Cyclotron Orbit Research Articles

Probing the tunable multi-cone band structure in Bernal bilayer graphene

Bernal bilayer graphene (BLG) offers a highly flexible platform for tuning the band structure, featuring two distinct regimes. One is a tunable band gap induced by large displacement fields. Another is a gapless metallic band occurring at low fields, featuring rich fine structure consisting of four linearly dispersing Dirac cones and van Hove singularities. Even though BLG has been extensively studied experimentally, the evidence of this band structure is still elusive, likely due to insufficient energy resolution. Here, we use Landau levels as markers of the energy dispersion and analyze the Landau level spectrum in a regime where the cyclotron orbits of electrons or holes in momentum space are small enough to resolve the distinct mini Dirac cones. We identify the presence of four Dirac cones and map out topological transitions induced by displacement field. By clarifying the low-energy properties of BLG bands, these findings provide a valuable addition to the toolkit for graphene electronics.

Evidence for unfolded Fermi surfaces in the charge-density-wave state of kagome metal FeGe revealed by de Haas–van Alphen effect

The antiferromagnetic kagome lattice compound FeGe has been revealed to host an emergent charge-density-wave (CDW) state which manifests complex interplay between the spin, charge, and lattice degrees of freedom. Here, we present a comprehensive study of the de Haas–van Alphen effect by measuring torque magnetometry under magnetic fields up to 45.2 T to map Fermi surfaces in this unusual CDW state. For a field along the c direction, we resolve four cyclotron orbits, with the largest one roughly corresponding to the area of the 2×2 folded Brillouin zone. Three smaller orbits are characterized by light effective cyclotron masses in the range of (0.18–0.30)me. Angle-resolved measurements identify one Fermi surface segment with weak anisotropy. Combined with band structure calculations, our results suggest that features of unfolded Fermi surfaces are robust against CDW reconstruction, corroborating the unconventional effect of a short-ranged CDW on the electronic structure. Published by the American Physical Society 2024

De Haas-van Alphen spectroscopy and magnetic breakdown in moiré graphene.

Quantum oscillations originating from the quantization of electron cyclotron orbits provide sensitive diagnostics of electron bands and interactions. We report on nanoscale imaging of the thermodynamic magnetization oscillations caused by the de Haas-van Alphen effect in moiré graphene. Scanning by means of superconducting quantum interference device (SQUID)-on-tip in Bernal bilayer graphene crystal axis-aligned to hexagonal boron nitride reveals large magnetization oscillations with amplitudes reaching 500 Bohr magneton per electron in weak magnetic fields, unexpectedly low frequencies, and high sensitivity to superlattice filling fraction. The oscillations allow us to reconstruct the complex band structure, revealing narrow moiré bands with multiple overlapping Fermi surfaces separated by unusually small momentum gaps. We identified sets of oscillations that violate the textbook Onsager Fermi surface sum rule, signaling formation of broad-band particle-hole superposition states induced by coherent magnetic breakdown.

Andreev reflection imaging and longitudinal shift of pseudospin-1 fermions in two-dimensional materials

In this work, the transverse magnetic focusing of pseudospin-1 fermions in two-dimensional materials with a superconducting contact is studied. The transmission coefficient and Andreev reflection coefficient from injector lead to collector lead are calculated based on the Landauer–Büttiker formula combined with the non-equilibrium Green's function method. The local state density diagrams of the electron and hole transmission in the center region are given, which provide a complete image of the ballistic electron–hole cyclotron orbits. Using these images, the positive longitudinal shift in Andreev reflection of the pseudospin-1 fermion can be obviously seen. Furthermore, it is found that the total offset is proportional to the number of Andreev reflection occurrence. This setup provides the possibility of detecting this shift experimentally.

Phonon-mediated magneto-resonances in biased graphene layers

We explore the non-equilibrium transport regime in graphene using a large dc current in combination with a perpendicular magnetic field. The strong in-plane Hall field generated in the graphene channel results in Landau levels that are tilted spatially. The energy of cyclotron orbits in the bulk varies as a function of the spatial position of the guiding center, enabling us to observe a series of compelling features. While Shubnikov–de Haas oscillations are predictably suppressed in the presence of the Hall field, a set of fresh magneto resistance oscillations emerge near the charge neutrality point as a function of dc current. Two branches of oscillations with linear dispersions are evident as we vary carrier density and dc current, the velocities of which closely resemble the transverse acoustic (TA) and longitudinal acoustic (LA) phonon modes, suggestive of phonon-assisted intra-Landau level transitions between adjacent cyclotron orbits. Our results offer unique possibilities to explore non-equilibrium phenomena in two-dimensional materials and van der Waals heterostructures.

Manipulating directional flow in a two-dimensional photonic quantum walk under a synthetic magnetic field

Matter transport is a fundamental process in nature. Understanding and manipulating flow in a synthetic media often have rich implications for modern device design. Here we experimentally demonstrate directional transport of photons in a two-dimensional quantum walk, where the light propagation is highly tunable through dissipation and synthetic magnetic flux. The directional flow hereof underlies the emergence of the non-Hermitian skin effect, with its orientation continuously adjustable through the photon-loss parameters. By contrast, the synthetic magnetic flux originates from an engineered geometric phase, which, by inducing localized cyclotron orbits, suppresses the bulk flow through magnetic confinement. We further demonstrate how the directional flow and synthetic flux impact the dynamics of the Floquet topological edge modes along an engineered boundary. Our results exemplify an intriguing strategy for engineering directed light transport, highlighting the interplay of non-Hermiticity and gauge fields in synthetic systems of higher dimensions.

Bloch oscillations in moiré flat band systems

Bloch oscillations of wave packets in moiré flat band systems are investigated. We find that the real space trajectories and group velocity of wave packet undergo Bloch oscillations in the moiré flat band. It is shown that the Bloch dynamics is affected significantly by the magnitude and orientation of an applied in-plane electric field. In the presence of both external perpendicular magnetic field and in-plane electric field, confinement and de-confinement of cyclotron orbits occur which strongly depend on the relative strength of the applied fields.

Chiral edge dynamics and quantum Hall physics in synthetic dimensions with an atomic erbium Bose-Einstein condensate

Quantum Hall physics is at the heart of research on both matter and artificial systems, such as cold atomic gases, with nontrivial topological order. We report on the observation of a chiral edge current by transferring atomic wave packets simultaneously to opposite edges of a synthetic Hall system realized in the two-dimensional state space formed by one spatial and one synthetic dimension encoded in the $J=6$ electronic spin of erbium atoms. To characterize the system, the Hall drift of the employed atomic Bose-Einstein condensate in the lowest Landau-like level is determined. The topological properties are verified by determining the local Chern marker, and upon performing low-lying excitations both cyclotron and skipping orbits are observed in the bulk and edges, respectively. Future prospects include studies of novel topological phases in cold-atom systems.

The thickness dependence of quantum oscillations in ferromagnetic Weyl metal SrRuO3

In a thin Weyl semimetal, a thickness dependent Weyl-orbit quantum oscillation was proposed to exist, originating from a nonlocal cyclotron orbit via electron tunnelings between top and bottom Fermi-arc surface states. Here, magneto-transport measurements were carried out on untwinned Weyl metal SrRuO3 thin films. In particular, quantum oscillations with a frequency Fs1 ≈ 30 T were identified, corresponding to a small Fermi pocket with a light effective mass. Its oscillation amplitude appears to be at maximum for thicknesses in a range of 10 to 20 nm, and the phase of oscillation exhibits a systematic change with film thickness. The constructed Landau fan diagram shows an unusual concave downward curvature in the 1/μ0Hn-n curve, where n is the Landau level index. From thickness and field-orientation dependence, the Fs1 oscillation is attributed to be of surface origin. Those findings can be understood within the framework of the Weyl-orbit quantum oscillation effect with non-adiabatic corrections.

The anatomy of Boris type solvers and the Lie operator formalism for deriving large time-step magnetic field integrators

This work gives a Lie operator derivation of various Boris solvers via a detailed study of trajectory errors in a constant magnetic field. These errors in the gyrocenter location and the gyroradius are the foundational basis for why Boris solvers existed, independent of any finite-difference schemes. This work shows that there are two distinct ways of eliminating these errors so that the trajectory of a charged particle in a constant magnetic field is exactly on the cyclotron orbit. One way reproduces the known second-order symmetric Boris solver. The other yields a previously unknown, but also on-orbit solver, not derivable from finite-difference schemes. By revisiting some historical calculations, it is found that many publications do not distinguish the poorly behaved leap-frog Boris solver from the symmetric second-order Boris algorithm. This symmetric second-order Boris solver's trajectory is much more accurate and remains close to the exact orbit in a combined nonuniform electric and magnetic field at time-steps greater than the cyclotron period. Finally, this operator formalism showed that Buneman's cycloid fitting scheme is mathematically identical to Boris' on-orbit solver and that Boris' E-B splitting is unnecessary.

Boundary conductance in macroscopic bismuth crystals

The interface between a solid and vacuum can become electronically distinct from the bulk. This feature, encountered in the case of quantum Hall effect, has a manifestation in insulators with topologically protected metallic surface states. Non-trivial Berry curvature of the Bloch waves or periodically driven perturbation are known to generate it. Here, by studying the angle-dependent magnetoresistance in prismatic bismuth crystals of different shapes, we detect a robust surface contribution to electric conductivity when the magnetic field is aligned parallel to a two-dimensional boundary between the three-dimensional crystal and vacuum. The effect is absent in antimony, which has an identical crystal symmetry, a similar Fermi surface structure and equally ballistic carriers, but an inverted band symmetry and a topological invariant of opposite sign. Our observation confirms that the boundary interrupting the cyclotron orbits remains metallic in bismuth, which is in agreement with what was predicted by Azbel decades ago. However, the absence of the effect in antimony indicates an intimate link between band symmetry and this boundary conductance.

Cyclotron dynamics of a Bose—Einstein condensate in a quadruple-well potential with synthetic gauge fields

We investigate the cyclotron dynamics of Bose-Einstein condensate (BEC) in a quadruple-well potential with synthetic gauge fields. We use laser-assisted tunneling to generate large tunable effective magnetic fields for BEC. The mean position of BEC follows an orbit that simulated the cyclotron orbits of charged particles in a magnetic field. In the absence of atomic interaction, atom dynamics may exhibit periodic or quasi-periodic cyclotron orbits. In the presence of atomic interaction, the system may exhibit self-trapping, which depends on synthetic gauge fields and atomic interaction strength. In particular, the competition between synthetic gauge fields and atomic interaction leads to the generation of several discontinuous parameter windows for the transition to self-trapping, which is obviously different from that without synthetic gauge fields.

Anyonic Molecules in Atomic Fractional Quantum Hall Liquids: A Quantitative Probe of Fractional Charge and Anyonic Statistics

We study the quantum dynamics of massive impurities embedded in a strongly interacting two-dimensional atomic gas driven into the fractional quantum Hall (FQH) regime under the effect of a synthetic magnetic field. For suitable values of the atom-impurity interaction strength, each impurity can capture one or more quasi-hole excitations of the FQH liquid, forming a bound molecular state with novel physical properties. An effective Hamiltonian for such anyonic molecules is derived within the Born-Oppenheimer approximation, which provides renormalized values for their effective mass, charge and statistics by combining the finite mass of the impurity with the fractional charge and statistics of the quasi-holes. The renormalized mass and charge of a single molecule can be extracted from the cyclotron orbit that it describes as a free particle in a magnetic field. The anyonic statistics introduces a statistical phase between the direct and exchange scattering channels of a pair of indistinguishable colliding molecules, and can be measured from the angular position of the interference fringes in the differential scattering cross section. Implementations of such schemes beyond cold atomic gases are highlighted, in particular in photonic systems.

Quantizing viscous transport in bilayer graphene

The momentum transport in ultraclean bilayer graphene is characterized by the viscous transport. In quantizing magnetic field the momentum current passes through the guiding center of the cyclotron orbit. In this study we derive the formula of the quantized Hall viscosity for bilayer graphene. This can be detected in the non-local magnetoresistivity measurements that varies with the quantized step. For weak magnetic field the Landau levels start overlapping and lead to the Shubnikov–de-Haas oscillations, superimposed on the classical formulae, reference Steinberg (1958 Phys. Rev. 109 1486). These oscillations are present in the longitudinal and Hall viscosities.

Magnetic flux quantum in 2D correlated states of multiparticle charged system

We demonstrate that in a correlated 2D systems of electrons in the presence of perpendicular magnetic field the magnetic flux quantum may not achieve its value determined for a single or a noncorrelated electron. Correlations induced by the repulsion of electrons at strong magnetic field presence impose topological-type limits on planar cyclotron orbits which cause specific homotopy of trajectories resulting in constraints of the magnetic field flux quantum value. These restrictions occur at discrete series of magnetic field values corresponding to hierarchy of 2D correlated Hall states observed experimentally in GaAs thin films and in graphene. The similar homotopy property is observed in 2D Chern topological insulators when the magnetic field is substituted by the Berry field.

Topological Lifshitz transition of the intersurface Fermi-arc loop in NbIrTe4

Surface arcs (SAs) or Fermi arcs connecting pairs of bulk Weyl points with opposite chiralities are the signatures of Weyl semimetals in angle-resolved photoemission spectroscopy (ARPES) studies. The nontrivial topology of the bulk band structure guarantees the existence of these exotic Fermi arcs with connectivity that is strongly dependent on the surface. It has been theoretically proposed and experimentally confirmed that Fermi arcs at opposite surfaces can complete an unusual closed cyclotron orbit called a Weyl orbit, which leads to various intriguing transport properties. In this paper, a systematic ARPES study on opposite terminations (001) of type-II Weyl semimetal ${\mathrm{NbIrTe}}_{4}$ reveals different Fermi arc connections which result in a unique closed intersurface Fermi arc loop configurations (combining both projections of SAs) containing two pairs of Weyl points. In particular, the top surface ARPES data and corresponding ab initio calculation suggests that a topological Lifshitz transition occurs by tuning the chemical potential. SA rewiring on the top surface opens the intersurface arc loop at the Weyl node energy level into an open line, challenging the close-orbit description and leading to an unexplored scenario. Our results demonstrate the intrinsic alteration of Fermi arc connections and propose ${\mathrm{NbIrTe}}_{4}$ as a potential platform to examine Fermi-arc related phenomenon.

Signatures of possible surface states in TaAs

A signature property of Weyl semimetals is the existence of topologically protected surface states - arcs in momentum space that connect Weyl points in the bulk. However, the presence of bulks states makes detection of surface contributions to the transport challenging. Here we present a magnetoresistance study of high-quality samples of the prototypical Weyl semimetal, TaAs. By measuring the Shubnikov de Haas effect, we reveal the presence of a two-dimensional cyclotron orbit. This orbit is quantitatively consistent with the interference of coherent quasiparticles traversing two distinct Fermi arcs on the [001] crystallographic surface. The observation of this effect suggests that high magnetic fields can be used to study not only the transport properties of Fermi arcs, but also the interference of their quantum mechanical wavefunctions.

Probing the anisotropy of Landau levels in phosphorene by magneto-capacitance with a parabolic potential confinement

We theoretically investigate the Landau levels (LLs) and magneto-capacitance (MC) of monolayer black phosphorus under a perpendicular magnetic field, on which a parabolic potential is applied along with the armchair and zigzag directions, respectively. By both analytically perturbative calculation and numerical diagonalization based on an effective k ⋅ p Hamiltonian, we find that the LLs parabolically depend on the wave vectors and show strong anisotropy as the parabolic potential is applied along with different crystal directions. Specifically, the analytical LLs obtained by perturbative calculation from a decoupled single-band Hamiltonian are in good agreement with the numerical results. Importantly, the LLs are no longer linearly dependent on the magnetic field and level index even in the low energy regime due to the confinement of parabolic potential which repaints the cyclotron orbits. Moreover, the MC spectrum clearly reflects the structure of the LLs and exhibits strong anisotropic oscillating patterns. It can be used to determine the band parameters of phosphorene, i.e., the effective masses and inter-band coupling in the absence of magnetic and electric fields.

Manifestations of classical size effect and electronic viscosity in the magnetoresistance of narrow two-dimensional conductors: Theory and experiment

We develop a classical kinetic theory of magnetotransport of 2D electrons in narrow channels with partly diffusive boundary scattering and apply it to description of magnetoresistance measured in the temperature interval 4.2-30 K in long mesoscopic bars fabricated from high-purity GaAs quantum well structures. Both experiment and theory demonstrate a number of characteristic features in the longitudinal and Hall resistances caused by the size effect in two dimensions owing to the high ballisticity of the transport. In addition to the features described previously, we also reveal a change in the slope of the first derivative of magnetoresistance when the cyclotron orbit diameter equals to half of the channel width. These features are suppressed with increasing temperature as a result of the electronic viscosity due to electron-electron interaction. By comparing theory and experiment, we determine the characteristic time of relaxation of angular distribution of electrons caused by electron-electron scattering.

Simulations of nw measurement using multiple detection electrodes in FTICR mass spectrometry

Using multiple detection electrodes to acquire a signal with a frequency that is a multiple of the cyclotron frequency offers the ability to decrease the analysis time of Fourier transform ion cyclotron resonance mass spectrometry while maintaining high resolving power by measuring the ion cloud-induced image current several times per cyclotron orbit. However, there are inherent difficulties associated with this method, including generation of unwanted spectral peaks and loss of sensitivity. Simulations of the image-charge produced by a population of ions, with multiple-frequency detection, provide insight into the origin of these problems, from which methods for their mitigation can be deduced. A particle-in-cell simulation with an image-charge calculator is used to examine the effect of magnetron offset and excitation radius on the measured signals for Nω detection. Simulated transients of an IgG-sized protein (150 kDa) at 1ω and 10ω detection are compared and beat patterns for Nω detection are examined. The amplitude of subharmonic peaks is found to increase significantly with the radius of the magnetron component of the ions’ orbit.