Flat-band Ferromagnetism Research Articles

Flat-band ferromagnetism in the SU(N) Hubbard and Kondo lattice models

We develop a general theory of flat-band ferromagnetism in the SU(N) Fermi–Hubbard model, which describes the behavior of N-component fermions with SU(N) symmetric interactions. We focus on the case where the single-particle spectrum has a flat band at the bottom and establish a necessary and sufficient condition for the SU(N) Hubbard model to exhibit ferromagnetism when the number of particles is the same as the degeneracy. We show that the occurrence of ferromagnetism is equivalent to the irreducibility of the projection matrix onto the space of single-particle ground states. We also demonstrate that this result can be exploited to establish a rigorous result for the ferromagnetic SU(N) Kondo lattice model with a flat band. Specifically, we prove that when the SU(N) Hubbard model is ferromagnetic, the ferromagnetic SU(N) Kondo lattice model with the same hopping matrix also exhibits SU(N) ferromagnetism.

Flat band ferromagnetism in Pb_2Sb_2O_7 via a self-doped mechanism

Electron systems with strong geometrical frustrations have flat bands, and their unusual band dispersions are expected to induce a wide variety of physical properties. However, for the emergence of such properties, the Fermi level must be pinned within the flat band. In this study, we performed first-principles calculations on pyrochlore oxide Pb_2Sb_2O_7 and theoretically clarified that the self-doping mechanism induces pinning of the Fermi level in the flat band in this system. Therefore, a very high density of states is realized at the Fermi level, and the ferromagnetic state transforms into the ground state via a flat band mechanism, although the system does not contain any magnetic elements. This compound has the potential to serve as a new platform for projecting the properties of flat band systems in the real world.

Ferromagnetism and skyrmions in the Hofstadter–Fermi–Hubbard model

Strongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms are added. While in many lattice models the fermions’ dispersion results in delocalization and destabilization of the ferromagnet, flat bands can restore strong interaction effects and ferromagnetic correlations. To reveal this interplay, here we propose to study the Hofstadter–Fermi–Hubbard model using ultracold atoms. We demonstrate, by performing large-scale density-matrix renormalization group simulations, that this model exhibits a lattice analog of the quantum Hall (QH) ferromagnet at magnetic filling factor ν = 1. We reveal the nature of the low energy spin-singlet states around ν ≈ 1 and find that they host quasi-particles and quasi-holes exhibiting spin-spin correlations reminiscent of skyrmions. Finally, we predict the breakdown of flat-band ferromagnetism at large fields. Our work paves the way towards experimental studies of lattice QH ferromagnetism, including prospects to study many-body states of interacting skyrmions and explore the relation to high- superconductivity.

Kondo resonance effects in emergent flat band materials

Macroscopic degrees of freedom that are involved in the transport of carriers through mesoscopic electronic devices are susceptible to the effects of strong many-body correlations. The presence of magnetic impurities in dilute magnetic alloys typically allow for insights into Kondo effect from the scattering of free carriers by localized electron states of the magnetic impurities but this effect is not well understood when there are no d-band electron states. Herein, the signatures of Kondo resonance effect are elucidated in quantum dots derived from a carbon-nanoline embedded monolayer hexagonal boron nitride whose electron states host flat band ferromagnetism as distinct broken symmetry states. Quantum transport state of mesoscopic devices modelled as quantum dots tunnel coupled to metallic leads is computed by direct diagonalization of the Hamiltonian. The possibility of realizing quantum dots with highly tunable electron states in energy interconversion devices is discussed to show the importance of screening effects on single-electron energy levels. The quantum master equation is solved within different formalisms to determine the stationary-state particle and energy currents. Stability diagrams are calculated to show the dependence of the conductance on experimental control variables of the quantum dot device. The computed responses of the stationary-state transport signatures are used to characterize Kondo resonance effects from flat band states of embedded carbon nanoline-based quantum dots. It is found that the local network structure of the hexagonal ring carbon cluster-based quantum dot has a broken particle-hole symmetry in the transport state. This signals the formation of the quasiparticle states expected in second order scattering when the macroscopic “charge” pseudospin symmetry of the tunnelling electron state is broken dynamically due to charging. The results are discussed to show the implications of a vanishing particle-hole symmetry in the carrier transport state of quantum dots for energy conversion applications.

Certain exact many-body results for Hubbard model ground states testable in small quantum dot arrays

We present several interesting phenomena related to flatband ferromagnetism in the Hubbard model. The first is a mathematical theorem stating certain conditions under which a flatband ferromagnetic must necessarily be degenerate with a nonferromagnetic state. This theorem is generally applicable and geometry-independent, but holds only for a small number of holes in an otherwise filled band. The second phenomenon is a peculiar example where the intuition fails that particles prefer to doubly occupy low-energy states before filling higher-energy states. Lastly, we show a pattern of ferromagnetism which appears in small pentagonal and hexagonal plaquettes at filling factors of roughly 3/10 and 1/4. These examples require only a small number of lattice sites, and may be observable in quantum dot arrays currently available as laboratory spin qubit arrays.

Magnetic investigation on the two-dimensional metallated graphdiyne nanosheets

Graphdiyne, being considered as a new potential spintronics material, possesses excellent electronic and magnetic properties. However, how to introduce ferromagnetic order into graphdiyne is still a pending issue not yet solved, which limits its further application. In this paper, transition metal cobalt is introduced into the alkynyl unit of graphdiyne by a bottom-up liquid-liquid interface synthesis method and the obtained cobalt-doped graphdiyne nanosheets are found to exhibit obvious room temperature ferromagnetism. The density function theory results show that cobalt-doped graphdiyne is half-metallic with a kagome lattice and the imbedded cobalt atoms are the source of magnetic moment. The special kagome structure presents flat band ferromagnetism, which consists with the magnetism behaviour observed in experiment. The successful synthesis of cobalt-doped graphdiyne can not only promote the magnetic investigation of graphdiyne, but provide a new route for the experimental synthesis of kagome lattice materials as well.

Flat-band ferromagnetism in a correlated topological insulator on a honeycomb lattice

We study the flat-band ferromagnetic phase of a spinfull and time-reversal symmetric Haldane-Hubbard model on a honeycomb lattice within a bosonization formalism for flat-band Z$_2$ topological insulators. Such a study extend our previous one [L. S. G. Leite and R. L. Doretto, Phys. Rev. B {\bf 104}, 155129 (2021)] concerning the flat-band ferromagnetic phase of a correlated Chern insulator described by a Haldane-Hubbard model. We consider the topological Hubbard model at $1/4$ filling of its corresponding noninteracting limit and in the nearly flat band limit of its lower free-electronic bands. We show that it is possible to define boson operators associated with two distinct spin-flip excitations, one that changes (mixed-lattice excitations) and a second one that preserves (same-lattice excitations) the index related with the two triangular sublattices. Within the bosonization scheme, the fermionic model is mapped into an effective interacting boson model, whose quadratic term is considered at the harmonic approximation in order to determine the spin-wave excitation spectrum. For both mixed and same-lattice excitations, we find that the spin-wave spectrum is gapped and has two branches, with an energy gap between the lower and the upper bands at the $K$ and $K'$ points of the first Brillouin zone. Such a behavior is distinct from the one of the corresponding correlated Chern insulator, whose spin-wave spectrum has a Goldstone mode at the center of the first Brillouin zone and Dirac points at $K$ and $K'$ points. We also find some evidences that the spin-wave bands for the same-lattice excitations might be topologically nontrivial even in the completely flat band limit.

Itinerant Topological Magnons in SU(2) Symmetric Topological Hubbard Models with Nearly Flat Electronic BandsSupported by the National Natural Science Foundation of China (Grant No. 11774152), and National Key R&D Program of China (Grant No. 2016YFA0300401).

We show that a suitable combination of flat-band ferromagnetism, geometry and nontrivial electronic band topology can give rise to itinerant topological magnons. An SU(2) symmetric topological Hubbard model with nearly flat electronic bands, on a Kagome lattice, is considered as the prototype. This model exhibits ferromagnetic order when the lowest electronic band is half-filled. Using the numerical exact diagonalization method with a projection onto this nearly flat band, we can obtain the magnonic spectra. In the flat-band limit, the spectra exhibit distinct dispersions with Dirac points, similar to those of free electrons with isotropic hoppings, or a local spin magnet with pure ferromagnetic Heisenberg exchanges on the same geometry. Significantly, the non-flatness of the electronic band may induce a topological gap at the Dirac points, leading to a magnonic band with a nonzero Chern number. More intriguingly, this magnonic Chern number changes its sign when the topological index of the electronic band is reversed, suggesting that the nontrivial topology of the magnonic band is related to its underlying electronic band. Our work suggests interesting directions for the further exploration of, and searches for, itinerant topological magnons.

Flat-band ferromagnetism in twisted bilayer graphene

We discuss twisted bilayer graphene (TBG) based on a theorem of flat band ferromagnetism put forward by Mielke and Tasaki. According to this theorem, ferromagnetism occurs if the single particle density matrix of the flat band states is irreducible and we argue that this result can be applied to the quasi-flat bands of TBG that emerge around the charge-neutrality point for twist angles around the magic angle $\theta\sim1.05^\circ$. We show that the density matrix is irreducible in this case, thus predicting a ferromagnetic ground state for neutral TBG ($n=0$). We then show that the theorem can also be applied only to the flat conduction or valence bands, if the substrate induces a single-particle gap at charge neutrality. Also in this case, the corresponding density matrix turns out to be irreducible, leading to ferromagnetism at half filling ($n=\pm2$).

Quantum geometry and stability of moiré flatband ferromagnetism

Several moir\'e systems created by various twisted bilayers have manifested magnetism under flatband conditions leading to enhanced interaction effects. We theoretically study stability of moir\'e flatband ferromagnetism against collective excitations, with a focus on the effects of Bloch band quantum geometry. The spin magnon spectrum is calculated using different approaches, including Bethe-Salpeter equation, single mode approximation, and an analytical theory. One of our main results is an analytical expression for the spin stiffness in terms of the Coulomb interaction potential, the Berry curvatures, and the quantum metric tensor, where the last two quantities characterize the quantum geometry of moir\'e bands. This analytical theory shows that Berry curvatures play an important role in stiffening the spin magnons. Furthermore, we construct an effective field theory for the magnetization fluctuations, and show explicitly that skyrmion excitations bind an integer number of electrons that is proportional to the Bloch band Chern number and the skyrmion winding number.

An Extension of the Cell-Construction Method for the Flat-Band Ferromagnetism

We present an extension of the cell-construction method for the flat-band ferromagnetism. In a rather general setting, we construct Hubbard models with highly degenerate single-electron ground states and obtain a formal representation of these single-electron ground states. By our version of the cell-construction method, various types of flat-band Hubbard models, including the one on line graphs, can be designed and shown to have the unique ferromagnetic ground states when the electron number is equal to the degeneracy of the single-electron ground states.

Gate-tunable flat bands in van der Waals patterned dielectric superlattices

Superlattice engineering provides the means to reshape the fabric felt by quasiparticles moving in a material. Here we argue that bandstructure engineering with superlattices can be pushed to the extreme limit by stacking gapped van der Waals (vdW) materials on patterned dielectric substrates. Specifically, we find that high quality vdW patterned dielectric superlattices (PDS) realize a series of robust flat bands that can be directly switched on and off by gate voltage in situ. In contrast to existing superlattice platforms, these flat bands are realized without the need for fine tuning. Instead, the bands become flat as the gate voltage increases in magnitude. The characteristics of PDS flatbands are highly tunable: the type of flatband (single non-degenerate or dirac-cone-like), localization length, and interaction energy are sensitive to the applied gate voltage. As a result, electron-electron interactions in the PDS flatbands can become stronger than both the bandwidth and disorder broadening, providing a setting for correlated behavior such as flatband ferromagnetism. We expect PDS flatbands can be experimentally realized in a range of readily available gapped vdW materials such as monolayer transition metal dichalcogenides, e.g. WSe2.

Flat Band and Hole-induced Ferromagnetism in a Novel Carbon Monolayer

In recent experiments, superconductivity and correlated insulating states were observed in twisted bilayer graphene (TBG) with small magic angles, which highlights the importance of the flat bands near Fermi energy. However, the moiré pattern of TBG consists of more than ten thousand carbon atoms that is not easy to handle with conventional methods. By density functional theory calculations, we obtain a flat band at EF in a novel carbon monolayer coined as cyclicgraphdiyne with the unit cell of eighteen atoms. By doping holes into cyclicgraphdiyne to make the flat band partially occupied, we find that cyclicgraphdiyne with 1/8, 1/4, 3/8 and 1/2 hole doping concentration shows ferromagnetism (half-metal) while the case without doping is nonmagnetic, indicating a hole-induced nonmagnetic-ferromagnetic transition. The calculated conductivity of cyclicgraphdiyne with 1/8, 1/4 and 3/8 hole doping concentration is much higher than that without doping or with 1/2 hole doping. These results make cyclicgraphdiyne really attractive. By studying several carbon monolayers, we find that a perfect flat band may occur in the lattices with both separated or corner-connected triangular motifs with only including nearest-neighboring hopping of electrons, and the dispersion of flat band can be tuned by next-nearest-neighboring hopping. Our results shed insightful light on the formation of flat band in TBG. The present study also poses an alternative way to manipulate magnetism through doping flat band in carbon materials.

Flat-band ferromagnetism of SU(N) Hubbard model on Tasaki lattices

We investigate the para-ferro magnetic transition of the repulsive SU(N) Hubbard model on a type of one- and two-dimensional decorated cubic lattices, referred as Tasaki lattices, which feature massive single-particle ground state degeneracy. Under certain restrictions for constructing localized many-particle ground states of flat-band ferromagnetism, the quantum model of strongly correlated electrons is mapped to a classical statistical geometric site-percolation problem, where the nontrivial weights of different configurations must be considered. We prove rigorously the existence of para-ferro transition for the SU(N) Hubbard model on one-dimensional Tasaki lattice and determine the critical density by the transfer-matrix method. In two dimensions, we numerically investigate the phase transition of SU(3), SU(4) and SU(10) Hubbard models by Metropolis Monte Carlo simulation. We find that the critical density exceeds that of standard percolation, and increases with spin degrees of freedom, implying that the effective repulsive interaction becomes stronger for larger N. We further rigorously prove the existence of flat-band ferromagnetism of the SU(N) Hubbard model when the number of particles equals to the degeneracy of the lowest band in the single-particle energy spectrum.

Disordered flat bands on the kagome lattice

We study two models of correlated bond- and site-disorder on the kagome lattice considering both translationally invariant and completely disordered systems. The models are shown to exhibit a perfectly flat ground state band in the presence of disorder for which we provide exact analytic solutions. Whereas in one model the flat band remains gapped and touches the dispersive band, the other model has a finite gap, demonstrating that the band touching is not protected by topology alone. Our model also displays fully saturated ferromagnetic groundstates in the presence of repulsive interactions, an example of disordered flat band ferromagnetism.

Ferromagnetism in monolayer MoS2 dictated by hydrogen adsorption sites and concentration

We show that hydrogen-induced magnetism in monolayer MoS2 is dictated by the hydrogen adsorption sites and concentration by using density functional theory calculations. Hydrogen adsorbed at the center of the hexagonal ring leads to an itinerant ferromagnetism at relatively high concentrations, whereas hydrogen adsorbed on sulfur leads to a flat-band ferromagnetism at a relatively low concentration. The electrons in the non-metallic flat-band ferromagnetism are equally distributed on hydrogen and nearby Mo and S atoms, in contrast to the non-magnetic case where they are concentrated on the nearby Mo atoms.

Ferromagnetism and Wigner crystallization in kagome graphene and related structures

Interaction in a flat band is magnified due to the divergence in the density of states, which gives rise to a variety of many-body phenomena such as ferromagnetism and Wigner crystallization. Until now, however, most studies of the flat band physics are based on model systems, making their experimental realization a distant future. Here, we propose a class of systems made of real atoms, namely, carbon atoms with realistic physical interactions (dubbed here as Kagome graphene/graphyne). Density functional theory calculations reveal that these Kagome lattices offer a controllable way to realize robust flat bands sufficiently close to the Fermi level. Upon hole doping, they split into spin-polarized bands at different energies to result in a flat-band ferromagnetism. At a half filling, this splitting reaches its highest level of 768 meV. At smaller fillings, e.g., when {\nu}=1/6, on the other hand, a Wigner crystal spontaneously forms, where the electrons form closed loops localized on the grid points of a regular triangular lattice. It breaks the translational symmetry of the original Kagome lattice. We further show that the Kagome lattices exhibit good mechanical stabilities, based on which a possible route for experimental realization of the Kagome graphene is also proposed.

Charge density wave phase, Mottness, and ferromagnetism in monolayer 1T−NbSe2

The recently investigated $1T$-polymorph of monolayer NbSe$_2$ revealed an insulating behaviour suggesting a star-of-David phase with $\sqrt{13}\,\times\sqrt{13}$ periodicity associated with a Mott insulator, reminiscent of $1T$-TaS$_2$. In this work, we examine this novel two-dimensional material from first principles. We find an instability towards the formation of an incommensurate charge-density-wave (CDW) and establish the star-of-David phase as the most stable commensurate CDW. The mottness in the star-of-David phase is confirmed and studied at various levels of theory: the spin-polarized generalized gradient approximation (GGA) and its extension involving the on-site Coulomb repulsion (GGA+$U$), as well as the dynamical mean-field theory (DMFT). Finally, we estimate Heisenberg exchange couplings in this material and find a weak nearest-neighbour ferromagnetic coupling, at odds with most Mott insulators. We point out the close resemblance between this star-of-David phase and flat-band ferromagnetism models.

(Invited) Synthesis and Electromagnetic Properties of Square-Symmetry π-Conjugated Phthalocyanato Metal-Organic Frameworks

Two-dimensional (2D) crystalline (semi)conductors, inspired by model systems such as graphene, silicenes and transition metal dichalcogenides, are a central topic of current research at the nanoscale. Exciting physical properties such as massless fermions, fractional quantum hall effects and flat-band ferromagnetism originate from the unique electronic band structures of these materials. Conductive 2D metal-organic frameworks (MOFs) are a recent and promising addition to these classes of materials due to features such as bottom-up tailorability and guest-accessible nanoporosity. Here, were present a new highly tunable platform of square-symmetry conductive MOFs. The electronic band structure of these materials is unique relative to the more common hexagonal (honeycomb) symmetry that characterizes many 2D materials and all previously reported π-conjugated MOFs. We will discuss the experimental and first-principles calculated physical properties of these new materials in relation to the hexagonal phases.

Entanglement and magnetism in high-spin graphene nanodisks

We investigate the ground-state properties of triangular graphene nanoflakes with zigzag edge configurations. The description of zero-dimensional nanostructures requires accurate many-body techniques since the widely used density-functional theory with local density approximation or Hartree-Fock methods cannot handle the strong quantum fluctuations. Applying the unbiased density-matrix renormalization group algorithm we calculate the magnetization and entanglement patterns with high accuracy for different interaction strengths and compare them to the mean-field results. With the help of quantum information analysis and subsystem density matrices we reveal that the edges are strongly entangled with each other. We also address the effect of electron and hole doping and demonstrate that the magnetic properties of triangular nanoflakes can be controlled by electric field, which reveals features of flat-band ferromagnetism. This may open up new avenues in graphene based spintronics.