Spatial aspects in quantum mechanics are often difficult to model in geometrically intricate settings that are typical of mesoscopic physics. In such cases, predicting the device behaviors is a vital but difficult challenge. Transverse magnetic focusing (TMF) is a prime example where a classically simple effect becomes difficult to approach in the quantum regime. Here, we have simulated a realistic TMF device and compared the results to those from experiments performed on GaAs/AlGaAs two-dimensional electron gas systems. Unlike previous studies, device features such as quantum point contacts and disorder were realized within the simulation. The simulated and experimental focusing spectra showed good agreement, and the analysis was extended to multichannel and energy-modulated scenarios. By revisiting the energy-modulated simulation with a quantum dot (QD) emitter, we confirmed that the unique geometry of a QD does not affect the focusing spectra, thereby validating the feasibility of such experiments in the study of monoenergetic excitations.
Spin-orbit (SO) interactions in two dimensional systems split the Fermi surface, and allow for the spatial separation of spin-states via transverse magnetic focusing (TMF). In this work, we consider the case of combined Rashba and Zeeman interactions, which leads to a Fermi surface without cylindrical symmetry. While the classical trajectories are effectively unchanged, we predict an additional contribution to the phase, linear in the applied in-plane magnetic field. We show that this term is unique to TMF, and vanishes for magnetic (Shubnikov de Haas) oscillations. Finally we propose some exp…
Interference effects form a fundamental pillar of quantum mechanics. In this paper, we examine the interference in spin-orbit coupled transverse magnetic focusing, where a weak magnetic field is used to focus charge carries over mesoscopic scales. We determine a semi-classical form for the Green's function in a weak magnetic field, for the case of both spin-less and spin-orbit coupled charge carriers. The obtained forms for the Greens' function are independent of particle dispersion and are thus applicable to a wide variety of systems.
Magnetic fields force ballistic electrons injected from a narrow contact to move along skipping orbits and form caustics. This leads to pronounced resistance peaks at nearby voltage probes as electrons are effectively focused inside them, a phenomenon known as magnetic focusing. This can be used not only for the demonstration of ballistic transport but also to study the electronic structure of metals. Here we use magnetic focusing to probe narrow bands in graphene bilayers twisted at 2 degrees. Their minibands are found to support long-range ballistic transport limited at low temperatures by i…
We present a quantum model which provides enhanced understanding of recent transverse magnetic focusing experiments on graphene $p$-$n$ junctions. Spatially resolved flow maps of local particle current density show quantum interference and $p$-$n$ junction filtering effects which are crucial to explaining the device operation. The Landauer-Büttiker formula is used alongside dephasing edge contacts to give exceptional agreement between simulated non-local resistance and the recent experiment by Chen $\textit{et al}$ ($\textit{Science}$, 2016). The origin of positive and negative focusing resona…
Recent theoretical and experimental results from quasi-one dimensional heavy hole systems have suggested that heavy hole gases have a strongly anisotropic g factor. In this theoretical paper, we propose a method for measuring this anisotropy using transverse magnetic focusing (TMF). We demonstrate that for experimentally accessible fields, the g factor anisotropy leads to a relative variation in the characteristic of spin-splitting of the TMF spectrum which allows for the measurement of the anisotropy of the g factor. We show that this variation is insensitive to additional spin-orbit interact…
Spatially separating electrons of different spins and efficiently generating spin currents are crucial steps towards building practical spintronics devices. Transverse magnetic focusing is a potential technique to accomplish both those tasks. In a material where there is significant Rashba spin--orbit interaction, electrons of different spins will traverse different paths in the presence of an external magnetic field. Experiments have demonstrated the viability of this technique by measuring conductance spectra that indicate the separation of spin-up and spin-down electrons. However the effect…
We compare classical versus quantum electron transport in recently investigated magnetic focusing devices [S. Bhandari et al., Nano Lett. 16, 1690 (2016)] exposed to the perturbing potential of a scanning gate microscope (SGM). Using the Landauer-Büttiker formalism for a multi-terminal device, we calculate resistance maps that are obtained as the SGM tip is scanned over the sample. There are three unique regimes in which the scanning tip can operate (focusing, repelling, and mixed regime) which are investigated. Tip interacts mostly with electrons with cyclotron trajectories passing directly u…
Ultra-clean graphene sheets encapsulated between hexagonal boron nitride crystals host two-dimensional electron systems in which low-temperature transport is solely limited by the sample size. We revisit the theoretical problem of carrying out microscopic calculations of non-local ballistic transport in such micron-scale devices. By employing the Landauer-Buttiker scattering theory, we propose a novel scaling approach to tight-binding non-local transport in realistic graphene devices. We test our numerical method against experimental data on transverse magnetic focusing (TMF), a textbook examp…
We present low-temperature magnetotransport measurements on graphene rings encapsulated in hexagonal boron nitride. We investigate phase-coherent transport and show Aharonov-Bohm (AB) oscillations in quasi-ballistic graphene rings with hard confinement. In particular, we report on the observation of $h/e$, $h/2e$ and $h/3e$ conductance oscillations. Moreover we show signatures of magnetic focusing effects at small magnetic fields confirming ballistic transport. We perform tight binding calculations which allow to reproduce all significant features of our experimental findings and enable a deep…
Spin waves can transport both energy and angular momentum over long distances as they propagate. However, due to damping, their amplitude decreases exponentially as they move away from the source, leaving little capability for manipulating how much energy and angular momentum is to be delivered where. Here we show that a suitable local reduction of the effective field can lead to a large accumulation of spin wave energy far from the source. Moreover, both the location and the amount of energy to be delivered can be controlled accurately with geometry and externalm magnetic fields. Thus, we put…
Electron-electron (e-e) interactions assume a cardinal role in solid-state physics. Quantifying the e-e scattering length is hence critical. In this paper we show that the mesoscopic phenomenon of transverse magnetic focusing (TMF) in two-dimensional electron systems forms a precise and sensitive technique to measure this length scale. Conversely we quantitatively demonstrate that e-e scattering is the predominant effect limiting TMF amplitudes in high-mobility materials. Using high-resolution kinetic simulations, we show that the TMF amplitude at a maximum decays exponentially as a function o…
We use a cooled Scanning Probe Microscope (SPM) to electron motion in nanoscale devices. The charged tip of the SPM is raster scanned at a constant height above the surface as the conductance of the device is measured. The image charge scatters electrons away, changing the path of electrons through the sample.1-3 Using this technique, we have imaged cyclotron orbits3 for ballistic hBN-graphene-hBN devices that flow between two narrow contacts in the magnetic focusing regime. Here we present an analysis of our magnetic focusing imaging results based on the effects of the tip-created charge dens…
The response of superconductor-normal-metal-superconductor junctions to magnetic field is complicated and non-universal because all trajectories contributing to supercurrent have a different effective area, and therefore acquire arbitrary magnetic phases. We design an hourglass-shaped Josephson junction where due to the junction symmetry the magnetic phase of every trajectory is approximately equal. By doing so we are able to increase a critical field of the Josephson junction to many flux quanta per junction area. We then analyse how breaking the symmetry condition increases the sensitivity o…
We propose a new method to generate magnetic skyrmions through spin-wave focusing in chiral ferromagnets.A lens is constructed to focus spin waves by a curved interface between two ferromagnetic thin films with different perpendicular magnetic anisotropies. Based on the principle of identical magnonic path length, we derive the lens contour that can be either elliptical or hyperbolical depending on the magnon refractive index. Micromagnetic simulations are performed to verify the theoretical design. It is found that under proper condition magnetic skyrmions emerge near the focus point of the l…
Vectorial Reconstruction of Magnetic Order Parameters using Electron Magnetic Linear Dichroism
CEITEC BUT, Brno University of Technology（Brno理工大学CEITEC中心）；Institute of Physical Engineering, Brno University of Technology（Brno理工大学物理工程研究所）；Department of Physics and Astronomy, Uppsala University（乌普萨拉大学物理与天文学系）
We have studied mesoscopic Josephson junctions formed by highly $n$-doped InAs nanowires and superconducting Ti/Pb source and drain leads. The current-voltage properties of the system are investigated by varying temperature and external out-of-plane magnetic field. Superconductivity in the Pb electrodes persists up to $ \sim 7$ K and with magnetic field values up to 0.4 T. Josephson coupling at zero backgate voltage is observed up to 4.5 K and the critical current is measured to be as high as 615 nA. The supercurrent suppression as a function of the magnetic field reveals a diffraction pattern…
We propose a method to generate magnetic skyrmions by focusing spin waves totally reflected by a curved film edge. Based on the principle of identical magnonic path length, we derive the edge contour that is parabolic and frequency-independent. Micromagnetic simulations are performed to verify our theoretical design. It is found that under proper conditions, magnetic droplet first emerges near the focal point where the spin-wave intensity has been significantly enhanced, and then converts to magnetic skyrmion accompanied by a change of the topological charge. The phase diagram about the amplit…
We predict a mechanism of spontaneous stabilization of a uniaxial density wave in a two-dimensional metal with an isotropic Fermi surface in the presence of external magnetic field. The topological transformation of a closed Fermi surface into an open one decreases the electron band energy due to delocalization of electrons initially localized by magnetic field, additionally affected by the magnetic breakdown effect. The driving mechanism of such reconstruction is a periodic potential due to the self-consistently formed electron density wave. It is accompanied with quantum oscillations periodi…
Quantum mechanical systems with long-range interactions between quasiparticles provide a promising platform for coherent quantum information technology. Superconductors are a natural choice for solid-state based quantum devices, while magnetic impurities inside superconductors give rise to quasiparticle excitations of broken Cooper pairs that provide characteristic information about the host superconductor. Here, we reveal that magnetic impurities embedded below a superconducting La(0001) surface interact via quasiparticles extending to very large distances, up to several tens of nanometers. U…
Lorentz Transmission Electron Microscopy (TEM) observations of magnetic nanoparticles contain information on the magnetic and electrostatic potentials. Vector Field Electron Tomography (VFET) can be used to reconstruct electromagnetic potentials of the nanoparticles from their corresponding LTEM images. The VFET approach is based on the conventional filtered back projection approach to tomographic reconstructions and the availability of an incomplete set of measurements due to experimental limitations means that the reconstructed vector fields exhibit significant artifacts. In this paper, we o…
The paper considers the semiclassical dynamics of electrons on complex Fermi surfaces in the presence of strong magnetic fields. The reconstructions of the general topological structure of such dynamics are accompanied by the appearance of closed extremal trajectories of a special form, closely related to geometry and topology of the Fermi surface. The study of oscillation phenomena on such trajectories allows, in particular, to propose a relatively simple method for refining the parameters of the dispersion relation in metals with complex Fermi surfaces.
Exotic magnetic structures, such as magnetic skyrmions and domain walls, are becoming more important in nitrogen-vacancy center scanning magnetometry. However, a systematic imaging approach to mapping stray fields with fluctuation of several milliteslas generated by such structures is not yet available. Here we present a scheme to image a millitesla magnetic field by tracking the magnetic resonance frequency, which can record multiple contour lines for a magnetic field. The radial basis function algorithm is employed to reconstruct the magnetic field from the contour lines. Simulations with sh…
Predicting measurement outcomes from an underlying structure often follows directly from fundamental physical principles. However, a fundamental challenge is posed when trying to solve the inverse problem of inferring the underlying source-configuration based on measurement data. A key difficulty arises from the fact that such reconstructions often involve ill-posed transformations and that they are prone to numerical artefacts. Here, we develop a numerically efficient method to tackle this inverse problem for the reconstruction of magnetisation maps from measured magnetic stray field images. …
Stray magnetic fields contain significant information about the electronic and magnetic properties of condensed matter systems. For two-dimensional (2D) systems, stray field measurements can even allow full determination of the source quantity. For instance, a 2D map of the stray magnetic field can be uniquely transformed into the 2D current density that gave rise to the field and, under some conditions, into the equivalent 2D magnetisation. However, implementing these transformations typically requires truncation of the initial data and involves singularities that may introduce errors, artefa…
Accurate determination of microscopic transport and magnetization currents is of central importance for the study of the electric properties of low dimensional materials and interfaces, of superconducting thin films and of electronic devices. Current distribution is usually derived from the measurement of the perpendicular component of the magnetic field above the surface of the sample, followed by numerical inversion of the Biot-Savart law. The inversion is commonly obtained by deriving the current stream function $g$, which is then differentiated in order to obtain the current distribution. …
