arXiv subjects

Daniel E. Parker

Publications and source records attributed to Daniel E. Parker.

At least 19 recordsLinked to original sources

arXiv2026

Excitonic pattern formation from a wrinkling instability in a van der Waals heterostructure

We studied photoluminescence of spatially indirect excitons (IXs) in a MoSe$_2$/WSe$_2$ van der Waals heterostructure. We observed a quasi-periodic triangular pattern of IXs with a characteristic spatial wavelength $\sim{}2.6\,μ\mathrm{m}$. Our theoretical analysis using a Föppl-von Kármán theory finds an elastic instability that produces triangular patterns with micrometer-scale wavelengths. This mechanism is consistent with the wavelength, symmetry, excitation power dependence, and temperature dependence of the observed IX pattern.

cond-mat.mes-hall↗

arXiv2026

Fermiology and the Candidate Chiral Superconductor in Rhombohedral Tetralayer Graphene

Chiral superconductivity, in which the phase of the superconducting order parameter winds in momentum space, has long been sought for its close link to topological superconductivity. Recent work reported a superconductor in rhombohedral multilayer graphene emerging from a time-reversal symmetry broken normal state, suggesting that it could be a chiral superconductor. However, the possibility of chirality depends on the symmetry and structure of the normal-state Fermi surface, which have not been directly measured. Here we measure quantum oscillations in rhombohedral tetralayer graphene over a broad range of the phase diagram, including the superconducting region. At densities well above the onset of superconductivity, we reproduce previously-reported oscillations consistent with a spin- and valley-polarized quarter metal with a single simply-connected Fermi pocket. As the carrier density is reduced, we find a transition to a complex "multitone" state that persists through the superconducting region. This state's spectrum of quantum oscillations is incompatible with a simply-connected quarter metal. The next-simplest candidate normal states suggested by our microscopic modeling (fully-polarized annular, nematic, and three-pocket states) are inconsistent with our measurements, albeit difficult to rule out entirely. The normal state is thus seen to be richer than previously envisaged, reshaping the search for the superconducting mechanism and the possible chirality of the pairing channel.

cond-mat.supr-con↗

arXiv2026

Crystals Caught Doping: Metallic Wigner Crystals in Rhombohedral Graphene

Nearly a century after Wigner's initial proposal, electron crystals are now a topic of intense experimental and theoretical interest. However, most proposed crystalline phases are commensurate and therefore become insulating in the presence of even weak pinning. In this work we discuss when a commensurate Wigner crystal will spontaneously self dope and develop itinerant carriers, giving rise to an incommensurate and thus metallic Wigner crystal (MWC). We develop a general criterion for the instability of the commensurate crystal which involves the competition between the charge gap at commensurability and a ``packing bias'' whose sign selects whether electron or hole doping is preferred. We then apply these insights to rhombohedral multilayer graphene, where calculations for commensurate crystals reveal instabilities towards self-doping. Carrying out self-consistent Hartree-Fock over the landscape of incommensurate crystals reveals the phase diagram, where a broad MWC phase appears directly adjacent to an insulating Wigner crystal phase. Recent observations of an island of reversed Hall conductance near a putative Wigner crystal phase in rhombohedral graphene are naturally explained by our theory.

cond-mat.str-el↗

arXiv2026

Topological constraint on crystalline current

How much current does a sliding electron crystal carry? The answer to this simple question has important implications for the dynamic properties of the crystal, such as the frequency of its cyclotron motion, and its phonon spectrum. In this work we introduce a precise definition of a sliding crystal and compute the corresponding current $\mathbf{j}_c$ for topological electron crystals in the presence of magnetic field. Our result is fully non-perturbative, does not rely on Galilean invariance, and applies equally to Wigner crystals and (anomalous) Hall crystals. In terms of the electron density $ρ$ and magnetic flux density $ϕ$, we find that $\mathbf{j}_c = e(ρ-Cϕ)\mathbf{v}$. Surprisingly, the current receives a contribution from the many-body Chern number $C$ of the crystal. When $ρ= Cϕ$, sliding crystals therefore carry zero current. The crystalline current fixes the Lorentz force felt by the sliding crystal and the dispersion of low-energy phonons of such crystals. This gives us a simple counting rule for the number of gapless phonons: if a sliding crystal carries nonzero current in a magnetic field, there is a single gapless mode, while otherwise there are two gapless modes. This result can also be understood from anomaly-matching of emanant discrete translation symmetries -- an idea that is also applicable to the dispersion of skyrmion crystals. Our results lead to novel experimental implications and invite further conceptual developments for electron crystals.

cond-mat.str-el↗

arXiv2026

Dynamic twisting and imaging of moiré crystals

Moiré superlattices in stacked 2D crystals are powerful platforms for engineering correlated and topological quantum phases, with twisted graphene and transition metal dichalcogenides (TMDs) as prominent examples. Their angle-sensitive band structures enable rich tunability; however, conventional tear-and-stack methods fix the angle at assembly, limiting systematic exploration of angle-dependent phenomena. Here, we present a scanning-probe-based manipulation scheme that enables in situ, continuous post-fabrication twist control using nanostructured metal rotors. We demonstrate reproducible angle tuning and direct moiré imaging across three platforms: graphene, hBN, and encapsulated, air-sensitive MoTe2. Quantitative piezoresponse force microscopy (PFM) analysis confirms sub-degree precision with minimal induced heterostrain, preserving sample quality even in the marginally twisted regime. Crucially, the device architecture maintains open access to the active region, allowing optical, scanning-probe, and transport measurements. This work enables single-device mapping of the angular phase diagram of moiré materials, including the twisted TMD homobilayers.

cond-mat.mes-hall↗

arXiv2025

Quantum Geometry Driven Crystallization: A Neural-Network Variational Monte Carlo Study

Wigner crystals are a paradigmatic form of interaction driven electronic order. A key open question is how Berry curvature and, more generally, quantum geometry reshape crystallization. The discovery of two-dimensional materials with relatively flat bands and pronounced Berry curvature has added fresh urgency to this question. Recent mean-field studies have proposed a topological variant of the Wigner crystal, the anomalous Hall crystal (AHC), with non-zero Chern number. However it remains unclear whether the AHC survives beyond the mean-field approximation. Here, we map out the ground-state phase diagram of the $λ$-jellium model - a simple model whose interaction strength and Berry curvature are independently tunable - using state-of-the-art neural-network variational Monte Carlo. The AHC is found to remain stable against quantum fluctuations. Surprisingly, quantum geometric effects are found to dramatically enhance crystallization. Both the AHC and the standard Wigner Crystal are stabilized at densities up to an order of magnitude above the critical density in the absence of quantum geometry, yet still significantly below the threshold predicted by mean-field theory. These striking results highlight the rich interplay between quantum fluctuations, quantum geometry, and crystallization, providing concrete guidance for experiments and enabling future explorations of fractionalized crystals and chiral superconductors.

cond-mat.str-el↗

arXiv2025

Beyond the Lowest Landau Level: Unlocking More Robust Fractional States Using Flat Chern Bands with Higher Vortexability

Enhancing the many-body gap of a fractional state is crucial for realizing robust fractional excitations. For fractional Chern insulators, existing studies suggest that making flat Chern bands closely resemble the lowest Landau level (LLL) seems to maximize the excitation gap, providing an apparently optimal platform. In this work, we demonstrate that deforming away from the LLL limit can, in fact, produce substantially larger FQH gaps. Using moiré flat bands with strongly non-Landau-level wavefunctions, we show that the gap can exceed that of the LLL by more than two orders of magnitude for short-range interactions and by factors of two to three for long-range interactions. This enhancement is generic across Abelian FCI states and follows a universal enhancement factor within each hierarchy. Using the Landau level framework, we identify the amplification of pseudopotentials as the microscopic origin of the observed enhancement. This finding demonstrates that pseudopotential engineering can substantially strengthen fractional topological phases. We further examined non-Abelian states and found that, within finite-size resolution, this wavefunction construction method can also be used to manipulate and enhance the gap for certain interaction parameters.

cond-mat.str-el↗

arXiv2025

$λ$-Jellium Model for the Anomalous Hall Crystal

The jellium model is a paradigmatic problem in condensed matter physics, exhibiting a phase transition between metallic and Wigner crystal phases. However, its vanishing Berry curvature makes it ill-suited for studying recent experimental platforms that combine strong interactions with nontrivial quantum geometry. These experiments inspired the anomalous Hall crystal (AHC) -- a topological variant of the Wigner crystal. The AHC spontaneously breaks continuous translation symmetry but has a nonzero Chern number. In this work, we introduce $λ-$jellium, a minimal extension of the two-dimensional jellium model. Its Berry curvature distribution is controlled by a single parameter, $λ$, where $λ=0$ corresponds to the standard jellium model. This setup facilitates the systematic exploration of Berry curvature's impact on electron crystallization. The phase diagram of this model, established using self-consistent Hartree Fock calculations, reveals several interesting features: (i) The AHC phase occupies a large region of the phase diagram. (ii) Two distinct Wigner crystal phases, the latter enabled by quantum geometry, and two distinct Fermi liquid phases are present. (iii) A continuous phase transition separates the AHC and one of the WC phases. (iv) In some parts of the AHC phase, the lattice geometry is non-triangular, unlike in the classical Wigner crystal. In addition to elucidating the physics of correlated electrons with nonzero Berry curvature, we expect that the simplicity of the model makes it an excellent starting point for more advanced numerical methods.

cond-mat.str-el↗

arXiv2025

Phonons in Electron Crystals with Berry Curvature

Recent advances in 2D materials featuring nonzero Berry curvature have inspired extensions of the Wigner crystallization paradigm. This paper derives a low-energy effective theory for such quantum crystals, including the anomalous Hall crystal (AHC) with nonzero Chern number. First we show that the low frequency dispersion of phonons in AHC, despite the presence of Berry curvature, resembles that of the zero field (rather than finite magnetic field) Wigner crystal due to the commutation of translation generators. We explain how key parameters of the phonon theory such as elastic constants and effective mass can be extracted from microscopic models, and apply them to two families of models: the recently introduced $λ$-jellium model and a model of rhombohedral multilayer graphene (RMG). In the $λ$-jellium model, we explore the energy landscape as crystal geometry shifts, revealing that AHC can become `soft' under certain conditions. This causes transitions in lattice geometry, although the quantized Hall response remains unchanged. Surprisingly, the Berry curvature seems to enhance the effective mass, leading to a reduction in phonon speed. For the AHC in RMG, we obtain estimates of phonon speed and shear stiffness. We also identify a previously overlooked `kineo-elastic' term in the phonon effective action that is present in the symmetry setting of RMG, and leads to dramatic differences in phonon speeds in opposite directions. We numerically confirm these predictions of the effective actions by time-dependent Hartree-Fock calculations.

cond-mat.str-el↗

arXiv2025

3D microwave imaging of a van der Waals heterostructure

Van der Waals (vdW) heterostructures offer a tunable platform for the realization of emergent phenomena in layered electron systems. While scanning probe microscopy techniques have proven useful for the characterization of surface states and 2D crystals, the subsurface imaging of quantum phenomena in multi-layer systems presents a significant challenge. In 3D heterostructures, states that occupy different planes can simultaneously contribute to the signal detected by the microscope probe, which complicates image analysis and interpretation. Here we present a quantum imaging technique that offers a glimpse into the third dimension by resolving states out of plane: it extracts the charge density landscape of individual atomic planes inside a vdW heterostructure, layer by layer. As a proof-of-concept, we perform layer-resolved imaging of quantum Hall states and charge disorder in double-layer graphene using milliKelvin microwave impedance microscopy. Here the discrete energy spectrum of the top layer enables transmission of microwaves through gapped states, thus opening direct access to quantum phases in the subsurface layer. Resolving how charge is distributed out-of-plane offers a direct probe of interlayer screening, revealing signatures of negative quantum capacitance driven by many-body correlations. At the same time, we extract key features of the band structure and thermodynamics, including gap sizes. Notably, by imaging the charge distribution on different atomic planes beneath the surface, we shed light on the roles of surface impurities and screening on the stability of fractional quantum Hall states. We also show that the uppermost graphene layer can serve as a top gate: This unlocks access to a wide range of phenomena that require displacement field control, from fractional Chern insulators in Moiré superlattices to correlated states in multilayer graphene.

cond-mat.mes-hall↗

arXiv2025

hBN alignment orientation controls moiré strength in rhombohedral graphene

Rhombohedral multilayer graphene hosts a rich landscape of correlated symmetry-broken phases, driven by strong interactions from its flat band edges. Aligning to hexagonal boron nitride (hBN) creates a moiré pattern, leading to recent observations of exotic ground states such as integer and fractional quantum anomalous Hall effects. Here, we show that the moiré effects and resulting correlated phase diagrams are critically influenced by a previously underestimated structural choice: the hBN alignment orientation. This binary parameter distinguishes between configurations where the rhombohedral graphene and hBN lattices are aligned near 0° or 180°, a distinction that arises only because both materials break inversion symmetry. Although the two orientations produce the same moiré wavelength, we find their distinct local stacking configurations result in markedly different moiré potential strengths. Using low-temperature transport and scanning SQUID-on-tip magnetometry, we compare nearly identical devices that differ only in alignment orientation and observe sharply contrasting sequences of symmetry-broken states. Theoretical analysis reveals a simple mechanism based on lattice relaxation and the atomic-scale electronic structure of rhombohedral graphene, supported by detailed modeling. These findings establish hBN alignment orientation as a key control parameter in moiré-engineered graphene systems and provide a framework for interpreting both prior and future experiments.

cond-mat.mes-hall↗

arXiv2025

Higher vortexability: zero field realization of higher Landau levels

The rise of moiré materials has led to experimental realizations of integer and fractional Chern insulators in small or vanishing magnetic fields. At the same time, a set of minimal conditions sufficient to guarantee a Abelian fractional state in a flat band were identified, namely "ideal" or "vortexable" quantum geometry. Such vortexable bands share essential features with the lowest Landau level, while excluding the need for more fine-tuned aspects such as flat Berry curvature. A natural and important generalization is to ask if such conditions can be extended to capture the quantum geometry of higher Landau levels, particularly the first (1LL), where non-Abelian states at $ν= 1/2,2/5$ are known to be competitive. The possibility of realizing these states at zero magnetic field , and perhaps even more exotic ones, could become a reality if we could identify the essential structure of the 1LL in Chern bands. In this work, we introduce a precise definition of 1LL quantum geometry, along with a figure of merit that measures how closely a given band approaches the 1LL. We apply the definition to identify two models with 1LL structure -- a toy model of double bilayer twisted graphene and a more realistic model of strained Bernal graphene.

cond-mat.mes-hall↗

arXiv2024

Superconductivity in a Topological Lattice Model with Strong Repulsion

The highly tunable nature of synthetic quantum materials -- both in the solid-state and cold atom contexts -- invites examining which microscopic ingredients aid in the realization of correlated phases of matter such as superconductors. Recent experimental advances in moiré materials suggest that unifying the features of the Fermi-Hubbard model and quantum Hall systems creates a fertile ground for the emergence of such phases. Here, we introduce a minimal 2D lattice model that incorporates exactly these features: time-reversal symmetry, band topology, and strong repulsive interactions. By using infinite cylinder density matrix renormalization group methods (cylinder iDMRG), we investigate the ground state phase diagram of this model. We find that it hosts an interaction-induced quantum spin Hall (QSH) insulator and demonstrate that weakly hole-doping this state gives rise to a superconductor at a finite circumference, with indications that this behavior persists on larger cylinders. At the aforementioned circumference, the superconducting phase is surprisingly robust to perturbations including additional repulsive interactions in the pairing channel. By developing a technique to probe the superconducting gap function in iDMRG, we phenomenologically characterize the superconductor. Namely, we demonstrate that it is formed from the weak pairing of holes atop the QSH insulator. Furthermore, we determine the pairing symmetry of the superconductor, finding it to be $p$-wave -- reminiscent of the unconventional superconductivity reported in experiments on twisted bilayer graphene (TBG). Motivated by this, we elucidate structural similarities and differences between our model and those of TBG in its chiral limit. Finally, to provide a more direct experimental realization, we detail an implementation of our Hamiltonian in a system of cold fermionic alkaline-earth atoms in an optical lattice.

cond-mat.str-el↗

arXiv2024

Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model

We propose a minimal "three-patch model" for the anomalous Hall crystal (AHC), a topological electronic state that spontaneously breaks both time-reversal symmetry and continuous translation symmetry. The proposal for this state is inspired by the recently observed integer and fractional quantum Hall states in rhombohedral multilayer graphene at zero magnetic field. There, interaction effects appear to amplify the effects of a weak moiré potential, leading to the formation of stable, isolated Chern bands. It has been further shown that Chern bands are stabilized in mean field calculations even without a moiré potential, enabling a realization of the AHC state. Our model is built upon the dissection of the Brillouin zone into patches centered around high symmetry points. Within this model, the wavefunctions at high symmetry points fully determine the topology and energetics of the state. We extract two quantum geometrical phases of the non-interacting wavefunctions that control the stability of the topologically nontrivial AHC state. The model predicts that the AHC state wins over the topological trivial Wigner crystal in a wide range of parameters, and agrees very well with the results of full self-consistent Hartree-Fock calculations of the rhombohedral multilayer graphene Hamiltonian.

cond-mat.str-el↗

arXiv2024

Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field

Recent experiments on rhombohedral pentalayer graphene flakes with a substrate induced moiré potential have identified both Chern insulators and fractional Quantum Hall states in the absence of an applied magnetic field. Surprisingly, these states are observed in strong displacement fields where the effects of the moiré lattice are weak, and seem to be readily accessed without fine-tuning. To address these experimental puzzles we study an interacting model of electrons in this geometry, first within the self-consistent Hartree-Fock (SCHF) approximation. We find an isolated Chern band with Chern number $|C|=1$, that moreover is relatively flat and shows good quantum geometry. Exact diagonalization and density matrix renormalization group methods at fractional filling establish the presence of fractional quantum anomalous Hall (FQAH) states. The $|C|=1$ band in SCHF is remarkably robust to varying microscopic parameters, and is also found in the $N_L=4$ and $N_L=6$ layer systems. Remarkably, it appears stable even to switching off the moiré potential, pointing to spontaneous breaking of translation symmetry. We term this topological crystalline state the ``anomalous Hall crystal" (AHC), and argue that it constitutes a general mechanism for creating stable Chern bands in rhombohedral graphene. Our work elucidates the physics behind the recent rhombohedral pentalayer graphene observations, predicts the appearance of the same phase in other systems, and opens the door to studying the interplay between electronic topology and spontaneous translation symmetry breaking.

cond-mat.str-el↗

arXiv2024

Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators

Fractional Chern insulators realize the remarkable physics of the fractional quantum Hall effect (FQHE) in crystalline systems with Chern bands. The lowest Landau level (LLL) is known to host the FQHE, but not all Chern bands are suitable for realizing fractional Chern insulators (FCI). Previous approaches to stabilizing FCIs focused on mimicking the LLL through momentum space criteria. Here instead we take a real-space perspective by introducing the notion of vortexability. Vortexable Chern bands admit a fixed operator that introduces vortices into any band wavefunction while keeping the state entirely within the same band. Vortexable bands admit trial wavefunctions for FCI states, akin to Laughlin states. In the absence of dispersion and for sufficiently short ranged interactions, these FCI states are the ground state -- independent of the distribution of Berry curvature. Vortexable bands are much more general than the LLL, and we showcase a recipe for constructing them. We exhibit diverse examples in graphene-based systems with or without magnetic field, and with any Chern number. A special class of vortexable bands is shown to be equivalent to the momentum space "trace condition" or "ideal band condition". In addition, we also identify a more general form of vortexability that goes beyond this criterion. We introduce a modified measure that quantifies deviations from general vortexability which can be applied to generic Chern bands to identify promising FCI platforms.

cond-mat.str-el↗

arXiv2024

Strong interactions and isospin symmetry breaking in a supermoiré lattice

In multilayer moiré heterostructures, the interference of multiple twist angles ubiquitously leads to tunable ultra-long-wavelength patterns known as supermoiré lattices. However, their impact on the system's many-body electronic phase diagram remains largely unexplored. We present local compressibility measurements revealing numerous incompressible states resulting from supermoiré-lattice-scale isospin symmetry breaking driven by strong interactions. By using the supermoiré lattice occupancy as a probe of isospin symmetry, we observe an unexpected doubling of the miniband filling near $ν=-2$, possibly indicating a hidden phase transition or normal-state pairing proximal to the superconducting phase. Our work establishes supermoiré lattices as a tunable parameter for designing novel quantum phases and an effective tool for unraveling correlated phenomena in moiré materials.

cond-mat.mes-hall↗

arXiv2023

Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe$_2$

The pursuit of exotic phases of matter outside of the extreme conditions of a quantizing magnetic field has been a long standing quest of solid state physics. Recent experiments have observed spontaneous valley polarization and fractional Chern insulators (FCIs) in zero magnetic field in twisted bilayers of MoTe$_2$, at partial filling of the topological valence band ($ν=-2/3$ and $-3/5$). We study the topological valence band at $\textit{half}$ filling, using exact diagonalization and density matrix renormalization group calculations. We discover a composite Fermi liquid (CFL) phase even at zero magnetic field that covers a large portion of the phase diagram centered around twist angle ${\sim}3.6^\circ$. The CFL is a non-Fermi liquid phase that shows metallic behavior despite the absence of Landau quasiparticles. We discuss experimental implications including the competition between the CFL and a Fermi liquid, which can be tuned with a displacement field. The topological valence band has excellent quantum geometry over a wide range of twist angles and a small bandwidth that is, remarkably, reduced by interactions for a range of angles. These key properties are responsible for stabilizing the exotic quantum Hall phases we find at zero field. Finally, we present an optical signature involving "extinguished" optical responses as a means to identify Chern bands with ideal quantum geometry.

cond-mat.str-el↗