Ciao!
I am Filippo Gaggioli,
postdoc in the Condensed Matter Theory group
@ MIT.

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.

Self-attention neural networks provide powerful variational wavefunctions that surpass the expressivity of traditional variational ansätze. 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_e = 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_e = 91 and N_e = 169 are in near-perfect agreement, indicating convergence to the thermodynamic limit.

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 moiré physics driven by many-body quantum effects.

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.

The discovery of superconducting states in multilayer rhombohedral graphene with spin andvalley polarization [1] has raised an interesting question: how does superconductivity cope withtime-reversal symmetry breaking? In this work, using Ginzburg-Landau theory and microscopiccalculation, we predict the existence of a new superconducting state at low electron density, whichexhibits a spontaneously formed lattice of vortices and antivortices hosting Majorana zero-modes intheir cores. We further identify this vortex-antivortex lattice (VAL) state in the experimental phasediagram and describe its experimental manifestations.

Nonreciprocal currents 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 the 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.

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In the past decade, moiré materials have revolutionized how we engineer and control quantum phases of matter. Among incommensurate materials, moiré materials are aperiodic composite crystals whose long-wavelength moiré superlattices enable tunable properties without chemically modifying their layers. To date, nearly all reports of moiré materials have investigated van der Waals heterostructures assembled far from thermodynamic equilibrium. Here we introduce a conceptually new approach to synthesizing high-mobility moiré materials in thermodynamic equilibrium. We report a new family of foliated superlattice materials (Sr6TaS8)1+δ(TaS2)8 that are exfoliatable van der Waals crystals with atomically incommensurate lattices. Lattice mismatches between alternating layers generate moiré superlattices, analogous to those of 2D moiré 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 moiré metals, which can be tuned via the moiré superlattice structure. We find that the Fermi surface of the structurally simplest moiré 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 moiré 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 moiré materials for electronics applications and evidences a novel material design concept for accessing a broad range of physical phenomena proposed in higher dimensions.

Moiré lattices provide a highly tunable platform for exploring the interplay between electroniccorrelations and band topology [1]. Introducing a second moiré e pattern extends this paradigm:interference between the two moiré patterns produces a supermoiré modulation, opening a route tofurther tailor electronic properties. Twisted trilayer graphene generally exemplifies such a system:two distinct moiré 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 graphenedevices whose twist angles lie along two continuous lines in the twist-angle parameter space [2–5].Depending on the degree of lattice relaxation, twisted trilayer graphene falls into two classes [4]:moiré polycrystals [6, 7], composed of periodic domains with locally commensurate moiré order, andmoiré quasicrystals, characterized by smoothly varying local moir´e configurations [8]. In helicallytwisted moir´e polycrystals, we observe an anomalous Hall effect, consistent with topological bandsarising from domains with broken xy-inversion symmetry. In contrast, superconductivity appearsgenerically in our moir´e quasicrystals. A subset of these systems exhibits signatures of spatiallymodulated superconductivity, which we attribute to the supermoiré structure. Our findings uncoverthe organizing principles of the observed correlated phases in twisted trilayer graphene, highlight thecritical roles of the supermoir´e modulation and lattice relaxation, and suggest a broader frameworkin which magic conditions arise not as isolated points but as extended manifolds within the multidimensional twist-angle space of complex moir´e materials.

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.

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