Electrical generation and detection of spin waves in a quantum Hall ferromagnet

Landau-Level Mixing and SU(4) Symmetry Breaking in Graphene

Recent scanning tunneling microscopy experiments on graphene at charge neutrality under strong magnetic fields have uncovered a ground state characterized by Kekulé distortion (KD). In contrast, nonlocal spin and charge transport experiments in double-encapsulated graphene, which has a higher dielectric constant, have identified an antiferromagnetic (AF) ground state. We propose a mechanism to reconcile these conflicting observations by showing that Landau-level mixing can drive a transition from AF to KD with the reduction of the dielectric screening. Our conclusion is drawn from studying the effect of Landau-level mixing on the lattice-scale, valley-dependent interactions to leading order in graphene's fine structure constant κ=e^{2}/(ℏv_{F}ε). This analysis provides three key insights: (1) valley-dependent interactions remain predominantly short-range with the m=0 Haldane pseudopotential being at least an order of magnitude greater than the others, affirming the validity of delta-function approximation for these interactions. (2) The phase transition between the AF and KD states is driven by the microscopic process in the double-exchange Feynman diagram. (3) The magnitudes of the coupling constants are significantly boosted by remote Landau levels. Our model also provides a theoretical basis for numerical studies of fractional quantum Hall states in graphene.

Excitons in the fractional quantum Hall effect

Excitons, Coulomb-driven bound states of electrons and holes, are typically composed of integer charges1,2. However, in bilayer systems influenced by charge fractionalization3,4, a more interesting form of interlayer exciton can emerge, in which pairing occurs between constituents that carry fractional charges. Despite numerous theoretical predictions for these fractional excitons5-16, their experimental observation has remained unexplored. Here we report transport signatures of excitonic pairing in fractional quantum Hall effect states. By probing the composition of these excitons and their impact on the underlying wavefunction, we discover two new types of quantum phases of matter. One of these can be viewed as the fractional counterpart of the exciton condensate at a total filling of 1, whereas the other involves a more unusual type of exciton that obeys non-bosonic quantum statistics, challenging the standard model of bosonic excitons.

Emergent Inhomogeneity and Nonlocality in a Graphene Field-Effect Transistor on a Near-Parallel Moiré Superlattice of Transition Metal Dichalcogenides

At near-parallel orientation, twisted bilayers of transition metal dichalcogenides exhibit interlayer charge transfer-driven out-of-plane ferroelectricity. Here, we report detailed electrical transport in a dual-gated graphene field-effect transistor placed on a 2.1° twisted bilayer WSe2. We observe hysteretic transfer characteristics and an emergent charge inhomogeneity with multiple local Dirac points evolving with an increasing electric displacement field (D). Concomitantly, we also observe a strong nonlocal voltage signal at D ∼ 0 V/nm that decreases rapidly with increasing D. A linear scaling of the nonlocal signal with longitudinal resistance suggests edge mode transport, which we attribute to the breaking of valley symmetry of graphene due to the spatially fluctuating electric field from the underlying polarized moiré domains. A quantitative analysis suggests the emergence of finite-size domains in graphene that modulate the charge and the valley currents simultaneously. This work underlines the impact of interfacial ferroelectricity that can trigger a new generation of devices.

Electron wave and quantum optics in graphene

In the last decade, graphene has become an exciting platform for electron optical experiments, in some aspects superior to conventional two-dimensional electron gases (2DEGs). A major advantage, besides the ultra-large mobilities, is the fine control over the electrostatics, which gives the possibility of realising gap-less and compact p-n interfaces with high precision. The latter host non-trivial states,e.g., snake states in moderate magnetic fields, and serve as building blocks of complex electron interferometers. Thanks to the Dirac spectrum and its non-trivial Berry phase, the internal (valley and sublattice) degrees of freedom, and the possibility to tailor the band structure using proximity effects, such interferometers open up a completely new playground based on novel device architectures. In this review, we introduce the theoretical background of graphene electron optics, fabrication methods used to realise electron-optical devices, and techniques for corresponding numerical simulations. Based on this, we give a comprehensive review of ballistic transport experiments and simple building blocks of electron optical devices both in single and bilayer graphene, highlighting the novel physics that is brought in compared to conventional 2DEGs. After describing the different magnetic field regimes in graphene p-n junctions and nanostructures, we conclude by discussing the state of the art in graphene-based Mach-Zender and Fabry-Perot interferometers.

Magneto-Thermoelectric Transport in Graphene Quantum Dot with Strong Correlations

Disorder at etched edges of graphene quantum dots (GQD) enables random all-to-all interactions between localized charges in partially filled Landau levels, providing a potential platform to realize the Sachdev-Ye-Kitaev (SYK) model. We use quantum Hall edge states in the graphene electrodes to measure electrical conductance and thermoelectric power across the GQD. In specific temperature ranges, we observe a suppression of electric conductance fluctuations and slowly decreasing thermoelectric power across the GQD with increasing temperature, consistent with recent theory for the SYK regime.

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.

Giant electrically tunable magnon transport anisotropy in a van der Waals antiferromagnetic insulator

Anisotropy is a manifestation of lowered symmetry in material systems that have profound fundamental and technological implications. For van der Waals magnets, the two-dimensional (2D) nature greatly enhances the effect of in-plane anisotropy. However, electrical manipulation of such anisotropy as well as demonstration of possible applications remains elusive. In particular, in-situ electrical modulation of anisotropy in spin transport, vital for spintronics applications, has yet to be achieved. Here, we realized giant electrically tunable anisotropy in the transport of second harmonic thermal magnons (SHM) in van der Waals anti-ferromagnetic insulator CrPS₄ with the application of modest gate current. Theoretical modeling found that 2D anisotropic spin Seebeck effect is the key to the electrical tunability. Making use of such large and tunable anisotropy, we demonstrated multi-bit read-only memories (ROMs) where information is inscribed by the anisotropy of magnon transport in CrPS₄. Our result unveils the potential of anisotropic van der Waals magnons for information storage and processing.

Heat Equilibration of Integer and Fractional Quantum Hall Edge Modes in Graphene

Hole-conjugate states of the fractional quantum Hall effect host counterpropagating edge channels which are thought to exchange charge and energy. These exchanges have been the subject of extensive theoretical and experimental works; in particular, it is yet unclear if the presence of integer quantum Hall edge channels stemming from fully filled Landau levels affects heat equilibration along the edge. In this Letter, we present heat transport measurements in quantum Hall states of graphene demonstrating that the integer channels can strongly equilibrate with the fractional ones, leading to markedly different regimes of quantized heat transport that depend on edge electrostatics. Our results allow for a better comprehension of the complex edge physics in the fractional quantum Hall regime.

Imaging tunable quantum Hall broken-symmetry orders in graphene

ABSTARCT

When electrons populate a flat band their kinetic energy becomes negligible, forcing them to organize in exotic many-body states to minimize their Coulomb energy^1-5. The zeroth Landau level of graphene under a magnetic field is a particularly interesting strongly interacting flat band because interelectron interactions are predicted to induce a rich variety of broken-symmetry states with distinct topological and lattice-scale orders^6-11. Evidence for these states stems mostly from indirect transport experiments that suggest that broken-symmetry states are tunable by boosting the Zeeman energy¹² or by dielectric screening of the Coulomb interaction¹³. However, confirming the existence of these ground states requires a direct visualization of their lattice-scale orders¹⁴. Here we image three distinct broken-symmetry phases in graphene using scanning tunnelling spectroscopy. We explore the phase diagram by tuning the screening of the Coulomb interaction by a low- or high-dielectric-constant environment, and with a magnetic field. In the unscreened case, we find a Kekulé bond order, consistent with observations of an insulating state undergoing a magnetic-field driven Kosterlitz-Thouless transition^15,16. Under dielectric screening, a sublattice-unpolarized ground state¹³ emerges at low magnetic fields, and transits to a charge-density-wave order with partial sublattice polarization at higher magnetic fields. The Kekulé and charge-density-wave orders furthermore coexist with additional, secondary lattice-scale orders that enrich the phase diagram beyond current theory predictions^6-10. This screening-induced tunability of broken-symmetry orders may prove valuable to uncover correlated phases of matter in other quantum materials.

Coexistence of Canted Antiferromagnetism and Bond Order in ν=0 Graphene

Motivated by experimental studies of graphene in the quantum Hall regime, we revisit the phase diagram of a single sheet of graphene at charge neutrality. Because of spin and valley degeneracies, interactions play a crucial role in determining the nature of the ground state. We show that, generically within the Hartree-Fock approximation, in the regime of interest there is a region of coexistence between magnetic and bond orders in the phase diagram. We demonstrate this result both in continuum and lattice models, and argue that the coexistence phase naturally provides a possible explanation for unreconciled experimental observations on the quantum Hall effect in graphene.

Electrically switchable van der Waals magnon valves

Van der Waals magnets have emerged as a fertile ground for the exploration of highly tunable spin physics and spin-related technology. Two-dimensional (2D) magnons in van der Waals magnets are collective excitation of spins under strong confinement. Although considerable progress has been made in understanding 2D magnons, a crucial magnon device called the van der Waals magnon valve, in which the magnon signal can be completely and repeatedly turned on and off electrically, has yet to be realized. Here we demonstrate such magnon valves based on van der Waals antiferromagnetic insulator MnPS₃. By applying DC electric current through the gate electrode, we show that the second harmonic thermal magnon (SHM) signal can be tuned from positive to negative. The guaranteed zero crossing during this tuning demonstrates a complete blocking of SHM transmission, arising from the nonlinear gate dependence of the non-equilibrium magnon density in the 2D spin channel. Using the switchable magnon valves we demonstrate a magnon-based inverter. These results illustrate the potential of van der Waals anti-ferromagnets for studying highly tunable spin-wave physics and for application in magnon-base circuitry in future information technology.

A major challenge in magnon based approaches to information processing lies in developing valves to allow or supress the magnon signal. Here, Chen et al demonstrate a van der Waals magnet based magnon valve which can be tuned electrically over an exceptionally wide range.

Long-range nontopological edge currents in charge-neutral graphene

Van der Waals heterostructures display numerous unique electronic properties. Nonlocal measurements, wherein a voltage is measured at contacts placed far away from the expected classical flow of charge carriers, have been widely used in the search for novel transport mechanisms, including dissipationless spin and valley transport^1-9, topological charge-neutral currents^10-12, hydrodynamic flows¹³ and helical edge modes^14-16. Monolayer^1-5,10,15-19, bilayer^9,11,14,20 and few-layer²¹ graphene, transition-metal dichalcogenides^6,7 and moiré superlattices^8,10,12 have been found to display pronounced nonlocal effects. However, the origin of these effects is hotly debated^{3,11,17,22-24}. Graphene, in particular, exhibits giant nonlocality at charge neutrality^1,15-19, a striking behaviour that has attracted competing explanations. Using a superconducting quantum interference device on a tip (SQUID-on-tip) for nanoscale thermal and scanning gate imaging²⁵, here we demonstrate that the commonly occurring charge accumulation at graphene edges^23,26-31 leads to giant nonlocality, producing narrow conductive channels that support long-range currents. Unexpectedly, although the edge conductance has little effect on the current flow in zero magnetic field, it leads to field-induced decoupling between edge and bulk transport at moderate fields. The resulting giant nonlocality at charge neutrality and away from it produces exotic flow patterns that are sensitive to edge disorder, in which charges can flow against the global electric field. The observed one-dimensional edge transport is generic and nontopological and is expected to support nonlocal transport in many electronic systems, offering insight into the numerous controversies and linking them to long-range guided electronic states at system edges.

Quantum Hall Valley Splitters and a Tunable Mach-Zehnder Interferometer in Graphene

Graphene is a very promising test bed for the field of electron quantum optics. However, a fully tunable and coherent electronic beam splitter is still missing. We report the demonstration of electronic beam splitters in graphene that couple quantum Hall edge channels having opposite valley polarizations. The electronic transmission of our beam splitters can be tuned from zero to near unity. By independently setting the beam splitters at the two corners of a graphene p-n junction to intermediate transmissions, we realize a fully tunable electronic Mach-Zehnder interferometer. This tunability allows us to unambiguously identify the quantum interferences due to the Mach-Zehnder interferometer, and to study their dependence with the beam-splitter transmission and the interferometer bias voltage. The comparison with conventional semiconductor interferometers points toward universal processes driving the quantum decoherence in those two different 2D systems, with graphene being much more robust to their effect.

Scattering of Magnons at Graphene Quantum-Hall-Magnet Junctions

Motivated by recent nonlocal transport studies of quantum-Hall-magnet (QHM) states formed in monolayer graphene's N=0 Landau level, we study the scattering of QHM magnons by gate-controlled junctions between states with different integer filling factors ν. For the ν=1|-1|1 geometry we find that magnons are weakly scattered by electric potential variation in the junction region, and that the scattering is chiral when the junction lacks a mirror symmetry. For the ν=1|0|1 geometry, we find that kinematic constraints completely block magnon transmission if the incident angle exceeds a critical value. Our results explain the suppressed nonlocal-voltage signals observed in the ν=1|0|1 case. We use our theory to propose that valley waves generated at ν=-1|1 junctions and magnons can be used in combination to probe the spin or valley flavor structure of QHM states at integer and fractional filling factors.

Current-Driven Magnetization Reversal in Orbital Chern Insulators

Graphene multilayers with flat moiré minibands can exhibit the quantized anomalous Hall effect due to the combined influence of spontaneous valley polarization and topologically nontrivial valley-projected bands. The sign of the Hall effect in these Chern insulators can be reversed either by applying an external magnetic field, or by driving a transport current through the system. We propose a current-driven mechanism whereby reversal occurs along lines in the (current I, magnetic-field B) control parameter space with slope dI/dB=(e/h)MA_{M}(1-γ^{2})/γ, where M is the magnetization, A_{M} is the moiré unit cell area, and γ<1 is the ratio of the chemical potential difference between valleys along a domain wall to the electrical bias eV.

Excitonic density wave and spin-valley superfluid in bilayer transition metal dichalcogenide

Artificial moiré superlattices in 2d van der Waals heterostructures are a new venue for realizing and controlling correlated electronic phenomena. Recently, twisted bilayer WSe₂ emerged as a new robust moiré system hosting a correlated insulator at moiré half-filling over a range of twist angle. In this work, we present a theory of this insulating state as an excitonic density wave due to intervalley electron–hole pairing. We show that exciton condensation is strongly enhanced by a van Hove singularity near the Fermi level. Our theory explains the remarkable sensitivity of the insulating gap to the vertical electric field. In contrast, the gap is weakly reduced by a perpendicular magnetic field, with quadratic dependence at low field. The different responses to electric and magnetic field can be understood in terms of pair-breaking versus non-pair-breaking effects in a BCS analog of the system. We further predict superfluid spin transport in this electrical insulator, which can be detected by optical spin injection and spatial-temporal imaging.

A correlated insulator has recently been observed in twisted bilayer WSe₂ moiré superlattices. Here, Bi and Fu present a theory and predict the insulating state to be an excitonic density wave as well as a spin-valley superfluid, which can be tested by optical pump-probe experiments.

Helical Edge States and Quantum Phase Transitions in Tetralayer Graphene

Helical conductors with spin-momentum locking are promising platforms for Majorana fermions. Here we report observation of two topologically distinct phases supporting helical edge states in charge neutral Bernal-stacked tetralayer graphene in Hall bar and Corbino geometries. As the magnetic field B_{⊥} and out-of-plane displacement field D are varied, we observe a phase diagram consisting of an insulating phase and two metallic phases, with 0, 1, and 2 helical edge states, respectively. These phases are accounted for by a theoretical model that relates their conductance to spin-polarization plateaus. Transitions between them arise from a competition among interlayer hopping, electrostatic and exchange interaction energies. Our work highlights the complex competing symmetries and the rich quantum phases in few-layer graphene.

A new class of nonreciprocal spin waves on the edges of 2D antiferromagnetic honeycomb nanoribbons

Antiferromagnetic two-dimensional (2D) materials are currently under intensive theoretical and experimental investigations in view of their potential applications in antiferromagnet-based magnonic and spintronic devices. Recent experimental studies revealed the importance of magnetic anisotropy and of Dzyaloshinskii-Moriya interactions (DMI) on the ordered ground state and the magnetic excitations in these materials. In this work we present a robust classical field theory approach to study the effects of anisotropy and the DMI on the edge and bulk spin waves in 2D antiferromagnetic nanoribbons. We predict the existence of a new class of nonreciprocal edge spin waves, characterized by opposite polarizations in counter-propagation. These novel edge spin waves are induced by the DMI and are fundamentally different from conventional nonreciprocal spin waves for which the polarization is independent of the propagation direction. We further analyze the effects of the edge structures on the magnetic excitations for these systems. In particular, we show that anisotropic bearded edge nanoribbons act as topologically trivial magnetic insulators with potentially interesting applications in magnonics. Our results constitute an important finding for current efforts seeking to establish unconventional magnonic devices utilizing spin wave polarization.

Discretized dynamics of exchange spin wave bulk and edge modes in honeycomb nanoribbons with armchair edge boundaries

We develop a field theory to study the dynamics of long wavelength exchange spin wave excitations on honeycomb nanoribbons characterized by armchair edge boundaries and the Néel antiferromagnetic ordering state. Appropriate boundary conditions are established by requiring that the bulk and edge spins precess with the same frequency for any given spin wave eigenmode in these systems. A set of characteristic boundary equations, common for bulk and edge spin wave modes, are hence derived. The equations of motion for the spin dynamics are then solved to determine the propagating and evanescent exchange spin wave modes. We obtain the expected discretized bulk spin waves spectrum due to the finite width of the nanoribbon. For an isotropic magnetic nanoribbon, the Dirac cone is reduced to a single linear dispersion curve due to this discretization. The number and wavelengths of allowed bulk modes for isotropic and anisotropic nanoribbons are determined from the derived characteristic boundary equations. As witnessed by our numerical results for different examples it is shown that the characteristics of these modes depend on the width of the nanoribbon and its antiferromagnetic anisotropy. Further, anisotropic nanoribbons, even those with the slightest anisotropy, present evanescent modes with non-linear dispersion relations. The spatial variation of the amplitudes of the evanescent exchange spin waves across the finite widths of the nanoribbons, is found to be strongly dependent on the system magnetic anisotropy and its width. The developed theoretical approach is general and can be applied for nanoribbons with all types of boundary edges.

Asymmetric dynamics of edge exchange spin waves in honeycomb nanoribbons with zigzag and bearded edge boundaries

We report on the theoretical prediction of asymmetric edge spin waves, propagating in opposite directions at the boundaries of antiferromagnetic honeycomb nanoribbons with zigzag and bearded edges. The simultaneous propagation of edge spin waves along the same direction on both edges of the nanoribbons is forbidden. These asymmetric exchange spin waves at the edge boundaries are analogous to the nonreciprocal surface spin waves reported in magnetic thin films. Their existence is related to the nontrivial symmetry underlying these nanoribbons types. The discretized bulk and the edge exchange spin waves are calculated for the long wavelength part of the nanoribbon Brillouin zone (BZ), using the classical field spin wave theory and notably appropriate boundary conditions. In the absence of an external magnetic field in our study, the asymmetric edge spin waves propagate with equal frequencies and along opposite directions. The edge spin waves are characterized by linear dispersion relations for magnetically isotropic nanoribbons. For magnetically anisotropic nanoribbons, our calculations show that the energy gap between the edge and bulk spin waves is enhanced for both types of zigzag and bearded nanoribbons. The large energy gap separates the edge modes from overlapping the bulk ones. Also, we explain why our results for anisotropic zigzag nanoribbons go beyond previous studies based on a quantum approach in the linear spin wave approximation.