Quantum Hall Ferromagnet Research Articles

Vanishing bulk heat flow in the ν = 0 quantum Hall ferromagnet in monolayer graphene

Vanishing bulk heat flow in the ν = 0 quantum Hall ferromagnet in monolayer graphene

Beating Fabry-Pérot interference pattern in a magnonic scattering junction in the graphene quantum Hall ferromagnet

Beating Fabry-Pérot interference pattern in a magnonic scattering junction in the graphene quantum Hall ferromagnet

Particle-Hole Asymmetric Ferromagnetism and Spin Textures in the Triangular Hubbard-Hofstadter Model

In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the “Hofstadter regime,” where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo and density matrix renormalization group techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor ν≤1, bounded below by filling factor ν=1 and bounded above by half filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors ν=1 and ν=3. The phases near ν=1 are particle-hole asymmetric, and we observe a rapid decrease in ground-state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands. Published by the American Physical Society 2024

Pseudospin Quantum Hall Ferromagnetism Probed by Electron Spin Resonance.

We study the effect of the pseudospin ferromagnetism with the aid of an electrically detected electron spin resonance in a wide AlAs quantum well containing a high quality two-dimensional electron system. Here, pseudospin emerges as a two-component degree of freedom, that labels degenerate energy minima in momentum space populated by electrons. The built-in mechanical strain in the sample studied imposes a finite "Zeeman" splitting between the pseudospin "up" and "down" states. Because of the anisotropy of the electron spin splitting we were able to independently measure the electron spin resonances originating from the two in-plane valleys. By analyzing the relative resonance amplitudes, we were able to investigate the ferromagnetic phase transitions taking place at integer filling factors of the quantum Hall effect when the magnetic field is tilted. The pseudospin nature of these transitions is demonstrated.

Electrical noise spectroscopy of magnons in a quantum Hall ferromagnet

Collective spin-wave excitations, magnons, are promising quasi-particles for next-generation spintronics devices, including platforms for information transfer. In a quantum Hall ferromagnets, detection of these charge-neutral excitations relies on the conversion of magnons into electrical signals in the form of excess electrons and holes, but if the excess electron and holes are equal, detecting an electrical signal is challenging. In this work, we overcome this shortcoming by measuring the electrical noise generated by magnons. We use the symmetry-broken quantum Hall ferromagnet of the zeroth Landau level in graphene to launch magnons. Absorption of these magnons creates excess noise above the Zeeman energy and remains finite even when the average electrical signal is zero. Moreover, we formulate a theoretical model in which the noise is produced by equilibration between edge channels and propagating magnons. Our model also allows us to pinpoint the regime of ballistic magnon transport in our device.

Hilbert space structure and classical limit of the low energy sector of U(N) quantum Hall ferromagnets

Using the Lieb–Mattis ordering theorem of electronic energy levels, we identify and construct the Hilbert space of the low energy sector of U(N) quantum Hall/Heisenberg ferromagnets at filling factor M for L Landau/lattice sites. The carrier Hilbert space of irreducible representations of U(N) is described by rectangular Young tableaux of M rows and L columns, and associated with Grassmannian phase spaces U(N)/U(M)×U(N-M). Replacing U(N)-spin operators by their expectation values in a Grassmannian coherent state allows for a semi-classical treatment of the low energy U(N)-spin-wave coherent excitations (skyrmions) of U(N) quantum Hall ferromagnets in terms of Grasmannian nonlinear sigma models.

Atomic Valley Filter Effect Induced by an Individual Flower Defect in Graphene

Owing to the bipartite nature of honeycomb lattice, the electrons in graphene host valley degree of freedom, which gives rise to a rich set of unique physical phenomena including chiral tunneling, Klein paradox, and quantum Hall ferromagnetism. Atomic defects in graphene can efficiently break the local sublattice symmetry, and hence, have significant effects on the valley-based electronic behaviors. Here we demonstrate that an individual flower defect in graphene has the ability of valley filter at the atomic scale. With the combination of scanning tunneling microscopy and Landau level measurements, we observe two valley-polarized density-of-states peaks near the outside of the flower defects, implying the symmetry breaking of the K and K′ valleys in graphene. Moreover, the electrons in the K valley can highly penetrate inside the flower defects. In contrast, the electrons in the K′ valley cannot directly penetrate, instead, they should be assisted by the valley switch from the K′ to K. Our results demonstrate that an individual flower defect in graphene can be regarded as a nanoscale valley filter, providing insight into the practical valleytronics.

Spontaneous isospin polarization and quantum Hall ferromagnetism in a rhombohedral trilayer graphene superlattice

Moiré superlattices in van der Waals heterostructures have recently attracted enormous interests, due to the highly controllable electronic correlation that gives rise to superconductivity, ferromagnetism, and nontrivial topological properties. To gain a deep understanding of such exotic properties, it is essential to clarify the broken symmetry between spin and valley flavors which universally exists in these ground states. Here in a rhombohedral trilayer graphene crystallographically aligned with a hexagonal boron nitride, we report various kinds of symmetry-breaking transition tuned by displacement fields (D) and magnetic fields: (i) While it is well known that a finite D can enhance correlation to result in correlated insulators at fractional fillings of a flat band, we find the correlation gap emerges before the flavor is fully filled at a positive D, but the sequence is reversed at a negative D. (ii) Around zero D, electronic correlation can be invoked by narrow Landau levels, leading to quantum Hall ferromagnetism that lifts all the degeneracies including not only spin and valley but also orbital degrees of freedom. Our result unveils the complication of transitions between symmetry-breaking phases, shedding light on the mechanisms of various exotic phenomena in strongly correlated systems.

Global phase diagram of charge-neutral graphene in the quantum Hall regime for generic interactions

Monolayer graphene at charge neutrality in a quantizing magnetic field is a quantum Hall ferromagnet. Due to the spin and valley (near) degeneracies, there is a plethora of possible ground states. Previous theoretical work, based on a stringent ultra short-range assumption on the symmetry-allowed interactions, predicts a phase diagram with distinct regions of spin-polarized, canted antiferromagnetic, inter-valley coherent, and charge density wave order. While early experiments suggested that the system was in the canted antiferromagnetic phase at a perpendicular field, recent scanning tunneling studies universally find Kekul\'e bond order, and sometimes also charge density wave order. Recently, it was found that if one relaxes the stringent assumption mentioned above, a phase with coexisting canted antiferromagnetic and Kekul\'e order exists in the region of the phase diagram believed to correspond to real samples. In this work, starting from the continuum limit appropriate for experiments, we present the complete phase diagram of $\nu=0$ graphene in the Hartree-Fock approximation, using generic symmetry-allowed interactions, assuming translation invariant ground states up to an intervalley coherence. Allowing for a sublattice potential (valley Zeeman coupling), we find numerous phases with different types of coexisting order. We conclude with a discussion of the physical signatures of the various states.

Anomalous magnons in quantum Hall ferromagnet with strong interaction at filling factor 2

In two-dimensional electronic systems, at large values of the Wigner–Seitz parameter, an anomalous branch of magnons was found. In a quantum Hall ferromagnet state with ν = 2, the magnon dispersion reveals a magnetoroton minimum with depth dependent on electron density. Magnetorotons with opposite momenta are shown to attract each other.

Anomalous Magnons in a Quantum Hall Ferromagnet with Strong Interaction at Filling Factor 2

Anomalous Magnons in a Quantum Hall Ferromagnet with Strong Interaction at Filling Factor 2

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.

Competing spin-valley entangled and broken symmetry states in the N=1 Landau level of graphene

We study many-body ground states for the partial integer fillings of the $N=1$ Landau level in graphene, by constructing a model that accounts for the lattice scale corrections to the Coulomb interactions. Interestingly, in contrast to the $N=0$ Landau level, this model contains not only pure delta function interactions but also some of its derivatives. Due to this we find several important differences with respect to the $N=0$ Landau level. For example at quarter filling when only a single component is filled, there is a degeneracy lifting of the quantum hall ferromagnets and ground states with entangled spin and valley degrees of freedom can become favourable. Moreover at half-filling of the $N=1$ Landau level, we have found a new phase that is absent in the $N=0$ Landau level, that combines characteristics of the Kekul\'{e} state and an antiferromagnet. We also find that according to the parameters extracted in a recent experiment, at half-filling of the $N=1$ Landau level graphene is expected to be in a delicate competition between an AF and a CDW state, but we also discuss why the models for these recent experiments might be missing some important terms.

Quantum Hall spin textures far beyond the skyrmion limit

In strongly correlated quantum Hall ferromagnets with noninteger filling factors between $\ensuremath{\nu}=1$ and $\ensuremath{\nu}=3/2$, evidence of offbeat spin textures is obtained. The platforms for the study are two-dimensional electron systems based on MgZnO/ZnO heterostructures, in which the parameters of Zeeman and exchange energies are inconsistent with ordinary skyrmions. Experimental probing of magnetic order is fulfilled via exploration of the spectra of collective spin excitations by means of inelastic light scattering. In addition to the ferromagnetic spin exciton, a low-energy spin mode is observed, bearing witness to broken spin-rotational symmetry in the ground state. The two spin modes exhibit a pronounced anticrossing behavior, depending on the two-dimensional momentum, electron concentration, filling factor, and magnetic field tilt. The properties of the electron system are simulated using the exact diagonalization technique, showing that Landau level mixing and crossing play a key role in the nontrivial spin configuration. The corresponding spin textures emerging between $\ensuremath{\nu}=1$ and $\ensuremath{\nu}=3/2$ involve the orbital degree of freedom and are qualitatively different from skyrmions. Experiments at elevated temperatures show the destruction of this orbital spin texture phase with critical temperature far below the Zeeman energy. On the other side of $\ensuremath{\nu}=1$ the textures are absent.

Robust Quantum Hall Ferromagnetism near a Gate-Tuned ν=1 Landau Level Crossing.

In a low-disorder two-dimensional electron system, when two Landau levels of opposite spin or pseudospin cross at the Fermi level, the dominance of the exchange energy can lead to a ferromagnetic, quantum Hall ground state whose gap is determined by the exchange energy and has skyrmions as its excitations. This is normally achieved via applying either hydrostatic pressure or uniaxial strain. We study here a very high-quality, low-density, two-dimensional hole system, confined to a 30-nm-wide (001) GaAs quantum well, in which the two lowest-energy Landau levels can be gate tuned to cross at and near filling factor ν=1. As we tune the field position of the crossing from one side of ν=1 to the other by changing the hole density, the energy gap for the quantum Hall state at ν=1 remains exceptionally large, and only shows a small dip near the crossing. The gap overall follows a sqrt[B] dependence, expected for the exchange energy. Our data are consistent with a robust quantum Hall ferromagnet as the ground state.

Fractional quantum Hall effect for extended objects: from skyrmionic membranes to dyonic strings

It is well known that in two spatial dimensions the fractional quantum Hall effect (FQHE) deals with point-like anyons that carry fractional electric charge and statistics. Moreover, in presence of a SO(3) order parameter, point-like skyrmions emerge and play a central role in the corresponding quantum Hall ferromagnetic phase. In this work, we show that in six spatial dimensions, the FQHE for extended objects shares very similar features with its two-dimensional counterpart. In the higher-dimensional case, the electromagnetic and hydrodynamical one-form gauge fields are replaced by three-form gauge fields and the usual point-like anyons are replaced by membranes, namely two-dimensional extended objects that can carry fractional charge and statistics. We focus on skyrmionic membranes, which are associated to a SO(5) order parameter and give rise to an higher-dimensional generalizaton of the quantum Hall ferromagnetism. We show that skyrmionic membranes naturally couple to the curved background through a generalized Wen-Zee term and can give us some insights about the chiral conformal field theory on the boundary. We then present a generalization of the Witten effect in six spatial dimensions by showing that one-dimensional extended monopoles (magnetic strings) in the bulk of the FQH states can acquire electric charge through an axion field by becoming dyonic strings.

Theory of competing charge density wave, Kekulé, and antiferromagnetically ordered fractional quantum Hall states in graphene aligned with boron nitride

We investigate spin and valley symmetry-broken fractional quantum Hall phases within a formalism that naturally extends the paradigm of quantum Hall ferromagnetism from integer to fractional quantum Hall states, allowing us to construct detailed phase diagrams for a large class of multi-component states. Motivated by recent experiments on Graphene aligned with a Boron Nitride substrate, we predict a sequence of transitions realized by increasing the magnetic field, starting from a sub-lattice polarized state to a valley coherent Kekule charge density wave state and further to an anti-ferromagnetic phase. Moreover for filling fractions such as $\nu=\pm 1/3$, we predict that the system undergoes a transition at low fields, that not only differ by the spin-valley orientation of the fractionally filled flavors but also by their intrinsic fractional quantum Hall nature. This transition is from a Laughlin-like state to a two component Halperin-like state both with a charge density wave order. Moreover for $\nu=\pm 1/3,\pm 2/3$, we predict a "canted Kekule density phase"(CaKD) where the spinors of integer and fractionally occupied components have different orientations in the valley Bloch sphere, in contrast to the Kekule state for the integer quantum Hall state at neutrality where both occupied components have the same orientation in the valley Bloch sphere.

Hilbert Space Structure of the Low Energy Sector of U(N) Quantum Hall Ferromagnets and Their Classical Limit

Using the Lieb–Mattis ordering theorem of electronic energy levels, we identify the Hilbert space of the low energy sector of U(N) quantum Hall/Heisenberg ferromagnets at filling factor M for L Landau/lattice sites with the carrier space of irreducible representations of U(N) described by rectangular Young tableaux of M rows and L columns, and associated with Grassmannian phase spaces U(N)/U(M)×U(N−M). We embed this N-component fermion mixture in Fock space through a Schwinger–Jordan (boson and fermion) representation of U(N)-spin operators. We provide different realizations of basis vectors using Young diagrams, Gelfand–Tsetlin patterns and Fock states (for an electron/flux occupation number in the fermionic/bosonic representation). U(N)-spin operator matrix elements in the Gelfand–Tsetlin basis are explicitly given. Coherent state excitations above the ground state are computed and labeled by complex (N−M)×M matrix points Z on the Grassmannian phase space. They adopt the form of a U(N) displaced/rotated highest-weight vector, or a multinomial Bose–Einstein condensate in the flux occupation number representation. Replacing U(N)-spin operators by their expectation values in a Grassmannian coherent state allows for a semi-classical treatment of the low energy (long wavelength) U(N)-spin-wave coherent excitations (skyrmions) of U(N) quantum Hall ferromagnets in terms of Grasmannian nonlinear sigma models.

Renormalization of the Exchange Energy Scale in Quantum Hall Ferromagnets with a Filling Factor of 1

Renormalization of the Exchange Energy Scale in Quantum Hall Ferromagnets with a Filling Factor of 1

Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet.

The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic (QHFM) phases with broken spin or valley symmetry. Visualizing atomic-scale electronic wave functions with scanning tunneling spectroscopy (STS), we resolved microscopic signatures of valley ordering in QHFM phases and spectral features of fractional quantum Hall phases of graphene. At charge neutrality, we observed a field-tuned continuous quantum phase transition from a valley-polarized state to an intervalley coherent state, with a Kekulé distortion of its electronic density. Mapping the valley texture extracted from STS measurements of the Kekulé phase, we could visualize valley skyrmion excitations localized near charged defects. Our techniques can be applied to examine valley-ordered phases and their topological excitations in a wide range of materials.