Showing papers on "Landau quantization published in 2021"

Correlation-driven topological phases in magic-angle twisted bilayer graphene

Abstract: Magic-angle twisted bilayer graphene (MATBG) exhibits a range of correlated phenomena that originate from strong electron-electron interactions. These interactions make the Fermi surface highly susceptible to reconstruction when ±1, ±2 and ±3 electrons occupy each moire unit cell, and lead to the formation of various correlated phases1-4. Although some phases have been shown to have a non-zero Chern number5,6, the local microscopic properties and topological character of many other phases have not yet been determined. Here we introduce a set of techniques that use scanning tunnelling microscopy to map the topological phases that emerge in MATBG in a finite magnetic field. By following the evolution of the local density of states at the Fermi level with electrostatic doping and magnetic field, we create a local Landau fan diagram that enables us to assign Chern numbers directly to all observed phases. We uncover the existence of six topological phases that arise from integer fillings in finite fields and that originate from a cascade of symmetry-breaking transitions driven by correlations7,8. These topological phases can form only for a small range of twist angles around the magic angle, which further differentiates them from the Landau levels observed near charge neutrality. Moreover, we observe that even the charge-neutrality Landau spectrum taken at low fields is considerably modified by interactions, exhibits prominent electron-hole asymmetry, and features an unexpectedly large splitting between zero Landau levels (about 3 to 5 millielectronvolts). Our results show how strong electronic interactions affect the MATBG band structure and lead to correlation-enabled topological phases.

Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene

Abstract: Flat bands in magic-angle twisted bilayer graphene (MATBG) have recently emerged as a rich platform to explore strong correlations1, superconductivity2–5 and magnetism3,6,7. However, the phases of MATBG in a magnetic field and what they reveal about the zero-field phase diagram remain relatively uncharted. Here we report a rich sequence of wedge-like regions of quantized Hall conductance with Chern numbers C = ±1, ±2, ±3 and ±4, which nucleate from integer fillings of the moire unit cell v = ±3, ±2, ±1 and 0, respectively. We interpret these phases as spin- and valley-polarized many-body Chern insulators. The exact sequence and correspondence of the Chern numbers and filling factors suggest that these states are directly driven by electronic interactions, which specifically break the time-reversal symmetry in the system. We further study the yet unexplored higher-energy dispersive bands with a Rashba-like dispersion. The analysis of Landau-level crossings enables a parameter-free comparison to a newly derived ‘magic series’ of level crossings in a magnetic field and provides constraints on the parameters of the Bistritzer–MacDonald MATBG Hamiltonian. Overall, our data provide direct insights into the complex nature of symmetry breaking in MATBG and allow for the quantitative tests of the proposed microscopic scenarios for its electronic phases. In magic-angle twisted bilayer graphene, topological Chern bands that are driven by electron–electron interactions appear at all the integer fillings of the moire unit cell. The Rashba-like higher-energy bands also show Landau-level crossings.

Signatures of Wigner crystal of electrons in a monolayer semiconductor.

Abstract: When the Coulomb repulsion between electrons dominates over their kinetic energy, electrons in two-dimensional systems are predicted to spontaneously break continuous-translation symmetry and form a quantum crystal1. Efforts to observe2–12 this elusive state of matter, termed a Wigner crystal, in two-dimensional extended systems have primarily focused on conductivity measurements on electrons confined to a single Landau level at high magnetic fields. Here we use optical spectroscopy to demonstrate that electrons in a monolayer semiconductor with density lower than 3 × 1011 per centimetre squared form a Wigner crystal. The combination of a high electron effective mass and reduced dielectric screening enables us to observe electronic charge order even in the absence of a moire potential or an external magnetic field. The interactions between a resonantly injected exciton and electrons arranged in a periodic lattice modify the exciton bandstructure so that an umklapp resonance arises in the optical reflection spectrum, heralding the presence of charge order13. Our findings demonstrate that charge-tunable transition metal dichalcogenide monolayers14 enable the investigation of previously uncharted territory for many-body physics where interaction energy dominates over kinetic energy. The signature of a Wigner crystal—the analogue of a solid phase for electrons—is observed via the optical reflection spectrum in a monolayer transition metal dichalcogenide.

Phases of the ( 2+1 ) Dimensional SO(5) Nonlinear Sigma Model with Topological Term

Abstract: We use the half-filled zeroth Landau level in graphene as a regularization scheme to study the physics of the SO(5) nonlinear sigma model subject to a Wess-Zumino-Witten topological term in 2+1 dimensions. As shown by Ippoliti et al. [Phys. Rev. B 98, 235108 (2019)PRBMDO2469-995010.1103/PhysRevB.98.235108], this approach allows for negative sign free auxiliary field quantum Monte Carlo simulations. The model has a single free parameter U_{0} that monitors the stiffness. Within the parameter range accessible to negative sign free simulations, we observe an ordered phase in the large U_{0} or stiff limit. Remarkably, upon reducing U_{0} the magnetization drops substantially, and the correlation length exceeds our biggest system sizes, accommodating 100 flux quanta. The implications of our results for deconfined quantum phase transitions between valence bond solids and antiferromagnets are discussed.

Singular flat bands

Abstract: We review recent progresses in the study of flat band systems, especially focusing on the fundamental physics related to the singularity of the flat band’s Bloch wave functions. We first explain th...

Magnetic-field-induced robust zero Hall plateau state in MnBi2Te4 Chern insulator.

Abstract: The intrinsic antiferromagnetic topological insulator MnBi2Te4 provides an ideal platform for exploring exotic topological quantum phenomena. Recently, the Chern insulator and axion insulator phases have been realized in few-layer MnBi2Te4 devices at low magnetic field regime. However, the fate of MnBi2Te4 in high magnetic field has never been explored in experiment. In this work, we report transport studies of exfoliated MnBi2Te4 flakes in pulsed magnetic fields up to 61.5 T. In the high-field limit, the Chern insulator phase with Chern number C = −1 evolves into a robust zero Hall resistance plateau state. Nonlocal transport measurements and theoretical calculations demonstrate that the charge transport in the zero Hall plateau state is conducted by two counter-propagating edge states that arise from the combined effects of Landau levels and large Zeeman effect in strong magnetic fields. Our result demonstrates the intricate interplay among intrinsic magnetic order, external magnetic field, and nontrivial band topology in MnBi2Te4. The antiferromagnetic topological insulator MnBi2Te4 exhibits Chern and axion insulator phases at low magnetic field; however, its behaviour in high magnetic field has remained unexplored. Here, using transport measurements at high magnetic field, the authors report a zero Hall plateau composed of two counter-propagating edge channels.

Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures

Abstract: The use of ultra-low temperature cooling and of high hydrostatic pressure techniques has significantly expanded our understanding of the two-dimensional electron gas confined to GaAs/AlGaAs structures. This chapter reviews a selected set of experiments employing these specialized techniques in the study of the fractional quantum Hall states and of the charged ordered phases, such as the reentrant integer quantum Hall states and the quantum Hall nematic. Topics discussed include a successful cooling technique used, novel odd denominator fractional quantum Hall states, new transport results on even denominator fractional quantum Hall states and on reentrant integer quantum Hall states, and phase transitions observed in half-filled Landau levels.

Large- N theory of critical Fermi surfaces

Abstract: Critical Fermi surfaces appear in many physical systems, including the half-filled Landau level, and certain spin liquids. Many theories have studied the nonquasiparticle excitations near the Fermi surface, and possible instabilities to pairing or density wave orders, but without a fully systematic method. Here, the authors study an ensemble of self-averaging theories with random coupling constants, and obtain a controlled large-$N$ expansion.

A tunable Fabry-Pérot quantum Hall interferometer in graphene

Abstract: Electron interferometry with quantum Hall (QH) edge channels in semiconductor heterostructures can probe and harness the exchange statistics of anyonic excitations. However, the charging effects present in semiconductors often obscure the Aharonov–Bohm interference in QH interferometers and make advanced charge-screening strategies necessary. Here we show that high-mobility monolayer graphene constitutes an alternative material system, not affected by charging effects, for performing Fabry–Perot QH interferometry in the integer QH regime. In devices equipped with gate-tunable quantum point contacts acting on the edge channels of the zeroth Landau level, we observe—in agreement with theory—high-visibility Aharonov–Bohm interference widely tunable through electrostatic gating or magnetic fields. A coherence length of 10 μm at a temperature of 0.02 K allows us to further achieve coherently coupled double Fabry–Perot interferometry. In future, QH interferometry with graphene devices may enable investigations of anyonic excitations in fractional QH states. Similar to optical waves, electrons can also interfere, but they require high-quality devices with minimal scattering for an experimental observation of this effect. An interferometer based on a single sheet of graphene provides an alternative to the more standard semiconductor devices and may in future enable access to exotic quantum effects, such as anyon braiding.

Fractional edge reconstruction in integer quantum Hall phases

Abstract: Protected edge modes are the cornerstone of topological states of matter. The simplest example is provided by the integer quantum Hall state at Landau level filling unity, which should feature a single chiral mode carrying electronic excitations. In the presence of a smooth confining potential it was hitherto believed that this picture may only be partially modified by the appearance of additional counterpropagating integer-charge modes. Here, we demonstrate the breakdown of this paradigm: The system favors the formation of edge modes supporting fractional excitations. This accounts for previous observations, and leads to additional predictions amenable to experimental tests.

Topological phases of quantized light.

Abstract: Topological photonics is an emerging research area that focuses on the topological states of classical light. Here we reveal the topological phases that are intrinsic to the quantum nature of light, i.e. solely related to the quantized Fock states and the inhomogeneous coupling strengths between them. The Hamiltonian of two cavities coupled with a two-level atom is an intrinsic one-dimensional Su-Schriefer-Heeger model of Fock states. By adding another cavity, the Fock-state lattice is extended to two dimensions with a honeycomb structure, where the strain due to the inhomogeneous coupling strengths of the annihilation operator induces a Lifshitz topological phase transition between a semimetal and three band insulators within the lattice. In the semimetallic phase, the strain is equivalent to a pseudomagnetic field, which results in the quantization of the Landau levels and the valley Hall effect. We further construct an inhomogeneous Fock-state Haldane model where the topological phases can be characterized by the topological markers. With d cavities being coupled to the atom, the lattice is extended to d - 1 dimensions without an upper limit. In this study we demonstrate a fundamental distinction between the topological phases in quantum and classical optics and provide a novel platform for studying topological physics in dimensions higher than three.

Hidden wave function of twisted bilayer graphene: The flat band as a Landau level

Abstract: We study zero-energy states of the chirally symmetric continuum model (CS-CM) of twisted bilayer graphene. The zero-energy state obeys the Dirac equation on a torus in the external non-Abelian magnetic field. These zero-energy states could form a flat band---a band where the energy is constant across the Brillouin zone. We prove that the existence of the flat band implies that the wave function of any state from the flat band has a zero and vice versa. We found a hidden flat band of unphysical states in the CS-CM that has a pole instead of a zero. Our main result is that in the basis of the flat band and hidden wave functions the flat band could be interpreted as a Landau level in the external magnetic field. From that interpretation we show the existence of extra flat bands in the magnetic field.

Topological charge density waves at half-integer filling of a moiré superlattice

Abstract: At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and Hofstadter bands; in both cases, a large magnetic field is required to engineer the underlying flat band. The recent observation of quantum anomalous Hall effects (QAH) in narrow band moire systems has led to the theoretical prediction that such phases may be realized even at zero magnetic field. Here we report the experimental observation of insulators with Chern number $C=1$ in the zero magnetic field limit at $ u=3/2$ and $7/2$ filling of the moire superlattice unit cell in twisted monolayer-bilayer graphene (tMBG). Our observation of Chern insulators at half-integer values of $ u$ suggests spontaneous doubling of the superlattice unit cell, in addition to spin- and valley-ferromagnetism. This is confirmed by Hartree-Fock calculations, which find a topological charge density wave ground state at half filling of the underlying $C=2$ band, in which the Berry curvature is evenly partitioned between occupied and unoccupied states. We find the translation symmetry breaking order parameter is evenly distributed across the entire folded superlattice Brillouin zone, suggesting that the system is in the flat band, strongly correlated limit. Our findings show that the interplay of quantum geometry and Coulomb interactions in moire bands allows for topological phases at fractional superlattice filling that spontaneously break time-reversal symmetry, a prerequisite in pursuit of zero magnetic field phases harboring fractional statistics as elementary excitations or bound to lattice dislocations.

Dual Haldane sphere and quantized band geometry in chiral multifold fermions

Abstract: We show that the chiral multifold fermions present a dual Haldane sphere problem in momentum space. Owing to the Berry monopole at the degenerate point, a dual Landau level emerges in the trace of quantum metric, with which a quantized geometric invariant is defined through a surface integration. We further demonstrate potential manifestations in the measurable, physical observables. With a lower bound derived for the finite spread of Wannier functions, anomalous phase coherence is identified accordingly for the flat band superconductivity. We briefly comment on the stability of these results under perturbations. Potential experimental probes of the quantum metric are also discussed.

Landau Levels as a Probe for Band Topology in Graphene Moire Superlattices

Abstract: We propose Landau levels as a probe for the topological character of electronic bands in two-dimensional moir\'e superlattices. We consider two configurations of twisted double bilayer graphene (TDBG) that have very similar band structures, but show different valley Chern numbers of the flat bands. These differences between the $AB\text{\ensuremath{-}}AB$ and $AB\text{\ensuremath{-}}BA$ configurations of TDBG clearly manifest as different Landau level sequences in the Hofstadter butterfly spectra calculated using the tight-binding model. The Landau level sequences are explained from the point of view of the distribution of orbital magnetization in momentum space that is governed by the rotational ${C}_{2}$ and time-reversal $\mathcal{T}$ symmetries. Our results can be readily extended to other twisted graphene multilayers and $h\text{\ensuremath{-}}\mathrm{BN}$/graphene heterostructures thus establishing the Hofstadter butterfly spectra as a powerful tool for detecting the nontrivial valley band topology.

Light-Matter Interactions in Synthetic Magnetic Fields: Landau-Photon Polaritons.

Abstract: We study light-matter interactions in two-dimensional photonic systems in the presence of a spatially homogeneous synthetic magnetic field for light. Specifically, we consider one or more two-level emitters located in the bulk region of the lattice, where for increasing magnetic field the photonic modes change from extended plane waves to circulating Landau levels. This change has a drastic effect on the resulting emitter-field dynamics, which becomes intrinsically non-Markovian and chiral, leading to the formation of strongly coupled Landau-photon polaritons. The peculiar dynamical and spectral properties of these quasiparticles can be probed with state-of-the-art photonic lattices in the optical and the microwave domain and may find various applications for the quantum simulation of strongly interacting topological models.

Spin-valley locking and bulk quantum Hall effect in a noncentrosymmetric Dirac semimetal BaMnSb2.

Abstract: Spin-valley locking in monolayer transition metal dichalcogenides has attracted enormous interest, since it offers potential for valleytronic and optoelectronic applications. Such an exotic electronic state has sparsely been seen in bulk materials. Here, we report spin-valley locking in a Dirac semimetal BaMnSb2. This is revealed by comprehensive studies using first principles calculations, tight-binding and effective model analyses, angle-resolved photoemission spectroscopy measurements. Moreover, this material also exhibits a stacked quantum Hall effect (QHE). The spin-valley degeneracy extracted from the QHE is close to 2. This result, together with the Landau level spin splitting, further confirms the spin-valley locking picture. In the extreme quantum limit, we also observed a plateau in the z-axis resistance, suggestive of a two-dimensional chiral surface state present in the quantum Hall state. These findings establish BaMnSb2 as a rare platform for exploring coupled spin and valley physics in bulk single crystals and accessing 3D interacting topological states. Valley dependent spin polarization called spin-valley locking appears in absence of magnetism but it is limited to rare examples of transition metal dichalcogenides. Here, the authors report evidence of spin-valley locking and stacked quantum Hall effect in a bulk Dirac semimetal BaMnSb2.

Flat bands, strains, and charge distribution in twisted bilayer h − BN

Abstract: We study the effect of twisting on bilayer $h\text{\ensuremath{-}}\mathrm{BN}$. The effect of lattice relaxation is included; we look at the electronic structure, piezoelectric charges, and spontaneous polarization. We show that the electronic structure without lattice relaxation shows a set of extremely flat in-gap states similar to Landau levels, where the spacing scales with twist angle. With lattice relaxation we still have flat bands, but now the spectrum becomes independent of twist angle for sufficiently small angles. We describe in detail the nature of the bands and we study appropriate continuum models, at the same time explaining the structure of the in-gap states. We find that even though the spectra for both parallel and antiparallel alignment are very similar, the spontaneous polarization effects only occur for parallel alignment. We argue that this suggests a large interlayer hopping between boron and nitrogen.

Pole and screening masses of neutral pions in a hot and magnetized medium: A comprehensive study in the Nambu-Jona-Lasinio model

Abstract: In this work, we investigate not only the pole masses but also the screening masses of neutral pions at finite temperature and magnetic field by utilizing the random phase approximation (RPA) approach in the framework of the two-flavor Nambu--Jona-Lasinio model. And two equivalent formalisms in the presence of a magnetic field, i.e., the Landau level representation and the proper-time representation (PTR), are applied to obtain the corresponding analytical expressions of the polarization functions (except the expressions for the pole masses in the PTR). In order to evaluate the applicable region of the low-momentum expansion (LME), we compare the numerical results within the full RPA (FRPA) with those within the reduced RPA, i.e., the RPA in the LME. It is confirmed that the pole masses of ${\ensuremath{\pi}}^{0}$ in the FRPA suffer a sudden mass jump at the Mott transition temperature when in the presence of external magnetic field, the Mott transition temperature is catalyzed by the magnetic field. And by analyzing the behaviors of the directional sound velocities of ${\ensuremath{\pi}}^{0}$, which are associated with the breaking of the Lorentz invariance by the heat bath and the magnetic field, we clarify the two problems existing in previous literatures: one is that the transverse sound velocities in the medium are always larger than unity and thus violate the law of causality on account of the noncovariant regularization scheme, and the other is that the longitudinal sound velocities are identically equal unity at finite temperature on account of the limitation of the derivative expansion method used.

Relations between topology and the quantum metric for Chern insulators

Abstract: We investigate relations between topology and the quantum metric of two-dimensional Chern insulators. The quantum metric is the Riemannian metric defined on a parameter space induced from quantum states. Similar to the Berry curvature, the quantum metric provides a geometrical structure associated to quantum states. We consider the volume of the parameter space measured with the quantum metric, which we call the quantum volume of the parameter space. We establish an inequality between the quantum volume of the Brillouin zone and that of the twist-angle space. Exploiting this inequality and the inequality between the Chern number and the quantum volume, we investigate how the quantum volume can be used as a good measure to infer the Chern number. The inequalities are found to be saturated for fermions filling Landau levels. Through various concrete models, we elucidate conditions when the quantum volume gives a good estimate of the topology of the system.

Chiral Magic-Angle Twisted Bilayer Graphene in a Magnetic Field: Landau Level Correspondence, Exact Wavefunctions and Fractional Chern Insulators

Abstract: We show that the flat bands in the chiral model of magic-angle twisted bilayer graphene remain exactly flat in the presence of a perpendicular magnetic field. This is shown by an exact mapping between the model and the lowest Landau level wavefunctions at an effective magnetic field, in which the external field is either augmented or reduced by one flux quantum per unit cell. When the external field reaches one flux quantum per unit cell, the model exhibits a topological phase transition. These findings allow us to analyze a Jain-series of Fractional Chern Insulators states in the exactly flat band, and to point out an unconventional dependence of the energy gap on the magnetic field.

Rashba valleys and quantum Hall states in few-layer black arsenic.

Abstract: Exciting phenomena may emerge in non-centrosymmetric two-dimensional electronic systems when spin-orbit coupling (SOC)1 interplays dynamically with Coulomb interactions2,3, band topology4,5 and external modulating forces6-8. Here we report synergetic effects between SOC and the Stark effect in centrosymmetric few-layer black arsenic, which manifest as particle-hole asymmetric Rashba valley formation and exotic quantum Hall states that are reversibly controlled by electrostatic gating. The unusual findings are rooted in the puckering square lattice of black arsenic, in which heavy 4p orbitals form a Brillouin zone-centred Γ valley with pz symmetry, coexisting with doubly degenerate D valleys of px origin near the time-reversal-invariant momenta of the X points. When a perpendicular electric field breaks the structure inversion symmetry, strong Rashba SOC is activated for the px bands, which produces spin-valley-flavoured D± valleys paired by time-reversal symmetry, whereas Rashba splitting of the Γ valley is constrained by the pz symmetry. Intriguingly, the giant Stark effect shows the same px-orbital selectiveness, collectively shifting the valence band maximum of the D± Rashba valleys to exceed the Γ Rashba top. Such an orchestrating effect allows us to realize gate-tunable Rashba valley manipulations for two-dimensional hole gases, hallmarked by unconventional even-to-odd transitions in quantum Hall states due to the formation of a flavour-dependent Landau level spectrum. For two-dimensional electron gases, the quantization of the Γ Rashba valley is characterized by peculiar density-dependent transitions in the band topology from trivial parabolic pockets to helical Dirac fermions.

Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering

Abstract: Starting from the Luttinger model for the band structure of GaAs, we derive an effective theory that describes the coupling of the fractional quantum Hall (FQH) system with photons in resonant Raman scattering experiments. Our theory is applicable in the regime when the energy of the photons $\omega_0$ is close to the energy gap $E_G$, but $|\omega_0-E_G|$ is much larger than the energy scales of the quantum Hall problem. In the literature, it is often assumed that Raman scattering measures the dynamic structure factor $S(\omega,\mathbf{k})$ of the FQH. However, in this paper, we find that the light scattering spectrum measured in the experiments are proportional to the spectral densities of a pair of operators which we identified with the spin-2 components of the kinetic part of the stress tensor. In contrast with the dynamic structure factor, these spectral densities do not vanish in the long-wavelength limit $k\to0$. We show that Raman scattering with circularly polarized light can measure the spin of the magnetoroton excitation in the FQH system. We give an explicit expression for the kinetic stress tensor that works on any Landau level and which can be used for numerical calculations of the spectral densities that enter the Raman scattering amplitudes. We propose that Raman scattering provides a way to probe the bulk of the $ u=5/2$ quantum Hall state to determine its nature.

Experimental Determination of the Energy per Particle in Partially Filled Landau Levels

Abstract: We describe an experimental technique to measure the chemical potential μ in atomically thin layered materials with high sensitivity and in the static limit. We apply the technique to a high quality graphene monolayer to map out the evolution of μ with carrier density throughout the N=0 and N=1 Landau levels at high magnetic field. By integrating μ over filling factor ν, we obtain the ground state energy per particle, which can be directly compared to numerical calculations. In the N=0 Landau level, our data show exceptional agreement with numerical calculations over the whole Landau level without adjustable parameters as long as the screening of the Coulomb interaction by the filled Landau levels is accounted for. In the N=1 Landau level, a comparison between experimental and numerical data suggests the importance of valley anisotropic interactions and reveals a possible presence of valley-textured electron solids near odd filling.

Quantum Hall phases emerging from atom–photon interactions

Abstract: We reveal the emergence of quantum Hall phases, topological edge states, spectral Landau levels, and Hofstadter butterfly spectra in the two-particle Hilbert space of an array of periodically spaced two-level atoms coupled to a waveguide (waveguide quantum electrodynamics). While the topological edge states of photons require fine-tuned spatial or temporal modulations of the parameters to generate synthetic magnetic fields and the quantum Hall effect, here we demonstrate that a synthetic magnetic field can be self-induced solely by atom–photon interactions. The fact that topological order can be self-induced in what is arguably the simplest possible quantum structure shows the richness of these waveguide quantum electrodynamics systems. We believe that our findings will advance several research disciplines including quantum optics, many-body physics, and nonlinear topological photonics, and that it will set an important reference point for the future experiments on qubit arrays and quantum simulators.

Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy

Abstract: The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded the concept of topological order in physics bringing into focus the intimate relation between the "bulk" topology and the edge states. The QH effect in graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials. However, the broken-symmetry edge states have eluded spatial measurements. In this article, we spatially map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of [Formula: see text] across the quantum Hall edge boundary using high-resolution atomic force microscopy (AFM) and show a gapped ground state proceeding from the bulk through to the QH edge boundary. Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moire superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.

Di-lepton production from a single photon in strong magnetic fields: vacuum dichroism

Abstract: We study di-lepton production from a single photon in the presence of a strong constant magnetic field. By the use of the Ritus-basis formalism, we analytically evaluate the photon-to-di-lepton conversion vertex with fully taking into account the non-perturbative interactions between the produced fermions and the strong magnetic field. We show that the di-lepton spectrum becomes anisotropic with respect to the magnetic-field direction and depends on the photon polarization as a manifestation of the vacuum dichroism in a strong magnetic field. According to the energy conservation in the presence of the Landau quantization, not only the transverse momentum of the produced fermions but also the longitudinal momentum is discretized, and the di-lepton spectrum exhibits spike structures as functions of the incident photon energy and the magnetic field strength. We also show that the di-lepton production is strictly prohibited for massless fermions in the lowest Landau levels as an analogue of the so-called helicity suppression.

Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction

Abstract: We introduce a unique model for a fermion-antifermion pair interacting via Dirac oscillator coupling in the presence of an external uniform magnetic field. This model is based on an exact solution of the corresponding form of a fully-covariant two-body Dirac equation (one-time). The dynamic symmetry of the system allows to study in $$2+1$$ dimensions and we choose the interaction of the particles with the external uniform magnetic field in the symmetric gauge. The corresponding equation leads $$4\times 4$$ dimensional matrix equation for such a static composite system. For spin antisymmetric state of the fermion-antifermion pair, we perform an exact solution of the matrix equation and obtain relativistic Landau levels of a fermion-antifermion pair interacting via Dirac oscillator coupling. The results show that such a composite system behaves like a single relativistic quantum oscillator carrying total rest mass of the particles. We discuss several interesting features of this system and show that the obtained energy spectrum agrees well with the previously announced results for one-body systems. We think that the introduced model in this manuscript has a great potential for many theoretical and experimental applications.