arXiv subjects

Oskar Vafek

Publications and source records attributed to Oskar Vafek.

At least 19 recordsLinked to original sources

arXiv2026

Distinguishing Mott and strain-induced anisotropic semimetals in magic-angle twisted bilayer graphene using Landau level spectroscopy

Recent quantum twisting microscopy experiments [1] have provided unprecedented momentum- and energy-resolved imaging of magic-angle twisted bilayer graphene, revealing a stark dichotomy between the heavy and light electronic characters of its narrow bands. In this work, we provide a sharp distinguishing criterion between the two most likely candidate states that exhibit spectroscopic features consistent with the experimental results. Focusing on charge neutrality, these states are 1) the 'Mott semimetal', governed by strong dynamical correlations, and 2) the 'strain-induced anisotropic semimetal', characterized by weak Hartree-Fock effects. We demonstrate that an out-of- plane magnetic field serves as a sharp discriminating probe based on the expected Landau level gap size hierarchy. We find that the strain-induced anisotropic semimetal has a robust gap hierarchy where the Chern C gaps, Δ_C , decrease in order Δ_{\pm 4} > Δ_{\pm 8} > Δ_{\pm 12}. In contrast, for the Mott semimetal, Δ_{\pm 4} remains the largest gap, while the relative magnitude of the C = \pm 8, \pm 12 gaps depends sensitively on the applied magnetic field. We test the robustness of these results against strain orientation and lattice relaxation finding consistency between the gap hierarchy of the strained semimetal and previous incompressibility measurements at finite magnetic field [2].

cond-mat.str-el↗

arXiv2026

Extracting the full conductivity tensor in a rectangular sample

Electrical transport measurements reveal that many 2D materials exhibit anisotropic conductivity. However, current methodologies for rectangular geometries can only extract a partial conductivity tensor or are difficult to execute experimentally. Here, we propose a simple experimental procedure to extract the full conductivity tensor (or the resistivity tensor by inversion) including the principal axes angle. Our procedure is developed by using a conformal mapping approach to obtain an analytical expression for the potential with a point source and drain on the perimeter. Our solution agrees very well with numerical simulations using COMSOL and the known limiting case where the principal axes angle vanishes. Finite source/drains can be modeled using superposition.

cond-mat.mtrl-sci↗

arXiv2026

Ferromagnetism vs. Antiferromagnetism in Narrow-Band Systems: Competition Between Quantum Geometry and Band Dispersion

Magnetism in narrow-band systems arises from the interplay between electronic correlations, quantum geometry, and band dispersion. In particular, both ferro and anti-ferro magnets are known to occur as ground states of (different) models featuring narrow bands. This poses the question of which is favored and under what conditions. In this work, we present a unified theoretical framework to investigate spin physics within narrow bands. By deriving an effective spin model, we show that the non-atomic wavefunction of the narrow bands generally favors ferromagnetic ordering, while band dispersion promotes antiferromagnetic correlations. We find that the competition between these effects gives rise to a tunable magnetic phase and rich spin phenomena. Our approach offers a systematic way to study the magnetic properties of narrow-band systems, integrating the roles of wave function, band structure, and correlation effects.

cond-mat.str-el↗

arXiv2026

Visualizing Symmetry Broken Chern Insulators and their Quantum Melting

In the presence of a magnetic field, electronic states of moiré quantum materials develop a Hofstadter spectrum that provides a unique setting for studying the interplay between band topology and strong electron-electron interaction. Using scanning tunneling microscopy, we study Hofstadter's states in bilayer graphene aligned with hexagonal BN and directly visualize the formation of interaction-driven symmetry breaking Chern insulators. Our measurements reveal the formation of phases that double, triple or quadruple the moiré unit cell at fractional filling of the Hofstadter bands, as well as states with complex intra-unit-cell wave functions. We visualize two distinct quantum phenomena in different Chern states, including quantum melting driven by the appearance and proliferation of topological defects, and a quantum transition co-occurring with phase competition and separation.

cond-mat.mes-hall↗

arXiv2026

Orbital magnetization and magnetic susceptibility of interacting electrons

We present a rigorous derivation of the orbital magnetization for interacting electrons within the self-consistent Hartree-Fock approximation. Our method also allows us to derive formulas for the orbital magnetic susceptibility. The results are expressed entirely in terms of the self-consistent wavefunctions and the Hartree-Fock energy spectrum at zero magnetic field. We find that the formula for the orbital magnetization is the same as in the non-interacting case, provided that the Hamiltonian and Bloch wave functions are replaced by their Hartree-Fock counterparts. By contrast, the orbital magnetic susceptibility contains an additional interaction-induced contribution that cannot be obtained by such a replacement. We test the formulas on an interacting Rashba model, finding an agreement with calculations performed at a small but non-zero external magnetic field.

cond-mat.str-el↗

arXiv2025

Analytical solution for the relaxed atomic configuration of twisted bilayer graphene including heterostrain

Continuum atomic relaxation models for twisted bilayer graphene involve minimization of the sum of intralayer elastic energy and interlayer adhesion energy. The elastic energy favors a rigid twist i.e. no distortion in the twisted honeycomb lattices, while the adhesion energy favors Bernal stacking and breaking the relaxation into triangular AB and BA stacked domains. We compare the results of two relaxation models with the published Bragg interferometry data, finding good agreement with one of the models. We then provide a method for finding a highly accurate approximation to the solution of this model which holds above the twist angle of $\approx0.7^\circ$ and thus covers the first magic angle. We find closed form expressions in the absence, as well as in the presence, of external heterostrain. These expressions are not written as a Taylor series in the ratio of adhesion and elastic energy, because, as we show, the radius of convergence of such a series is too small to access the first magic angle.

cond-mat.str-el↗

arXiv2025

Extended Fractional Chern Insulators Near Half Flux in Twisted Bilayer Graphene Above the Magic Angle

Fractional Chern insulators (FCIs) -- the lattice analog of fractional quantum Hall states -- form as fractionalized quasiparticles emerge in a partially-filled Chern band. This fractionalization is driven by the interplay of electronic interaction and quantum geometry of the underlying wavefunctions. Bilayer graphene with an interlayer twist near the magic angle of 1.1\textdegree\ hosts diverse correlated electronic states at zero magnetic field. When the twist angle exceeds 1.3\textdegree, the electronic bandwidth is sufficient to suppress the zero-field correlated states. Yet applying a magnetic field can restore the importance of electron-electron interactions. Here, we report strongly-correlated phases when a 1.37\textdegree\ twisted bilayer graphene sample is tuned to near half a magnetic flux quantum per moiré cell, deep into the Hofstadter regime. Most notably, well-quantized odd-denominator FCI states appear in multiple Hofstadter subbands over unusually large ranges of density. We also observe a bending and resetting of the Landau minifan reminiscent of behavior commonly seen in magic-angle samples near integer filling at low magnetic field.

cond-mat.mes-hall↗

arXiv2025

Observation of giant nonlinear Hall conductivity in Bernal bilayer graphene

In a system of two-dimensional electrons, a combination of broken symmetry, interactions, and nontrivial topology can conspire to give rise to a nonlinear transport regime, where electric current density scales as the square of electric field. This regime has become a venue for exciting discoveries such as the nonlinear Hall effect and diode-like nonreciprocal transport. However, interpretation of experimental data is challenging in the nonlinear regime as DC transport is described by a rank-3 conductivity tensor with 6 free parameters. Here, we resolve this challenge by analytically solving for the nonlinear potential distribution across the disk sample for an arbitrary linear and nonlinear conductivity tensors. This allows us to unambiguously extract all components of the nonlinear tensor from experimental measurement. Using this novel tool, we identify giant nonlinear Hall effect in Bernal bilayer graphene. Our methodology provides the first systematic framework for interpreting nonlinear transport and uncovers a new route towards understanding quasi-2D materials.

cond-mat.mes-hall↗

arXiv2025

Heavy Fermions as an Efficient Representation of Atomistic Strain and Relaxation in Twisted Bilayer Graphene

Although the strongly interacting flat bands in twisted bilayer graphene (TBG) have been approached using the minimal Bistritzer-MacDonald (BM) Hamiltonian, there is mounting evidence that strain and lattice relaxation are essential in correctly determining the order of the correlated insulator groundstates. These effects can be incorporated in an enhanced continuum model by introducing additional terms computed from the relaxation profile. To develop an analytical and physical understanding of these effects, we include strain and relaxation in the topological heavy fermion (HF) model of TBG. We find that strain and relaxation are very well captured in first order perturbation theory by projection onto the fully symmetric HF Hilbert space, and remarkably do not alter the interacting terms in the periodic Anderson model. Their effects are fully incorporated in the single-particle HF Hamiltonian, and can be reproduced in a minimal model with only 4 symmetry-breaking terms. Our results demonstrate that the heavy fermion framework of TBG is an efficient and robust representation of the perturbations encountered in experiment.

cond-mat.mes-hall↗

arXiv2025

Kekulé Spiral Order from Strained Topological Heavy Fermions

The topological heavy fermion (THF) model of twisted bilayer graphene is a framework for treating its strongly interacting topological flat bands. In this work, we employ the THF model with heterostrain and particle-hole symmetry breaking corrections to study its symmetry-broken ground states. We find that the heterostrain correction motivates a specific parent-state wavefunction which dictates the presence or absence of an incommensurate Kekulé spiral (IKS) at each integer filling by invoking Dirac node braiding and annihilation as a mechanism to achieve low energy gapped states. We then show that one-shot Hartree-Fock faithfully replicates the numerical results of fully self-consistent states and motivates an analytical approximation for the IKS wavevector. We can also account for the particle-hole asymmetry in the correlated insulator gaps. In particular, the THF model predicts stronger correlated states on the electron side rather than hole side in agreement with magic angle experiments, despite the electron side being more dispersive in the single-particle band structure. This work demonstrates that we can analytically explain even the more subtle symmetry breaking order properties observed in experiments where heterostrain, relaxation, and interactions together determine the ground state.

cond-mat.str-el↗

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

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 phase diagram of twisted bilayer MoTe$_2$ in magnetic field

We study electron-electron interaction induced states of twisted bilayer MoTe$_2$ in an out-of-plane magnetic field $B\hat{\bf z}$ near one hole per moiré unit cell filling. The 3D phase diagram showing the evolution of competing phases with $B$, interaction strength and an out-of-plane electric field is presented at electron fillings that follow the Diophantine equation along Chern number $-\text{sign}\left(B\right)$ line, that is pointing away from the charge neutral filling, where we find prominent Chern insulators consistent with the experiments. We also explain the experimental absence of prominent Chern insulators along the Chern number $+\text{sign}\left(B\right)$ line.

cond-mat.str-el↗

arXiv2024

Theory of correlated Chern insulators in twisted bilayer graphene

Magic-angle twisted bilayer graphene is the best studied physical platform featuring moire potential induced narrow bands with non-trivial topology and strong electronic correlations. Despite their significance, the Chern insulating states observed at a finite magnetic field -- and extrapolating to a band filling, $s$, at zero field -- remain poorly understood. Unraveling their nature is among the most important open problems in the province of moiré materials. Here we present the first comprehensive study of interacting electrons in finite magnetic field while varying the electron density, twist angle and heterostrain. Within a panoply of correlated Chern phases emerging at a range of twist angles, we uncover a unified description for the ubiquitous sequence of states with the Chern number $t$ for $(s,t)=\pm (0,4), \pm(1,3),\pm(2,2)$ and $\pm(3,1)$. We also find correlated Chern insulators at unconventional sequences with $s+t\neq \pm 4$, as well as with fractional $s$, and elucidate their nature.

cond-mat.mes-hall↗

arXiv2023

Revisiting Bloch electrons in magnetic field: Hofstadter physics via hybrid Wannier states

We revisit the Hofstadter butterfly for a subset of topologically trivial Bloch bands arising from a continuum free electron Hamiltonian in a periodic lattice potential. We employ the recently developed procedure -- which was previously used to analyze the case of topologically non-trivial bands [\href{https://journals.aps.org/prb/abstract/10.1103/PhysRevB.106.L121111}{Phys. Rev. B \textbf{106}, L121111 (2022)}] -- to construct the finite field Hilbert space from the zero-field hybrid Wannier basis states. Such states are Bloch extended along one direction and exponentially localized along the other. The method is illustrated for square and triangular lattice potentials and is shown to reproduce all the main features of the Hofstadter spectrum obtained from a numerically exact Landau level expansion method. In the regime when magnetic length is much longer than the spatial extent of the hybrid Wannier state in the localized direction we recover the well known Harper equation. Because the method applies to both topologically trivial and non-trivial bands, it provides an alternative and efficient approach to moiré materials in magnetic field.

cond-mat.mes-hall↗

arXiv2023

Anisotropic resistivity tensor from disk geometry magneto-conductance

Magneto-transport measurements on two dimensional van der Waals heterostructures have recently shown signatures of uniaxial anisotropy. Such measurements are almost exclusively performed in a Hall bar geometry which makes it difficult to extract the full resistivity tensor. The goal of this paper is to theoretically analyze anisotropic magneto-conductance in a homogeneous disk geometry and to provide a closed form expression for the electrical potential anywhere on the disk if the current source and drain are located somewhere on the circumference. This expression can then be used to experimentally extract the full conductivity tensor, and by a simple inversion, the full resistivity tensor.

cond-mat.mes-hall↗

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↗