arXiv subjects

Benjamin E. Feldman

Publications and source records attributed to Benjamin E. Feldman.

At least 19 recordsLinked to original sources

arXiv2025

Link between thermodynamic correlation signatures and superconductivity in twisted trilayer graphene

Twisted graphene multilayers exhibit strong electronic correlations, which manifest in a range of experimental signatures. Yet how these signatures relate to each other and the microscopic ground states-and how twist angle and band structure reshape them-remains poorly understood. Here we study this interplay by correlating local thermodynamic and transport measurements in a twisted trilayer graphene (TTG) sample with unequal angles and flat electronic bands. We use a scanning single-electron transistor to map the impact of electron-electron interactions in a region of the sample where the local twist angle evolves smoothly. We observe gapped correlated insulators and a sawtooth in electronic compressibility, both exhibiting pronounced electron-hole (e-h) asymmetry with distinct magic angles for conduction and valence bands. Subsequent transport measurements in the same region reveal robust superconductivity with a similar e-h asymmetry. Our measurements indicate that superconductivity is not directly tied to the correlated insulators. Instead, its critical temperature correlates closely with the strength of the sawtooth in compressibility, suggesting a common origin or link between the two. By combining a local probe with transport measurements, we uncover connections between superconductivity and thermodynamic correlation signatures that are not apparent from either technique in isolation, highlighting the power of our dual approach and establishing their dependence on interlayer twist angles in TTG.

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arXiv2024

Magnetic Hofstadter cascade in a twisted semiconductor homobilayer

Transition metal dichalcogenide moiré homobilayers have emerged as a platform in which magnetism, strong correlations, and topology are intertwined. In a large magnetic field, the energetic alignment of states with different spin in these systems is dictated by both strong Zeeman splitting and the structure of the Hofstadter's butterfly spectrum, yet the latter has been difficult to probe experimentally. Here we conduct local thermodynamic measurements of twisted WSe$_2$ homobilayers that reveal a cascade of magnetic phase transitions. We understand these transitions as the filling of individual Hofstadter subbands, allowing us to extract the structure and connectivity of the Hofstadter spectrum of a single spin. The onset of magnetic transitions is independent of twist angle, indicating that the exchange interactions of the component layers are only weakly modified by the moiré potential. In contrast, the magnetic transitions are associated with stark changes in the insulating states at commensurate filling. Our work achieves a spin-resolved measurement of Hofstadter's butterfly despite overlapping states, and it disentangles the role of material and moiré effects on the nature of the correlated ground states.

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arXiv2024

Imaging supermoir\'e relaxation in helical trilayer graphene

In twisted van der Waals materials, local atomic relaxation can alter the underlying electronic structure. Characterizing lattice reconstruction and its susceptibility to strain is essential for understanding emergent electronic states, especially in multilayers in which interference between moir\'e lattices yields larger supermoir\'e patterns whose energy is highly sensitive to local stacking. Here we image spatial modulations in the electronic character of helical trilayer graphene, which indicate relaxation into a superstructure of large domains with uniform moir\'e periodicity. We show that the supermoir\'e domain size is increased by strain and can be altered in the same device while preserving the local properties within each domain. Finally, we observe a higher conductance at the domain boundaries, consistent with predictions that they host counter-propagating edge modes. Our work provides a real-space visualization of moir\'e-periodic domains, reveals two independently tunable length scales and demonstrates strain engineering as a route towards designing correlated topological networks at the supermoir\'e scale.

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arXiv2024

Mapping twist-tuned multiband topology in bilayer WSe$_2$

Semiconductor moiré superlattices have been shown to host a wide array of interaction-driven ground states. However, twisted homobilayers have been difficult to study in the limit of large moiré wavelength, where interactions are most dominant. Here, we conduct local electronic compressibility measurements of twisted bilayer WSe$_2$ (tWSe$_2$) at small twist angles. We demonstrate multiple topological bands which host a series of Chern insulators at zero magnetic field near a 'magic angle' around $1.23^\circ$. Using a locally applied electric field, we induce a topological quantum phase transition at one hole per moiré unit cell. Our work establishes the topological phase diagram of a generalized Kane-Mele-Hubbard model in tWSe$_2$, demonstrating a tunable platform for strongly correlated topological phases.

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arXiv2024

Uncovering the spin ordering in magic-angle graphene via edge state equilibration

Determining the symmetry breaking order of correlated quantum phases is essential for understanding the microscopic interactions in their host systems. The flat bands in magic angle twisted bilayer graphene (MATBG) provide an especially rich arena to investigate such interaction-driven ground states, and while progress has been made in identifying the correlated insulators and their excitations at commensurate moire filling factors, the spin-valley polarizations of the topological states that emerge at high magnetic field remain unknown. Here we introduce a new technique based on twist-decoupled van der Waals layers that enables measurements of their electronic band structure and, by studying the backscattering between counter-propagating edge states, determination of relative spin polarization of the their edge modes. Applying this method to twist-decoupled MATBG and monolayer graphene, we find that the broken-symmetry quantum Hall states that extend from the charge neutrality point in MATBG are spin-unpolarized at even integer filling factors. The measurements also indicate that the correlated Chern insulator emerging from half filling of the flat valence band is spin-unpolarized, but suggest that its conduction band counterpart may be spin-polarized. Our results constrain models of spin-valley ordering in MATBG and establish a versatile approach to study the electronic properties of van der Waals systems.

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arXiv2024

Particle-hole asymmetric ferromagnetism and spin textures in the triangular Hubbard-Hofstadter model

In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the "Hofstadter regime," where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo (DQMC) and density matrix renormalization group (DMRG) techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor $ν\leq 1$, bounded below by filling factor $ν= 1$ and bounded above by half-filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors $ν=1$ and $ν=3$. The phases near $ν=1$ are particle-hole asymmetric, and we observe a rapid decrease in ground state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands.

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arXiv2024

Characterization of two fast-turnaround dry dilution refrigerators for scanning probe microscopy

Low-temperature scanning probe microscopes (SPMs) are critical for the study of quantum materials and quantum information science. Due to the rising costs of helium, cryogen-free cryostats have become increasingly desirable. However, they typically suffer from comparatively worse vibrations than cryogen-based systems, necessitating the understanding and mitigation of vibrations for SPM applications. Here we demonstrate the construction of two cryogen-free dilution refrigerator SPMs with minimal modifications to the factory default and we systematically characterize their vibrational performance. We measure the absolute vibrations at the microscope stage with geophones, and use both microwave impedance microscopy and a scanning single electron transistor to independently measure tip-sample vibrations. Additionally, we implement customized filtering and thermal anchoring schemes, and characterize the cooling power at the scanning stage and the tip electron temperature. This work serves as a reference to researchers interested in cryogen-free SPMs, as such characterization is not standardized in the literature or available from manufacturers.

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arXiv2024

Anomalous Landau level gaps near magnetic transitions in monolayer WSe$_2$

First-order phase transitions produce abrupt changes to the character of both ground and excited electronic states. Here we conduct electronic compressibility measurements to map the spin phase diagram and Landau level (LL) energies of monolayer WSe$_2$ in a magnetic field. We resolve a sequence of first-order phase transitions between completely spin-polarized LLs and states with LLs of both spins. Unexpectedly, the LL gaps are roughly constant over a wide range of magnetic fields below the transitions, which we show reflects a preference for opposite spin excitations of the spin-polarized ground state. These transitions also extend into compressible regimes, with a sawtooth boundary between full and partial spin polarization. We link these observations to the important influence of LL filling on the exchange energy beyond a smooth density-dependent contribution. Our results show that WSe$_2$ realizes a unique hierarchy of energy scales where such effects induce re-entrant magnetic phase transitions tuned by density and magnetic field.

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arXiv2023

Harnessing excitons at the nanoscale -- photoelectrical platform for quantitative sensing and imaging

Excitons -- quasiparticles formed by the binding of an electron and a hole through electrostatic attraction -- hold promise in the fields of quantum light confinement and optoelectronic sensing. Atomically thin transition metal dichalcogenides (TMDs) provide a versatile platform for hosting and manipulating excitons, given their robust Coulomb interactions and exceptional sensitivity to dielectric environments. In this study, we introduce a cryogenic scanning probe photoelectrical sensing platform, termed exciton-resonant microwave impedance microscopy (ER-MIM). ER-MIM enables ultra-sensitive probing of exciton polarons and their Rydberg states at the nanoscale. Utilizing this technique, we explore the interplay between excitons and material properties, including carrier density, in-plane electric field, and dielectric screening. Furthermore, we employ deep learning for automated data analysis and quantitative extraction of electrical information, unveiling the potential of exciton-assisted nano-electrometry. Our findings establish an invaluable sensing platform and readout mechanism, advancing our understanding of exciton excitations and their applications in the quantum realm.

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arXiv2023

Spin skyrmion gaps as signatures of strong-coupling insulators in magic-angle twisted bilayer graphene

The flat electronic bands in magic-angle twisted bilayer graphene (MATBG) host a variety of correlated insulating ground states, many of which are predicted to support charged excitations with topologically non-trivial spin and/or valley skyrmion textures. However, it has remained challenging to experimentally address their ground state order and excitations, both because some of the proposed states do not couple directly to experimental probes, and because they are highly sensitive to spatial inhomogeneities in real samples. Here, using a scanning single-electron transistor, we observe thermodynamic gaps at even integer moiré filling factors at low magnetic fields. We find evidence of a field-tuned crossover from charged spin skyrmions to bare particle-like excitations, suggesting that the underlying ground state belongs to the manifold of strong-coupling insulators. From the spatial dependence of these states and the chemical potential variation within the flat bands, we infer a link between the stability of the correlated ground states and local twist angle and strain. Our work advances the microscopic understanding of the correlated insulators in MATBG and their unconventional excitations.

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arXiv2023

Tunable spin and valley excitations of correlated insulators in $Γ$-valley moiré bands

Moiré superlattices formed from transition metal dichalcogenides (TMDs) have been shown to support a variety of quantum electronic phases that are highly tunable using applied electromagnetic fields. While the valley character of the low-energy states dramatically affects optoelectronic properties in the constituent TMDs, this degree of freedom has yet to be fully explored in moiré systems. Here, we establish twisted double bilayer WSe$_2$ as an experimental platform to study electronic correlations within $Γ$-valley moiré bands. Through a combination of local and global electronic compressibility measurements, we identify charge-ordered phases at multiple integer and fractional moiré band fillings $ν$. By measuring the magnetic field dependence of their energy gaps and the chemical potential upon doping, we reveal spin-polarized ground states with novel spin polaron quasiparticle excitations. In addition, an applied displacement field allows us to realize a new mechanism of metal-insulator transition at $ν= -1$ driven by tuning between $Γ$- and $K$-valley moiré bands. Together, our results demonstrate control over both the spin and valley character of the correlated ground and excited states in this system.

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arXiv2023

1/4 is the new 1/2 when topology is intertwined with Mottness

In non-interacting systems, bands from non-trivial topology emerge strictly at half-filling and exhibit either the quantum anomalous Hall or spin Hall effects. Here we show using determinantal quantum Monte Carlo and an exactly solvable strongly interacting model that these topological states now shift to quarter filling. A topological Mott insulator is the underlying cause. The peak in the spin susceptibility is consistent with a possible ferromagnetic state at $T=0$. The onset of such magnetism would convert the quantum spin Hall to a quantum anomalous Hall effect. While such a symmetry-broken phase typically is accompanied by a gap, we find that the interaction strength must exceed a critical value for this to occur. Hence, we predict that topology can obtain in a gapless phase but only in the presence of interactions in dispersive bands. These results explain the recent quarter-filled quantum anomalous Hall effects seen in moire systems.

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arXiv2023

Topological Mott Insulator at Quarter Filling in the Interacting Haldane Model

While the recent advances in topology have led to a classification scheme for electronic bands described by the standard theory of metals, a similar scheme has not emerged for strongly correlated systems such as Mott insulators in which a partially filled band carries no current. By including interactions in the topologically non-trivial Haldane model, we show that a quarter-filled state emerges with a non-zero Chern number provided the interactions are sufficiently large. We first motivate this result on physical grounds and then by two methods: analytically by solving exactly a model in which interactions are local in momentum space and then numerically through the corresponding Hubbard model. All methods yield the same result: For sufficiently large interaction strengths, the quarter-filled Haldane model is a ferromagnetic topological Mott insulator with a Chern number of unity. Possible experimental realizations in cold-atom and solid state systems are discussed.

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arXiv2023

Interaction-driven Spontaneous Ferromagnetic Insulating States with Odd Chern Numbers

Motivated by recent experimental work on moiré systems in a strong magnetic field, we compute the compressibility as well as the spin correlations and Hofstadter spectrum of spinful electrons on a honeycomb lattice with Hubbard interactions using the determinantal quantum Monte Carlo method. While the interactions in general preserve quantum and anomalous Hall states, emergent features arise corresponding to an antiferromagnetic insulator at half-filling and other incompressible states following the Chern sequence $\pm (2N+1)$. These odd integer Chern states exhibit strong ferromagnetic correlations and arise spontaneously without any external mechanism for breaking the spin-rotation symmetry. Analogs of these magnetic states should be observable in general interacting quantum Hall systems. In addition, the interacting Hofstadter spectrum is qualitatively similar to the experimental data at intermediate values of the on-site interaction.

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arXiv2022

Hofstadter states and reentrant charge order in a semiconductor moiré lattice

The emergence of moiré materials with flat bands provides a platform to systematically investigate and precisely control correlated electronic phases. Here, we report local electronic compressibility measurements of a twisted WSe$_2$/MoSe$_2$ heterobilayer which reveal a rich phase diagram of interpenetrating Hofstadter states and electron solids. We show that this reflects the presence of both flat and dispersive moiré bands whose relative energies, and therefore occupations, are tuned by density and magnetic field. At low densities, competition between moiré bands leads to a transition from commensurate arrangements of singlets at doubly occupied sites to triplet configurations at high fields. Hofstadter states (i.e., Chern insulators) are generally favored at high densities as dispersive bands are populated, but are suppressed by an intervening region of reentrant charge-ordered states in which holes originating from multiple bands cooperatively crystallize. Our results reveal the key microscopic ingredients that favor distinct correlated ground states in semiconductor moiré systems, and they demonstrate an emergent lattice model system in which both interactions and band dispersion can be experimentally controlled.

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arXiv2021

Correlated Hofstadter Spectrum and Flavor Phase Diagram in Magic Angle Graphene

In magic angle twisted bilayer graphene (MATBG), the moiré superlattice potential gives rise to narrow electronic bands1 which support a multitude of many-body quantum phases. Further richness arises in the presence of a perpendicular magnetic field, where the interplay between moiré and magnetic length scales leads to fractal Hofstadter subbands. In this strongly correlated Hofstadter platform, multiple experiments have identified gapped topological and correlated states, but little is known about the phase transitions between them in the intervening compressible regimes. Here, using a scanning single-electron transistor microscope to measure local electronic compressibility, we simultaneously unveil novel sequences of broken-symmetry Chern insulators (CIs) and resolve sharp phase transitions between competing states with different topological quantum numbers and spin/valley flavor occupations. Our measurements provide a complete experimental mapping of the energy spectrum and thermodynamic phase diagram of interacting Hofstadter subbands in MATBG. In addition, we observe full lifting of the degeneracy of the zeroth Landau levels (zLLs) together with level crossings, indicating moiré valley splitting. We propose a unified flavor polarization mechanism to understand the intricate interplay of topology, interactions, and symmetry breaking as a function of density and applied magnetic field in this system.

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arXiv2019

Interacting multi-channel topological boundary modes in a quantum Hall valley system

Symmetry and topology play key roles in the identification of phases of matter and their properties. Both concepts are central to understanding quantum Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties. Domain walls between distinct broken symmetry QHFM phases are predicted to host gapless one-dimensional (1D) modes that emerge due to a topological change of the underlying electronic wavefunctions at such interfaces. Although a variety of QHFMs have been identified in different materials, probing interacting electronic modes at these domain walls has not yet been accomplished. Here we use a scanning tunneling microscope (STM) to directly visualize the spontaneous formation of boundary modes, within a sign-changing topological gap, at domain walls between different valley-polarized quantum Hall phases on the surface of bismuth. By changing the valley occupation and the corresponding number of modes at the domain wall, we can realize different regimes where the valley-polarized channels are either metallic or develop a spectroscopic gap. This behavior is a consequence of Coulomb interactions constrained by the symmetry-breaking valley flavor, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting Luttinger liquids.

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arXiv2018

Ferroelectric quantum Hall phase revealed by visualizing Landau level wavefunction interference

Novel broken symmetry states can spontaneously form due to Coulomb interactions in electronic systems with multiple internal degrees of freedom. Multi-valley materials offer an especially rich setting for the emergence of such states, which have potential electronic and optical applications. To date, identification of these broken symmetry phases has mostly relied on the examination of macroscopic transport or optical properties. Here we demonstrate a powerful direct approach by visualizing the wave functions of bismuth surface states with a scanning tunneling microscope. Strong spin-orbit coupling on the surface of bismuth leads to six degenerate teardrop-shaped hole pockets. Our spectroscopic measurements reveal that this degeneracy is fully lifted at high magnetic field as a result of exchange interactions, and we are able to determine the nature of valley ordering by imaging the broken symmetry Landau level (LL) wave functions. The remarkable spatial features of singly degenerate LL wave functions near isolated defects contain unique signatures of interference between spin-textured valleys, which identify the electronic ground state as a quantum Hall ferroelectric. Our observations confirm the recent prediction that interactions in strongly anisotropic valley systems favor the occupation of a single valley, giving rise to emergent ferroelectricity in the surface state of bismuth.

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