arXiv subjects

Jonah Herzog-Arbeitman

Publications and source records attributed to Jonah Herzog-Arbeitman.

At least 37 records · Page 2Linked to original sources

arXiv2024

Semi-Dirac Fermions in a Topological Metal

Topological semimetals with massless Dirac and Weyl fermions represent the forefront of quantum materials research. In two dimensions (2D), a peculiar class of fermions that are massless in one direction and massive in the perpendicular direction was predicted sixteen years ago. These highly exotic quasiparticles - the semi-Dirac fermions - ignited intense theoretical and experimental interest but remain undetected. Using magneto-optical spectroscopy, we demonstrate the defining feature of semi-Dirac fermions - $B^{2/3}$ scaling of Landau levels - in a prototypical nodal-line metal ZrSiS. In topological metals, including ZrSiS, nodal-lines extend the band degeneracies from isolated points to lines, loops or even chains in the momentum space. With $\textit{ab initio}$ calculations and theoretical modeling, we pinpoint the observed semi-Dirac spectrum to the crossing points of nodal-lines in ZrSiS. Crossing nodal-lines exhibit a continuum absorption spectrum but with singularities that scale as $B^{2/3}$ at the crossing. Our work sheds light on the hidden quasiparticles emerging from the intricate topology of crossing nodal-lines and highlights the potential to explore quantum geometry with linear optical responses.

cond-mat.mtrl-sci↗

arXiv2024

Topological Heavy Fermion Principle For Flat (Narrow) Bands With Concentrated Quantum Geometry

We propose a general principle for the low-energy theory of narrow bands with concentrated Berry curvature and Fubini-Study metric in the form of a map to Anderson-"+" models composed of heavy fermions hybridizing and interacting with semi-metallic modes. This map resolves the obstruction preventing topological bands from being realized in a local Hamiltonian acting on the low-energy degrees of freedom. The concentrated quantum geometry is reproduced through band inversion with a dispersive semi-metal, leaving a nearly flat, trivial band which becomes the heavy fermion. This representation is natural when the narrow band is not energetically isolated on the scale of the interaction and an enlarged Hilbert space is inescapable, but also provides analytical insight into the projected-interaction limit. First exemplified in twisted bilayer graphene (TBG), we extend it to (1) the twisted checkerboard, which we find has a chiral symmetric stable anomaly that forbids a lattice realization at all energies, and (2) the Lieb lattice with gapless flat bands, where we show the heavy fermions can be obtained by minimizing a Euclidean instanton action to saturate its BPS bound. The heavy fermion approach is widely applicable and physically transparent: heavy electrons carry the strong correlations and dispersive electrons carry the topology. This simple picture unifies the dichotomous phenomena observed in TBG and points to connections between moiré and stoichiometric materials.

cond-mat.str-el↗

arXiv2024

Strongly interacting Hofstadter states in magic-angle twisted bilayer graphene

Magic-angle twisted bilayer graphene (MATBG) hosts a multitude of strongly correlated states at partial fillings of its flat bands. In a magnetic field, these flat bands further evolve into a unique Hofstadter spectrum renormalized by strong Coulomb interactions. Here, we study the interacting Hofstadter states spontaneously formed within the topological magnetic subbands of an ultraclean MATBG device, notably including symmetry-broken Chern insulator (SBCI) states and fractional quantum Hall (FQH) states. The observed SBCI states form a cascade with their Chern numbers mimicking the main sequence correlated Chern insulators. The FQH states in MATBG form in Jain sequence; however, they disappear at high magnetic field, distinct from conventional FQH states which strengthen with increasing magnetic field. We reveal a unique magnetic field-driven phase transition from composite fermion phases to a dissipative Fermi liquid. Our theoretical analysis of the magnetic subbands hosting FQH states predicts non uniform quantum geometric properties far from the lowest Landau level. This points towards a more natural interpretation of these FQH states as in-field fractional Chern insulators of the magnetic subbands.

cond-mat.mes-hall↗

arXiv2024

Moiré Fractional Chern Insulators IV: Fluctuation-Driven Collapse of FCIs in Multi-Band Exact Diagonalization Calculations on Rhombohedral Graphene

The fractional Chern insulators (FCIs) observed in pentalayer rhombohedral graphene/hexagonal boron nitride superlattices have a unique origin contrary to theoretical expectations: their non-interacting band structure is gapless, unlike standard FCIs and the Landau level. Hartree-Fock (HF) calculations at filling $ν=1$ yield a gapped ground state with Chern number 1 through band mixing, identifying a possible parent state. However, many-body calculations restricted to the occupied HF band predispose the system towards FCIs and are essentially uncontrolled. In this work, we use unbiased multi-band exact diagonalization (ED) to allow fluctuations into the gapless bands for two normal-ordering schemes. In the "charge neutrality" scheme, the weak moiré potential leads to theoretical proposals based on Wigner crystal-like states. However, we find that FCIs seen in 1-band ED calculations are destroyed by band mixing, becoming gapless as fluctuations are included. In the "average" scheme, the Coulomb interaction with the periodic valence charge background sets up a stronger moiré potential. On small systems, FCIs at $ν=1/3$ are destroyed in multi-band calculations, while those at $ν=2/3$ are initially strengthened. However we do not converge to a stable FCI at $ν=2/3$ even on the largest accessible systems. These findings question prior results obtained within projection to a single HF band. They suggest that current models do not support FCIs with correlation length small enough to be converged in accessible, unbiased ED calculations, or do not support FCIs at all.

cond-mat.str-el↗

arXiv2024

Topological heavy fermions in magnetic field

The recently introduced topological heavy fermion model (THFM) provides a means for interpreting the low-energy electronic degrees of freedom of the magic angle twisted bilayer graphene as hybridization amidst highly dispersing topological conduction and weakly dispersing localized heavy fermions. In order to understand the Landau quantization of the ensuing electronic spectrum, a generalization of THFM to include the magnetic field B is desired, but currently missing. Here we provide a systematic derivation of the THFM in B and solve the resulting model to obtain the interacting Hofstadter spectra for single particle charged excitations. While naive minimal substitution within THFM fails to correctly account for the total number of magnetic subbands within the narrow band i.e. its total Chern number, our method -- based on projecting the light and heavy fermions onto the irreducible representations of the magnetic translation group -- reproduces the correct total Chern number. Analytical results presented here offer an intuitive understanding of the nature of the (strongly interacting) Hofstadter bands.

cond-mat.str-el↗

arXiv2024

Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants

The topological phases of non-interacting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained (in part) from momentum space. Recently, Real Space Invariants (RSIs) have provided a spatially local description of the global momentum space indices. The present work generalizes this real space classification to interacting 2D states. We construct many-body local RSIs as the quantum numbers of a set of symmetry operators on open boundaries, but which are independent of the choice of boundary. Using the $U(1)$ particle number, they yield many-body fragile topological indices, which we use to identify which single-particle fragile states are many-body topological or trivial at weak coupling. To this end, we construct an exactly solvable Hamiltonian with single-particle fragile topology that is adiabatically connected to a trivial state through strong coupling. We then define global many-body RSIs on periodic boundary conditions. They reduce to Chern numbers in the band theory limit, but also identify strongly correlated stable topological phases with no single-particle counterpart. Finally, we show that the many-body local RSIs appear as quantized coefficients of Wen-Zee terms in the topological quantum field theory describing the phase.

cond-mat.str-el↗

arXiv2023

Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices

We investigate in detail the $ν=+1$ displacement-field-tuned interacting phase diagram of $L=3,4,5,6,7$ layer rhombohedral graphene aligned to hBN (R$L$G/hBN). Our calculations account for the 3D nature of the Coulomb interaction, the inequivalent stacking orientations $ξ=0,1$, the effects of the filled valence bands, and the choice of `interaction scheme' for specifying the many-body Hamiltonian. We show that the latter has a dramatic impact on the Hartree-Fock phase boundaries and the properties of the phases, including for pentalayers (R5G/hBN) with large displacement field $D$ where recent experiments observed a Chern insulator at $ν=+1$ and fractional Chern insulators for $ν<1$. In this large $D$ regime, the low-energy conduction bands are polarized away from the aligned hBN layer, and are hence well-described by the folded bands of moiréless rhombohedral graphene at the non-interacting level. Despite this, the filled valence bands develop moiré-periodic charge density variations which can generate an effective moiré potential, thereby explicitly breaking the approximate continuous translation symmetry in the conduction bands, and leading to contrasting electronic topology in the ground state for the two stacking arrangements. Within time-dependent Hartree-Fock theory, we further characterize the strength of the moiré pinning potential in the Chern insulator phase by computing the low-energy $\mathbf{q}=0$ collective mode spectrum, where we identify competing gapped pseudophonon and valley magnon excitations. Our results emphasize the importance of careful examination of both the single-particle and interaction model for a proper understanding of the correlated phases in R$L$G/hBN.

cond-mat.str-el↗

arXiv2023

Moiré Fractional Chern Insulators II: First-principles Calculations and Continuum Models of Rhombohedral Graphene Superlattices

The experimental discovery of fractional Chern insulators (FCIs) in rhombohedral pentalayer graphene twisted on hexagonal boron nitride (hBN) has preceded theoretical prediction. Supported by large-scale first principles relaxation calculations at the experimental twist angle of $0.77^\circ$, we obtain an accurate continuum model of $n=3,4,5,6,7$ layer rhombohedral graphene-hBN moiré systems. Focusing on the pentalayer case, we analytically explain the robust $|C|=0,5$ Chern numbers seen in the low-energy single-particle bands and their flattening with displacement field, making use of a minimal two-flavor continuum Hamiltonian derived from the full model. We then predict nonzero valley Chern numbers at the $ν= -4,0$ insulators observed in experiment. Our analysis makes clear the importance of displacement field and the moiré potential in producing localized "heavy fermion" charge density in the top valence band, in addition to the nearly free conduction band. Lastly, we study doubly aligned devices as additional platforms for moiré FCIs with higher Chern number bands.

cond-mat.mes-hall↗

arXiv2023

Moiré Fractional Chern Insulators I: First-principles calculations and Continuum Models of Twisted Bilayer MoTe$_2$

Recent experiments observed fractional Chern insulators (FCI) in twisted bilayer MoTe$_2$ at zero magnetic field, yet even the single-particle model of this material is controversial, leading to unreliable predictions of the experimental phase diagram as discussed in [Yu et al., 2023]. In this light, we revisit the single-particle model of twisted bilayer MoTe$_2$. Utilizing large-scale density functional theory, we calculate the band structure of twisted AA-stacked bilayer MoTe$_2$ at various twist angles relevant to experiment. We find that a band inversion occurs near $4.41^\circ$ between the second and third bands. Our ab initio band structure is in qualitative agreement with [Wang et al., 2023], but shows important differences in the remote bands and in the $Γ$ valley. We incorporate two higher harmonic terms into the continuum model to capture the highest 3 valence bands per valley. We confirm that the two highest valence bands per valley have opposite Chern numbers with $|C|=1$ for small angles, and also use our model to predict a variety of Chern states in the remote bands accessible by displacement field. Finally, we perform DFT calculations and build models for the AB stacking configuration. Our work serves as a foundation for accurate determination of the correlated phases in twisted bilayer MoTe$_2$.

cond-mat.mes-hall↗

arXiv2023

Fractional Chern Insulators vs. Non-Magnetic States in Twisted Bilayer MoTe$_2$

Fractionally filled Chern bands with strong interactions may give rise to fractional Chern insulator (FCI) states, the zero-field analogue of the fractional quantum Hall effect. Recent experiments have demonstrated the existence of FCIs in twisted bilayer MoTe$_2$ without external magnetic fields -- most robust at $ν=-2/3$ -- as well as Chern insulators (CIs) at $ν=-1$. Although the appearance of both of these states is theoretically natural in an interacting topological system, experiments repeatedly observe nonmagnetic states (lacking FCIs) at $ν=-1/3$ and $-4/3$, a puzzling result which has not been fully theoretically explained. In this work, we perform Hartree-Fock and exact diagonalization calculations to test whether the standard MoTe$_2$ moiré model with the (greatly varying) parameter values available in the literature can reproduce the non-magnetic states at $ν=-1/3$ and $-4/3$ in unison with the FCI at $ν=-2/3$ and CI state at $ν= -1$. We focus on the experimentally relevant twist angles and, crucially, include remote bands. We find that the parameters proposed in [Wang et al. (2023)] can nearly capture the experimental phenomena at $ν=-1/3,-2/3,-1,-4/3$ simultaneously, though the predicted ground states at $ν=-1/3$ are still mostly fully-spin-polarized and a larger dielectric constant $ε>10$ than is typical of hexagonal boron nitride (h-BN) substrate $ε\sim 6$ is required. Our results show the importance of remote bands in identifying the competing magnetic orders and lay the groundwork for further study of the realistic phase diagram.

cond-mat.mes-hall↗

arXiv2023

Pb$_9$Cu(PO4)$_6$(OH)$_2$: Phonon bands, Localized Flat Band Magnetism, Models, and Chemical Analysis

In a series of recent reports, doped lead apatite (LK-99) has been proposed as a candidate ambient temperature and pressure superconductor. However, from both an experimental and theoretical perspective, these claims are largely unsubstantiated. To this end, our synthesis and subsequent analysis of an LK-99 sample reveals a multiphase material that does not exhibit high-temperature superconductivity. We study the structure of this phase with single-crystal X-ray diffraction (SXRD) and find a structure consistent with doped $\text{Pb}_{10}(\text{PO}_4)_6(\text{OH})_2$. However, the material is transparent which rules out a superconducting nature. From ab initio defect formation energy calculations, we find that the material likely hosts $\text{OH}^-$ anions, rather than divalent $\text{O}^{2-}$ anions, within the hexagonal channels and that Cu substitution is highly thermodynamically disfavored. Phonon spectra on the equilibrium structures reveal numerous unstable phonon modes. Together, these calculations suggest it is doubtful that Cu enters the structure in meaningful concentrations, despite initial attempts to model LK-99 in this way. However for the sake of completeness, we perform ab initio calculations of the topology, quantum geometry, and Wannier function localization in the Cu-dominated flat bands of four separate doped structures. In all cases, we find they are atomically localized by irreps, Wilson loops, and the Fubini-Study metric. It is unlikely that such bands can support strong superfluidity, and instead are susceptible to ferromagnetism (or out-of-plane antiferromagnetism) at low temperatures, which we find in ab initio studies. In sum, $\text{Pb}_{9}\text{Cu}(\text{PO}_4)_6(\text{OH})_2$ could more likely be a magnet, rather than an ambient temperature and pressure superconductor.

cond-mat.supr-con↗

arXiv2023

Quantum textures of the many-body wavefunctions in magic-angle graphene

Interactions among electrons create novel many-body quantum phases of matter with wavefunctions that often reflect electronic correlation effects, broken symmetries, and novel collective excitations. A wide range of quantum phases has been discovered in MATBG, including correlated insulating, unconventional superconducting, and magnetic topological phases. The lack of microscopic information, including precise knowledge of possible broken symmetries, has thus far hampered our understanding of MATBG's correlated phases. Here we use high-resolution scanning tunneling microscopy to directly probe the wavefunctions of the correlated phases in MATBG. The squares of the wavefunctions of gapped phases, including those of the correlated insulators, pseudogap, and superconducting phases, show distinct patterns of broken symmetry with a $\sqrt{3}$ x $\sqrt{3}$ super-periodicity on the graphene atomic lattice that has a complex spatial dependence on the moiré superlattice scale. We introduce a symmetry-based analysis to describe our measurements of the wavefunctions of MATBG's correlated phases with a set of complex-valued local order parameters. For the correlated insulators in MATBG, at fillings of $ν$ = $\pm$ 2 electrons per moiré unit cell relative to charge neutrality, we compare the observed quantum textures to those expected for proposed theoretical ground states. In typical MATBG devices, the textures of correlated insulators' wavefunctions closely match those of the theoretically proposed IKS order, while in ultra-low-strain samples our data has local symmetries like those of a T-IVC phase. We also study the wavefunction of MATBG's superconducting state, revealing strong signatures of intervalley coherence that can only be distinguished from those of the insulator with our phase-sensitive measurements.

cond-mat.mes-hall↗

arXiv2022

Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries

Adding magnetic flux to a band structure breaks Bloch's theorem by realizing a projective representation of the translation group. The resulting Hofstadter spectrum encodes the non-perturbative response of the bands to flux. Depending on their topology, adding flux can enforce a bulk gap closing (a Hofstadter semimetal) or boundary state pumping (a Hofstadter topological insulator). In this work, we present a real-space classification of these Hofstadter phases. We give topological indices in terms of symmetry-protected Real Space Invariants (RSIs) which encode bulk and boundary responses of fragile topological states to flux. In fact, we find that the flux periodicity in tight-binding models causes the symmetries which are broken by the magnetic field to reenter at strong flux where they form projective point group representations. We completely classify the reentrant projective point groups and find that the Schur multipliers which define them are Arahanov-Bohm phases calculated along the bonds of the crystal. We find that a nontrivial Schur multiplier is enough to predict and protect the Hofstadter response with only zero-flux topology.

cond-mat.mes-hall↗

arXiv2022

Many-Body Superconductivity in Topological Flat Bands

In a flat band superconductor, bosonic excitations can disperse while unpaired electrons are immobile. To study this strongly interacting system, we construct a family of multi-band Hubbard models with exact eta-pairing ground states in all space groups. We analytically compute their many-body excitations and find that the Cooper pair bound states and density excitations obey an effective single-particle Hamiltonian written in terms of the non-interacting wavefunctions. These bound states possess a unique zero-energy excitation whose quadratic dispersion is determined by the minimal quantum metric. The rest of the bound state spectrum is classified by topological quantum chemistry, which we use to identify Cooper pairs with Weyl nodes, higher angular momentum pairing, and fragile topology. We also add electron kinetic energy as a perturbation to show that the strongest pairing occurs at half filling and not at the highest density of states. This is similar in spirit to the superconductivity observed in twisted bilayer graphene.

cond-mat.str-el↗

arXiv2022

Magnetic Bloch Theorem and Reentrant Flat Bands in Twisted Bilayer Graphene at $2π$ Flux

Bloch's theorem is the centerpiece of topological band theory, which itself has defined an era of quantum materials research. However, Bloch's theorem is broken by a perpendicular magnetic field, making it difficult to study topological systems in strong flux. For the first time, moiré materials have made this problem experimentally relevant, and its solution is the focus of this work. We construct gauge-invariant irreps of the magnetic translation group at $2π$ flux on infinite boundary conditions, allowing us to give analytical expressions in terms of the Siegel theta function for the magnetic Bloch Hamiltonian, non-Abelian Wilson loop, and many-body form factors. We illustrate our formalism using a simple square lattice model and the Bistritzer-MacDonald Hamiltonian of twisted bilayer graphene, obtaining reentrant ground states at $2π$ flux under the Coulomb interaction.

cond-mat.mes-hall↗

arXiv2022

Revisiting flat band superconductivity: dependence on minimal quantum metric and band touchings

A critical result in superconductivity is that flat bands, though dispersionless, can still host nonzero superfluid weight due to quantum geometry. We show that the derivation of the mean field superfluid weight in previous literature is incomplete, which can lead to severe quantitative and even qualitative errors. We derive the complete equations and demonstrate that the minimal quantum metric -- the metric with minimum trace -- is related to the superfluid weight in isolated flat bands. We complement this result with an exact calculation of the Cooper pair mass in attractive Hubbard models with the uniform pairing condition. When the orbitals are located at high symmetry positions, the Cooper pair mass is exactly given by the quantum metric, which is guaranteed to be minimal. Moreover, we study the effect of closing the band gap between the flat and dispersive bands, and develop a mean-field theory of pairing for different band-touching points via the $S$-matrix construction. In mean field, we show that a non-isolated flat band can actually be beneficial for superconductivity. This is a promising result in the search for high temperature superconductivity as the material does not need to have flat bands that are isolated from other bands by the thermal energy. Our work resolves a fundamental caveat in understanding the relation of multiband superconductivity to quantum geometry, and the results on band touchings widen the class of systems advantageous for the search of high temperature flat band superconductivity.

cond-mat.supr-con↗

arXiv2022

Superfluid weight bounds from symmetry and quantum geometry in flat bands

Flat-band superconductivity has theoretically demonstrated the importance of band topology to correlated phases. In two dimensions, the superfluid weight, which determines the critical temperature through the Berezinksii-Kosterlitz-Thouless criteria, is bounded by the Fubini-Study metric at zero temperature. We show this bound is nonzero within flat bands whose Wannier centers are obstructed from the atoms - even when they have identically zero Berry curvature. Next, we derive general lower bounds for the superfluid weight in terms of momentum space irreps in all 2D space groups, extending the reach of topological quantum chemistry to superconducting states. We find that the bounds can be naturally expressed using the formalism of real space invariants (RSIs) that highlight the separation between electronic and atomic degrees of freedom. Finally, using exact Monte Carlo simulations on a model with perfectly flat bands and strictly local obstructed Wannier functions, we find that an attractive Hubbard interaction results in superconductivity as predicted by the RSI bound beyond mean-field. Hence, a nonzero superfluid weight constitutes a nontrivial bulk property that distinguishes obstructed bands from trivial bands in the presence of interactions.

cond-mat.mes-hall↗

arXiv2021

Observation of re-entrant correlated insulators and interaction driven Fermi surface reconstructions at one magnetic flux quantum per moiré unit cell in magic-angle twisted bilayer graphene

The discovery of flat bands with non-trivial band topology in magic angle twisted bi-layer graphene (MATBG) has provided a unique platform to study strongly correlated phe-nomena including superconductivity, correlated insulators, Chern insulators and magnetism. A fundamental feature of the MATBG, so far unexplored, is its high magnetic field Hof-stadter spectrum. Here we report on a detailed magneto-transport study of a MATBG de-vice in external magnetic fields of up to B = 31 T, corresponding to one magnetic flux quan-tum per moiré unit cell Φ0. At Φ0, we observe a re-entrant correlated insulator at a flat band filling factor of ν = +2, and interaction-driven Fermi surface reconstructions at other fillings, which are identified by new sets of Landau levels originating from these. These ex-perimental observations are supplemented by theoretical work that predicts a new set of 8 well-isolated flat bands at Φ0 , of comparable band width but with different topology than in zero field. Overall, our magneto-transport data reveals a qualitatively new Hofstadter spec-trum in MATBG, which arises due to the strong electronic correlations in the re-entrant flat bands.

cond-mat.str-el↗