leads us to interesting geometrical structures. Both, onset and merger points are defined by local differential properties of the Hessian's determinant $D(\mathbf{R})$, specifically, its minima and saddle points. Extending our analysis to the case of a random two-dimensional pinning landscape, we discuss the topological properties of unstable and bistable regions as expressed through the Euler characteristic, with the latter related to the local differential properties of $D(\mathbf{R})$ through Morse theory.

cond-mat.supr-con↗

arXiv2021

Creep effects on the Campbell response in type II superconductors

Applying the strong pinning formalism to the mixed state of a type II superconductor, we study the effect of thermal fluctuations (or creep) on the penetration of an ac magnetic field as quantified by the so-called Campbell length $λ_\textrm{C}$. Within strong pinning theory, vortices get pinned by individual defects, with the jumps in the pinning energy ($Δe_\mathrm{pin}$) and force ($Δf_\mathrm{pin}$) between bistable pinned and free states quantifying the pinning process. We find that the evolution of the Campbell length $λ_{\rm C}(t)$ as a function of time $t$ is the result of two competing effects, the change in the force jumps $Δf_\mathrm{pin}(t)$ and a change in the trapping area $S_\mathrm{trap}(t)$ of vortices; the latter describes the area around the defect where a nearby vortex gets and remains trapped. Contrary to naive expectation, we find that during the decay of the critical state in a zero-field cooled (ZFC) experiment, the Campbell length $λ_{\rm C}(t)$ is usually nonmonotonic, first decreasing with time $t$ and then increasing for long waiting times. Field cooled (FC) experiments exhibit hysteretic effects in $λ_\textrm{C}$; relaxation then turns out to be predominantly monotonic, but its magnitude and direction depends on the specific phase of the cooling--heating cycle. Furthermore, when approaching equilibrium, the Campbell length relaxes to a finite value, different from the persistent current which vanishes at long waiting times $t$, e.g., above the irreversibility line. Finally, measuring the Campbell length $λ_\textrm{C}(t)$ for different states, zero-field cooled, field cooled, and relaxed, as a function of different waiting times $t$ and temperatures $T,$ allows to "spectroscopyse" the pinning potential of the defects.

cond-mat.supr-con↗