We model quantum Hall skyrmions in graphene monolayer at quarter filling by a theory of CP3 fields and study the energy minimizing skyrmions in presence of valley pseudospin anisotropy and Zeeman coupling. We present a diagram of all types of skyrmions in a wide range of the anisotropy parameters. For each type of skyrmion, we visualize it on three Bloch spheres, and present the profiles of its texture on the graphene honeycomb lattice, thus providing references for the STM/STS imaging of spin-pseudospin textures in graphene monolayer in quantum Hall regime. Besides the spin and pseudospin skyrmions for the corresponding degrees of freedom of an electron in the N=0 Landau level, we discuss two unusual types -- the "entanglement skyrmion" whose texture lies in the space of the entanglement of spin and pseudospin, as well as the "deflated pseudospin skyrmion" with partial entanglement. For all skyrmion types, we study the dependence of the energy and the size of a skyrmion on the anisotropy parameters and perpendicular magnetic field. We also propose three ways to modify the anisotropy energy, namely the sample tilting, the substrate anisotropy and the valley pseudospin analogue of Zeeman coupling.
We report measurements of the interaction-induced quantum Hall effect in a spin-polarized AlAs two-dimensional electron system where the electrons occupy two in-plane conduction band valleys. Via the application of in-plane strain, we tune the energies of these valleys and measure the energy gap of the quantum Hall state at filling factor $ν$ = 1. The gap has a finite value even at zero strain and, with strain, rises much faster than expected from a single-particle picture, suggesting that the lowest energy charged excitations at $ν=1$ are "valley Skyrmions".
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the sma…
Magnetic skyrmions are promising spin textures for building next-generation magnetic memories and spintronic devices. Nevertheless, one of the major challenges in realizing skyrmion-based devices is the stabilization of ordered arrays of these spin textures in different geometries. Here we numerically study the skyrmion-skyrmion interaction potential that arises due to the dynamics of itinerant electrons coupled to the magnetic texture in a ferromagnetic background with racetrack geometry. We consider different topological textures (ferromagnetic (FM) and antiferromagnetic (AFM)), namely: skyr…
Using gradient expansion method the particle density, the energy and the action were calculated at the formation of a vortex-skyrmion at high magnetic field. No approximation of single Landau level was used contrary to other papers on the subject. Taking into account the nearest Landau levels essentially changes the expression for the vortex energy and gives some simple physical interpretation of the main results. The local electron density coincides with the local density of states. It is shown that the formation of a vortex skyrmion gives the gain in the thermodynamic energy in the limit of …
We have investigated the effect of weak disorder on the ground state of a two dimensional electron gas in the quantum Hall regime at filling factors slightly deviating from unity. The skyrmions and antiskyrmions are found to be present even at filling factor $ν=1$. They may be strongly squeezed by the disorder. We have studied temperature effect on skyrmion density and size.
Monolayer graphene under a strong perpendicular field exhibit quantum Hall ferromagnetism with spontaneously broken spin and valley symmetry. The approximate SU(4) spin/valley symmetry is broken by small lattice scale effects in the central Landau level corresponding to filling factors $ν=0,\pm 1$. Notably the ground state at $ν=0$ is believed to be a canted antiferromagnetic (AF) or a ferromagnetic (F) state depending on the component of the magnetic field parallel to the layer and the strength of small anisotropies. We study the skyrmions for the filling factors $ν=\pm 1,0$ by using exact di…
The topological Hall effect (THE), given by a composite of electric and topologically non-trivial spin texture is commonly observed in magnetic skyrmion crystals. Here we present a study of the THE of electrons coupled to antiferromagnetic Skyrmion lattices (AF-SkX). We show that, in the strong Hund coupling limit, topologically non-trivial phases emerge at specific fillings. Interestingly, at low filling an external field controlling the magnetic texture, drives the system from a conventional insulator phase to a phase exhibiting THE. Such behavior suggests the occurrence of a topological tra…
We study quantum Hall ferromagnets with a finite density topologically charged spin textures in the presence of internal degrees of freedom such as spin, valley, or layer indices, so that the system is parametrised by a $d$-component complex spinor field. In the absence of anisotropies, we find formation of a hexagonal Skyrmion lattice which completely breaks the underlying SU(d) symmetry. The ground state charge density modulation, which inevitably exists in these lattices, vanishes exponentially in $d$. We compute analytically the complete low-lying excitation spectrum, which separates into …
Motivated by recent low-temperature magnetoresistance measurements in twisted bilayer graphene aligned with hexagonal Boron Nitride substrate, we perform a systematic study of possible symmetry breaking orders in this device at a filling of two electrons per Moiré unit cell. We find that the surprising non-monotonic dependence of the resistance on an out-of-plane magnetic field is difficult to reconcile with particle-hole charge carriers from the low-energy bands in symmetry broken phases. We invoke the non-zero Chern numbers of the twisted bilayer graphene flat bands to argue that skyrmion te…
A skyrmion crystal has internal degrees of freedom in terms of vorticity and helicity, which gives rise to fascinating types of skyrmion phases (Néel, Bloch, and anti-skyrmion). We show how the degeneracy lifting in tetragonal skyrmion crystals occurs in centrosymmetric itinerant magnets by focusing on microscopic interactions through the Fermi surface instability. We demonstrate that four types of skyrmion crystals can be realized according to the signs of the anisotropic Ruderman-Kittel-Kasuya-Yosida interaction, which are sensitive to band structures, electron fillings, atomic orbitals, and…
Experiments on the fractional quantized Hall effect in the zeroth Landau level of graphene have revealed some striking differences between filling factors in the ranges 0<|ν|<1 and 1<|ν|<2. We argue that these differences can be largely understood as a consequence of the effects of terms in the Hamiltonian which break SU(2) valley symmetry, which we find to be important for |ν|<1 but negligible for |ν| >1. The effective absence of valley anisotropy for |ν|>1 means that states with odd numerator, e.g. |ν|=5/3 or 7/5 can accommodate charged excitations in the form of large valley skyrmions, whic…
The coexistence of superconducting and charge-density-wave order in the half-filled attractive Hubbard model is interpreted as a consequence of the pseudospin SU(2) symmetry spontaneously broken to a `hidden' subgroup U(1). By topological arguments we show that there must exist new skyrmion textures associated with this symmetry breakdown. This fact is illustrated via a non-linear $σ$-model. Unlike the spin textures previously known in an antiferromagnetic background, doping the model away from half-filling leads the new skyrmions to unwrap.
The measured melting curve $T_{m}(ν)$ between the crystal and liquid phases is analyzed using thermodynamics to extract the change of magnetization $ΔM$ as a function of the Landau level filling factor \ $ν,$ near $ν=1$. \ An explanation of $ΔM$($ν)$ is proposed \ in terms of Skyrmions. \ Near $ν=3$, a Wigner crystal is the most probable solid phase, experiments excluding Skyrmions.
We use the circularly polarized resonant Rayleigh scattering (RRS) to study the quantum Hall ferromagnet at $ν$ = 1. At this filling factor we observe a right handed copolarized RRS which probes the Skyrmion spin texture of the electrons in the photoexcited grounds state. The resonant scattering is not present in the left handed copolarization, and this can be related to the correlation between Skymionic effects, screening and spin wave excitations. These results evidence that RRS is a valid method for the study of the spin texture of the quantum Hall states.
Magnetic skyrmions are swirling spin textures with topologically protected noncoplanarity. Recently, skyrmions with the topological number of unity have been extensively studied in both experiment and theory. We here show that a skyrmion crystal with an unusually high topological number of two is stabilized in itinerant magnets at zero magnetic field. The results are obtained for a minimal Kondo lattice model on a triangular lattice by an unrestricted large-scale numerical simulation and variational calculations. We find that the topological number can be switched by a magnetic field as $2\lef…
Recent experiments on twisted bilayer graphene show an anomalous quantum Hall (AQH) effect at filling of $3$ electrons per moirè unit cell. The AQH effect arises in an insulating state with both valley- and ferromagnetic order. We argue, that weak doping of such a system leads to the formation of a novel topological spin texture, a `double-tetarton lattice'. The building block of this lattice, the `double-tetarton', is a spin configuration which covers $1/4$ of the unit-sphere twice. In contrast to skyrmion lattices, the net magnetization of this magnetic texture vanishes. Only at large magnet…
Single-layer and Bilayer of graphene are new classes of two-dimensional electron systems with unconventional band structures and valley degrees of freedom. The ground states and excitations in the integer and fractional quantum Hall regimes are investigated on torus and spherical geometries with the use of the density matrix renormalization group (DMRG) method. At nonzero Landau level indices, the ground states at effective filling factors 1, 1/3, 2/3 and 2/5 are valley polarized both in single-layer and bilayer graphenes. We examine the elementary charge excitations which could couple with th…
We develop a weak coupling approach to superconductivity in twisted bilayer graphene, starting from the Fermi liquid regime. A key observation is that near half filling, the fermiology consists of well nested Fermi pockets derived from opposite valleys, leading to enhanced valley fluctuation, which in turn can mediate superconductivity. This scenario is studied within the random phase approximation. We find that inter-valley electron pairing with either chiral ($d+i d$ mixed with $p-i p$) or helical form factor is the dominant instability. An approximate SO(4) spin-valley symmetry implies a ne…
We analyze bilayer quantum Hall ferromagnets, whose underlying symmetry group is SU(4). Spin-pseudospin coherence develops spontaneously when the total electron density is low enough. Quasiparticles are CP^3 skyrmions. One skyrmion induces charge modulations on both of the two layers. At the filling factor$ν=2/m$ one elementary excitation consists of a pair of skyrmions and its charge is $2e/m$. Recent experimental data due to Sawada et al. [Phys. Rev. Lett. {\bf 80}, 4534 (1998)] support this conclusion.
Exotic correlated insulating phases emerge in the ABC-stacked trilayer graphene-boron nitride Moire super-lattice at both quarter and half-filling. A single-band minimal model with valley contrasting staggered-flux is proposed to capture the relevant band structure, where the conspiracy of perfect Fermi-surface nesting and van Hove singularity strongly enhance the valley fluctuation, leading to inter-valley spiral (IVS) order at half filling. In this paper, we consider a strong coupling U(1)$_{v}\times $SU(2)$_{s}$ symmetric spin-valley model to obtain the correlated insulating state and the p…
Fractional quantum Hall (FQH) effects in graphene are studied because of their relativistic characteristics and the valley degree of freedom. Recently FQH effects have been observed at various filling factors with graphene on a hexagonal boron nitride (h-BN) substrate. However, it is known that h-BN creates the mass term in the Dirac Hamiltonian that acts as the effective model of graphene. To understand recent experiments, we shall investigate many-body effects in the massive Dirac electron system. In this paper, we study the mass-term effects on the FQH states of Dirac electrons by exact dia…
We study two-component electrons in the lowest Landau level at total filling factor $ν_T=1/2$ with anisotropic mass tensors and principal axes rotated by $π/2$ as realized in Aluminum Arsenide (AlAs) quantum wells. Combining exact diagonalization and the density matrix renormalization group we demonstrate that the system undergoes a quantum phase transition from a gapless state in which both flavors are equally populated to another gapless state in which all the electrons spontaneously polarize into a single flavor beyond a critical mass anisotropy of {\bf $m_x/m_y \sim 7$}. We propose that th…
Quantum Hall states that result from interaction induced lifting of the eight-fold degeneracy of the zeroth Landau level in bilayer graphene are considered. We show that at even filling factors electric charge is injected into the system in the form of charge $2e$ skyrmions. This is a rare example of binding of charges in a system with purely repulsive interactions. We calculate the skyrmion energy and size as a function of the Zeeman interaction, and discuss signatures of the charge $2e$ skyrmions in the scanning tunneling microscopy experiments.
We examine the Si(111) multi-valley quantum Hall system and show that it exhibits an exceptionally rich interplay of broken symmetries and quantum Hall ordering already near integer fillings $ν$ in the range $ν=0-6$. This six-valley system has a large $[SU(2)]^3\rtimes D_3$ symmetry in the limit where the magnetic length is much larger than the lattice constant. We find that the discrete ${D}_3$ factor breaks over a broad range of fillings at a finite temperature transition to a discrete nematic phase. As $T \rightarrow 0$ the $[SU(2)]^3$ continuous symmetry also breaks: completely near $ν=3$,…
We investigate quasiparticles in bilayer quantum Hall systems around total filling factor nu =1 by current-pumped and resistively detected NMR. The measured Knight shift reveals that the spin component in the quasiparticle increases continuously with $Δ_{SAS}$. Combined with results for the pseudospin component obtained by activation gap measurements, this demonstrates that both spin and pseudospin are contained in a quasiparticle at intermediate $Δ_{SAS}$, providing evidence for the existence of the spin-pseudospin intermixed SU(4) skyrmion. Nuclear spin relaxation measurements show that the …
Partially filled Landau levels host competing orders, with electron solids prevailing close to integer fillings before giving way to fractional quantum Hall liquids as the Landau level fills. Here, we report the observation of an electron solid with noncolinear spin texture in monolayer graphene, consistent with solidification of skyrmions---topological spin textures characterized by quantized electrical charge. In electrical transport, electron solids reveal themselves through a rapid metal-insulator transition in the bulk electrical conductivity as the temperature is lowered, accompanied by …
A recent experiment reported a large anomalous Hall effect in Magic Angle Twisted Bilayer Graphene (TBG) aligned with a hexagonal boron nitride(h-BN) substrate at $\frac{3}{4}$ filling of the conduction band. In this paper we study this system theoretically, and propose explanations of this observation. We emphasize that the physics for this new system is qualitatively different from the pure TBG system. The aligned h-BN breaks in-plane two-fold rotation symmetry and gaps out the Dirac crossings of ordinary TBG. The resulting valence and conduction bands of each valley carry equal and opposite…
We consider the charged excitations in the quantum Hall effect with a large Zeeman splitting at filling factor nu=2. When the Zeeman splitting is increased over a critical value the groundstate undergoes a first order phase transition from a paramagnetic to a ferromagnetic phase. We have studied the possibility to form charged spin-textured excitations, "inter Landau level Skyrmions", close to this transition and find that these never are the lowest lying charged excitations but can under certain conditions provide an effective driving mechanism for the paramagnetic to ferromagnetic phase tran…
We predict that in a twisted homobilayer of transition-metal dichalcogenide MoS$_2$, spin-orbit coupling in the conduction band states from $\pm K$ valleys can give rise to moiré flat bands with nonzero Chern numbers in each valley. The nontrivial band topology originates from a unique combination of angular twist and local mirror symmetry breaking in each individual layer, which results in unusual skyrmionic spin textures in momentum space with skyrmion number $\mathcal{S} = \pm 2$. Our Hartree-Fock analysis further suggests that density-density interactions generically drive the system at $1…
The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic phases (QHFM), with broken spin or valley symmetry. Visualizing atomic scale electronic wavefunctions with scanning tunneling spectroscopy (STS), we resolve microscopic signatures of valley ordering in QHFM and fractional quantum Hall phases of graphene. At charge neutrality, we observe a field-tuned continuous quantum phase transition from a valley polarized state to an intervalley coherent state, with a Kekule distortion of its electronic density. Mapping …
Many graphene moiré superlattices host narrow bands with non-zero valley Chern numbers. We provide analytical and numerical evidence for a robust spin and/or valley polarized insulator at total integer band filling in nearly flat bands of several different moiré materials. In the limit of a perfectly flat band, we present analytical arguments in favor of the ferromagnetic state substantiated by numerical calculations. Further, we numerically evaluate its stability for a finite bandwidth. We provide exact diagonalization results for models appropriate for ABC trilayer graphene aligned with hBN,…
In two-dimensional electron systems confined to wide AlAs quantum wells, composite fermions around the filling factor $ν$ = 3/2 are fully spin polarized but possess a valley degree of freedom. Here we measure the energy needed to completely valley polarize these composite fermions as a function of electron density. Comparing our results to the existing theory, we find overall good quantitative agreement, but there is an unexpected trend: The measured composite fermion valley polarization energy, normalized to the Coulomb energy, decreases with decreasing density.
We theoretically study the correlated insulator states, quantum anomalous Hall (QAH) states, and field-induced topological transitions between different correlated states in twisted multilayer graphene systems. Taking twisted bilayer-monolayer graphene and twisted double-bilayer graphene as examples, we show that both systems stay in spin polarized, $C_{3z}$-broken insulator states with zero Chern number at 1/2 filling of the flat bands under finite displacement fields. In some cases these spin polarized, nematic insulator states are in the quantum valley Hall phase by virtue of the nontrivial…
Skyrmionic Transport and First Order Phase Transitions in Twisted Bilayer Graphene Quantum Hall Ferromagnet
Indian Institute of Technology, Kharagpur（印度理工学院哈格普尔分校）；S. N. Bose National Centre for Basic Sciences（S.N.玻色基础科学国家中心）；National Institute for Materials Science（日本国立材料研究所）
By tilting the samples in the magnetic field, we measured and compared the Skyrmion excitations in the bilayer quantum Hall (QH) state at the Landau-level filling factor $ν=2$ and in the monolayer QH state at $ν=1$. The observed number of flipped spins is $N_s=14$ in the bilayer system with a large tunneling gap, and $N_s=7$ in the bilayer system with a small tunneling gap, while it is $N_s=7$ in the monolayer system. The difference is interpreted due to the interlayer exchange interaction. Moreover, we have observed seemingly preferred numbers $N_s=14,7,1$ for the flipped spins by tilting bil…
Twisted double- and mono-bilayer graphene are graphene-based moiré materials hosting strongly correlated fermions in a gate-tunable conduction band with a topologically non-trivial character. Using unbiased exact diagonalization complemented by unrestricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahedral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moiré scale, competing with a set of ferromagnetic, topological …
We study spin and valley ordering in the quantum Hall fractions in monolayer graphene at Landau level filling factors $ν_G=-2+n/3$ $(n=2,4,5)$. We use exact diagonalizations on the spherical as well as toroidal geometry by taking into account the effect of realistic anisotropies that break the spin/valley symmetry of the pure Coulomb interaction. We also use a variational method based on eigenstates of the fully $SU(4)$ symmetric limit. For all the fractions we study there are two-component states for which the competing phases are generalizations of those occurring at neutrality $ν_G=0$. They…
A nuclear magnetic resonance (NMR) study is reported of multiple (30) Al$_{0.13}$Ga$_{0.87}$As quantum well (QW) sample near the Landau level filling factor $ν=1$. In these Al$_{0.13}$Ga$_{0.87}$As QWs the effective $g$ factor is nearly zero. This can lead to two effects: vanishing electronic polarization $(P)$ and skyrmionic excitations composed of a huge number of spins. As small $P$ values cause an overlap of the NMR signals from the QW and barriers, a special technique was employed to allow these two signals to be distinguished. The QW signal corresponds to a small, negative, and very broa…
The recent experimental confirmation of a transformation between meron and skyrmion topological spin textures in the chiral magnet Co$_8$Zn$_9$Mn$_3$ [S.-Z. Lin et al., Phys. Rev. B 91, 224407 (2015); X. Z. Yu et al., Nature 564, 95 (2018)] confirms that the skyrmion crystals discovered in 2009 [S. Mühlbauer et al., Science 323, 915 (2009)] are just the tip of the iceberg. Crystals of topological textures, including skyrmions, merons, vortices, and monopoles, can be stabilized by combining simple physical ingredients, such as lattice symmetry, frustration, and spin anisotropy. The current chal…
Recent experiment has shown that the ABC-stacked trilayer graphene-boron nitride Moire super-lattice at half-filling is a Mott insulator. Based on symmetry analysis and effective band structure calculation, we propose a valley-contrasting chiral tight-binding model with local Coulomb interaction to describe this Moire super-lattice system. By matching the positions of van Hove points in the low-energy effective bands, the valley-contrasting staggered flux per triangle is determined around $π/2$. When the valence band is half-filled, the Fermi surfaces are found to be perfectly nested between t…
Electrons in graphene have four flavors associated with low-energy spin and valley degrees of freedom. The fractional quantum Hall effect in graphene is dominated by long-range Coulomb interactions which are invariant under rotations in spin-valley space. This SU(4) symmetry is spontaneously broken at most filling factors, and also weakly broken by atomic scale valley-dependent and valley-exchange interactions with coupling constants $g_{z}$ and $g_{\perp}$. In this paper we demonstrate that when $g_{z}=-g_{\perp}$ an exact SO(5) symmetry survives which unifies the Néel spin order parameter of…
Twisted bilayer graphene (TBG) aligned with hexagonal boron nitride (h-BN) substrate can exhibit an anomalous Hall effect at 3/4 filling due to the spontaneous valley polarization in valley resolved moiré bands with opposite Chern number [Science 367, 900 (2020), Science 365, 605 (2019)]. It was observed that a small DC current is able to switch the valley polarization and reverse the sign of the Hall conductance [Science 367, 900 (2020), Science 365, 605 (2019)]. Here, we discuss the mechanism of the current switching of valley polarization near the transition temperature, where bulk dissipat…
The advent of Moiré materials has galvanized interest in the nature of charge carriers in topological bands. In contrast to conventional materials where charge carriers are electron-like quasiparticles, topological bands allow for more exotic possibilities where charge is carried by nontrivial topological textures, such as skyrmions. However, the real space description of skyrmions is ill-suited to address the limit of small or `baby' skyrmions which consist of an electron and a few spin flips. Here, we study the formation of the smallest skyrmions -- spin polarons, formed as bound states of a…
The experimentally observed correlated insulating states and quantum anomalous Hall (QAH) effect in twisted bilayer graphene (TBG) have drawn significant attention. However, up to date, the specific mechanisms of these intriguing phenomena are still open questions. Using a fully unrestricted Hartree-Fock variational method, we have explained the correlated insulating states and QAH effects at various integer fillings of the flat bands in TBG. Our results indicate that states breaking flavor (valley and spin) symmetries are energetically favored at all integer fillings. In particular, the corre…
We present a theory of superconductivity in twisted bilayer graphene in which attraction is generated between electrons on the same honeycomb sublattice when the system is close to a sublattice polarization instability. The resulting Cooper pairs are spin-polarized valley-singlets. Because the sublattice polarizability is mainly contributed by interband fluctuations, superconductivity occurs over a wide range of filling fraction. It is suppressed by i) applying a sublattice polarizing field (generated by an aligned BN substrate) or ii) changing moiré band filling to favor valley polarization. …
We consider stripe formation in quantum Hall systems at integer filling factors. We use Hartree-Fock calculations to obtain the phase diagram of bilayer quantum Hall systems at $ν=4n+1$ in a tilted magnetic field. We derive and analyze an effective low energy theory for the stripe phases which may be present in such systems. We discuss the possibility of stripe formation in wide well systems in a tilted magnetic field and suggest that the resistance anisotropy, observed recently by W. Pan et.al. [phys. Rev. B 64 (2001) 121305], may be due to the existence of a skyrmion stripe phase.
Magic-angle twisted bilayer graphene (tBLG) has been studied extensively owing to its wealth of symmetry-broken phases, correlated Chern insulators, orbital magnetism, and superconductivity. In particular, the anomalous Hall effect (AHE) has been observed at odd integer filling factors ($ν=1$ and $3$) in a small number of tBLG devices, indicating the emergence of a zero-field orbital magnetic state with spontaneously broken time-reversal symmetry. However, the AHE is typically not anticipated at half filling ($ν=2$) owing to competing intervalley coherent states, as well as spin-polarized and …
We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to non-local inter-layer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials, and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wavevectors. We find that at all non-zero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal symmetric and s…
Near a magic twist angle, the lowest energy conduction and valence bands of bilayer graphene moiré superlattices become extremely narrow. The band dispersion that remains is sensitive to the moiré's strain pattern, nonlocal tunneling between layers, and filling-factor dependent Hartree and exchange band renormalizations. In this article we analyze the influence of these band-structure details on the pattern of flavor-symmetry-breaking observed in this narrow band system, and on the associated pattern of Fermi surface reconstructions revealed by weak-field-Hall and Schubnikov-de Haas magneto-tr…
