Transverse Electron Focusing Research Articles

Probing the Shape of the Weyl Fermi Surface of NbP Using Transverse Electron Focusing.

Weyl semimetals are defined by their unique Fermi surface, comprising pairs of Weyl points of opposite chirality, connected through topological surface states. Angle-resolved photoemission spectroscopy (ARPES) has been used to verify the existence of the Weyl points and the Fermi arcs. However, ARPES is limited in resolution, leading to significant uncertainty when characterizing the shape of the Fermi surface of semimetals and measuring features such as the distance between the Weyl points. Here, to surpass the resolution of ARPES, we combine quantum oscillation measurements with transverse electron focusing experiments. These techniques offer complementary information, enabling the reconstruction of the distinctive peanut-shaped cross section of the Weyl Fermi surface and accurately determining the separation between Weyl points in the Weyl semimetal NbP. Our Letter showcases the integration of quantum oscillations and transverse electron focusing, allowing for the measurements of complex Fermi surface geometries, concurrently with carriers' transport properties, in high-mobility quantum materials.

Specular Electron Focusing between Gate-Defined Quantum Point Contacts in Bilayer Graphene.

We report multiterminal measurements in a ballistic bilayer graphene (BLG) channel, where multiple spin- and valley-degenerate quantum point contacts (QPCs) are defined by electrostatic gating. By patterning QPCs of different shapes along different crystallographic directions, we study the effect of size quantization and trigonal warping on transverse electron focusing (TEF). Our TEF spectra show eight clear peaks with comparable amplitudes and weak signatures of quantum interference at the lowest temperature, indicating that reflections at the gate-defined edges are specular, and transport is phase coherent. The temperature dependence of the focusing signal shows that, despite the small gate-induced bandgaps in our sample (≲45 meV), several peaks are visible up to 100 K. The achievement of specular reflection, which is expected to preserve the pseudospin information of the electron jets, is promising for the realization of ballistic interconnects for new valleytronic devices.

Transverse instability of electron phase-space holes in multi-dimensional Maxwellian plasmas

The stability of an initially one-dimensional electron hole to perturbations varying sinusoidally transverse to its trapping direction is analysed in detail. It is shown that the expected low-frequency eigenmode of the linearized Vlasov–Poisson system consists of a shift mode, proportional to the gradient of the equilibrium potential. The resulting dispersion relation is that the total jetting force exerted by a perturbed hole on the particles balances the electric restoring tension of the hole. The tension is quantitatively small and can often be ignored. The particle force is expressed as integrals of equilibrium parameters over the hole and is shown at low frequency to be exactly equal to what has recently been found (by different analysis) to express ‘kinematic’ hole momentum conservation. The mechanism of instability has nothing to do with the previously hypothesized transverse electron focusing. The unmagnetized growth rate$\unicode[STIX]{x1D6FE}(k)$is found numerically and is in excellent agreement with recent kinematic estimates. Magnetic field stabilization of the transverse mode is also evaluated. The resulting stability boundary for Maxwellian holes is in reasonable agreement with previously published criteria based on particle simulation. It arises from a change of trapped force sign across the resonance between bounce and cyclotron frequencies.

Coherent Spin Amplification Using a Beam Splitter.

We report spin amplification using a capacitive beam splitter in n-type GaAs where the spin polarization is monitored via a transverse electron focusing measurement. It is shown that partially spin-polarized current injected by the emitter can be precisely controlled, and the spin polarization associated with it can be amplified by the beam splitter, such that a considerably high spin polarization of around 50% can be obtained. Additionally, the spin remains coherent as shown by the observation of quantum interference. Our results illustrate that spin-polarization amplification can be achieved in materials without strong spin-orbit interaction.

Direct observation of spin polarization in GaAs quantum wires by transverse electron focusing

We present transverse electron focusing measurements in the two dimensional electrons gas formed at the interface of a GaAs/AlGaAs heterostructure. The experimental arrangement consists of two orthogonal quantum point contacts (QPCs), one acting as injector and the other as detector of the collimated 1D electrons as a function of transverse magnetic field. The focusing spectrum shows anomalous behaviour, the first and third focusing peaks split into two sub-peaks while second peak remains as a single peak. The observed splitting, a signature of spin states, arises from the spin-orbit interaction when the 1D electrons are injected into the 2D regime, thus allowing us to manipulate the spin states within the 1D channel.

Direct observation of exchange-driven spin interactions in one-dimensional system

We present experimental results of transverse electron focusing measurements performed on an n-type GaAs based mesoscopic device consisting of one-dimensional (1D) quantum wires as injector and detector. We show that non-adiabatic injection of 1D electrons at a conductance of e2h results in a single first focusing peak, which transforms into two asymmetric sub-peaks with a gradual increase in the injector conductance up to 2e2h, each sub-peak representing the population of spin-state arising from the spatially separated spins in the injector. Further increasing the conductance flips the spin-states in the 1D channel, thus reversing the asymmetry in the sub-peaks. On applying a source-drain bias, the spin-gap, so obtained, can be resolved, thus providing evidence of exchange interaction induced spin polarization in the 1D systems.

Ballistic miniband conduction in a graphene superlattice.

Rational design of long-period artificial lattices yields effects unavailable in simple solids. The moiré pattern in highly aligned graphene/hexagonal boron nitride (h-BN) heterostructures is a lateral superlattice with high electron mobility and an unusual electronic dispersion whose miniband edges and saddle points can be reached by electrostatic gating. We investigated the dynamics of electrons in moiré minibands by measuring ballistic transport between adjacent local contacts in a magnetic field, known as the transverse electron focusing effect. At low temperatures, we observed caustics of skipping orbits extending over hundreds of superlattice periods, reversals of the cyclotron revolution for successive minibands, and breakdown of cyclotron motion near van Hove singularities. At high temperatures, electron-electron collisions suppress focusing. Probing such miniband conduction properties is a necessity for engineering novel transport behaviors in superlattice devices.

High efficiency, multiterawatt x-ray free electron lasers

We study high efficiency, multi-terawatt peak power, few angstrom wavelength, X-ray Free Electron Lasers (X-ray FELs). To obtain these characteristics we consider an optimized undulator design: superconducting, helical, with short period and built-in strong focusing. This design reduces the length of the breaks between modules, decreasing diffraction effects, and allows using a stronger transverse electron focusing. Both effects reduce the gain length and the overall undulator length. The peak power and efficiency depend on the transverse electron beam distribution and on time dependent effects, like synchrotron sideband growth. The last effect is identified as the main cause for reduction of electron beam microbunching and FEL peak power. We show that the optimal functional form for the undulator magnetic field tapering profile, yielding the maximum output power, depends significantly on these effects. The output power achieved when neglecting time dependent effects for an LCLS-like X-ray FEL with a 100 m long tapered undulator is 7.3 TW, a 14 $\%$ electron beam energy extraction efficiency. When these effects are included the highest peak power is achieved reducing the tapering rate, thus minimizing the reduction in electron micro-bunching due to synchrotron sideband growth. The maximum efficiency obtained for this case is 9 $\%$, corresponding to 4.7 TW peak radiation power. Possible methods to suppress the synchrotron sidebands, and further enhance the FEL peak power, up to about 6 TW by increasing the seed power, are discussed.

Semiclassical study of edge states and transverse electron focusing for strong spin-orbit coupling

We studied the edge states and transverse electron focusing in the presence of spin-orbit interaction in a two-dimensional electron gas. Assuming strong spin-orbit coupling we derived semiclassical quantization conditions to describe the dispersion of the edge states. Using the dispersion relation we then make predictions about certain properties of the focusing spectrum. Comparison of our analytical results with quantum-mechanical transport calculations reveals that certain features of the focusing spectrum can be quite well understood in terms of the interference of the edge states while the explanation of other features seems to require a different approach.

Exploring the graphene edges with coherent electron focusing

We study theoretically the coherent electron focusing in graphene nanoribbons. Using semiclassical and numerical tight-binding calculations we show that armchair edges give rise to equidistant peaks in the focusing spectrum. In the case of zigzag edges at low magnetic fields one can also observe focusing peaks but with increasing magnetic field a more complex interference structure emerges in the spectrum. This difference in the spectra can be observed even if the zigzag edge undergoes structural reconstruction. Therefore transverse electron focusing can help in the identification and characterization of the edge structure of graphene samples.

Fabrication of point contacts by FIB patterning

We describe a new technique for the fabrication of point contacts using a focused ion beam (FIB) patterning. After sample coverage with a thin insulating layer (SiO), an FIB is used to mill a 100-nm-diameter hole through the insulator. Electrical contact to the sample is then made in-situ by filling the hole with a metal (Pt) using the ion beam assisted chemical vapor deposition capability of our FIB system. We have demonstrated the use of two such contacts (as an emitter and collector) in a transverse electron focusing (TEF) experiment. The contacts were made to a single crystal of bismuth, ballistic electrons were injected into the crystal through the emitter contact and then focused onto the collector by a magnetic field. We see the expected voltage peaks at the collector as a function of the applied magnetic field. Temperature dependent TEF measurements provided direct information about relaxation time of conduction electrons.

Magnetic breakdown of cyclotron orbits in systems with Rashba and Dresselhaus spin-orbit coupling

We study the effect of the interplay between the Rashba and the Dresselhaus spin-orbit couplings on the transverse electron focusing in two-dimensional electron gases. Depending on their relative magnitude, the presence of both couplings can result in the splitting of the first focusing peak into two or three. This splitting has information about the relative value of spin-orbit couplings and therefore about the shape of the Fermi surface. More interesting, the presence of the third peak is directly related to the tunneling probability (``magnetic breakdown'') between orbits corresponding to the different sheets of the Fermi surface. In addition, destructive interference effects between paths that involve tunneling and those that do not can be observed in the second focusing condition. Such electron paths (orbits) could be experimentally detected using current techniques for imaging the electron flow opening the possibility to directly observe and characterize the magnetic breakdown effect in this system.

Detection of spin polarized currents in quantum point contacts via transverse electron focusing

It has been predicted recently that an electron beam can be polarized when it flows adiabatically through a quantum point contact in a system with spin-orbit interaction. Here, we show that a simple transverse electron focusing setup can be used to detect such polarized current. It uses the amplitude's asymmetry of the spin-split transverse electron focusing peak to extract information about the electron's spin polarization. On the other hand, and depending on the quantum point contact geometry, including this one-body effect can be important when using the focusing setup to study many-body effects in quantum point contacts.

Current focusing in InSb heterostructures

We report transverse electron focusing in a symmetrically doped, InSb-based two-dimensional electron system. In a focusing device, the application of a perpendicular magnetic field steers the electron current from an injecting quantum point contact into a collector quantum point contact whenever the diameter of the cyclotron orbit corresponds to an integer fraction of the injector to collector spatial separation. In low-temperature measurements of in-plane gated devices, we observe peaks in the collector voltage at magnetic fields where focusing is expected. The first peak displays substructure which is preserved at temperatures as high as 10 K and under a variety of gating conditions. We speculate that this substructure originates from spatially distinct paths for electrons with different spin polarizations arising from the large Dresselhaus effect expected for InSb-based electron systems.

Design and control of spin gates in two quantum-dot arrays

We study the spin-spin interaction between quantum dots coupled through a two-dimensional electron gas with spin-orbit interaction. We show that the interplay between transverse electron focusing and spin-orbit coupling allows to dynamically change the symmetry of the effective spin-spin Hamiltonian. That is, the interaction can be changed from Ising-like to Heisenberg-like and vice versa. The sign and magnitude of the coupling constant can also be tuned.

Transverse electron focusing in systems with spin-orbit coupling

We study the transverse electron focusing in a two dimensional electron gas with Rashba spin-orbit coupling. We show that the interplay between the external magnetic field and the spin-orbit coupling gives two branches of states with different cyclotron radius within the same energy window. This effect generates a splitting of the first focusing peak in two contributions. Each one of these contributions is spin polarized. The surface reflection mixes the two branches and the second focusing peak does not present the same effect. While for GaAs/AlGaAs heterostructures the effect is small, in systems like InSb/InAlSb the effect should be clearly observed.

Transverse electron focusing as a way of studying phonon kinetics. Turbulence of phonon flow

AbstractNovel techniques have been created for studying phonon kinetics. A supersonic conduction electron flux is used to produce a phonon flux. Transverse electron focusing (TEF) is applied for checking the electron gas affected by phonons. A turbulent regime of phonon flow-phonon flux step broadening-reveals itself as step broadening of non-equilibrium electron flux.

Detecting spin-polarized currents in ballistic nanostructures.

We demonstrate a mesoscopic spin polarizer/analyzer system that allows the spin polarization of current from a quantum point contact in a large in-plane magnetic field to be measured. A transverse electron focusing geometry is used to couple current from an emitter point contact into a collector point contact. At large in-plane fields, with the point contacts biased to transmit only a single spin (g<e(2)/h), the voltage across the collector depends on the spin polarization of the current incident on it. Spin polarizations of >70% are found for both emitter and collector at 300 mK and 7 T in-plane field.

Studying conduction-electron/interface interactions using transverse electron focusing

Understanding the microscopic processes by which the electrons within conductors are scattered at surfaces and interfaces is important for both fundamental physics and technology. The authors review what has been learned so far about scattering of electrons at a variety of surfaces and interfaces using a technique, transverse electron focusing (TEF), that involves two point contacts in a uniform magnetic field. Transverse electron focusing is a sort of \ensuremath{\beta}-ray spectrometer in a metal, except that, whereas the \ensuremath{\beta}-ray spectrometer requires a narrow beam because the energy and momentum of a free electron can be arbitrary, in TEF the electrons of interest all have the Fermi energy and momentum, so focusing occurs even for electrons injected isotropically in angle. Transverse electron focusing is unique in its ability to probe localized and selectable portions of the interface from inside the conductor, using conduction electrons on only small parts of the Fermi surface. The authors first briefly review the essential features of TEF and of ideal and rough surfaces and describe the three techniques now used for injecting and detecting electrons: needle contacts, lithographically fabricated contacts, and light-induced injection. They then turn to measurements in metals and semimetals of the probability of specular reflection q from a given interface for electrons at the Fermi energy impinging at perpendicular incidence. They examine how q varies over different crystal faces for different electron orbits on the Fermi surfaces of a variety of conductors and how it is affected by changes in the de Broglie wavelength ${\ensuremath{\lambda}}_{\mathrm{dB}},$ by chemical etching, ion etching, or physical damage, by a molecular overlayer condensed from the surrounding atmosphere, and, for semimetals, by surface band bending (surface charge). The authors also explain how to measure the dependence of q upon the angle of incidence $q(\ensuremath{\theta}),$ which gives information about surface structure. Transverse electron focusing studies of a variety of quasiparticle effects arising because the electrons are in a solid are described. These include (a) scattering of excitations moving on ``holelike'' orbits---q can depend upon the sign of the particle charge; (b) scattering involving a surface reciprocal-lattice vector ${\mathbf{G}}_{\ensuremath{\tau}},$ including surface resonances induced by an artificial grating etched onto a Bi surface; and (c) scattering between different parts of the Fermi surface---intervalley scattering (IVS)---including scattering in which the sign of the quasiparticle charge changes. The authors review studies of scattering of electrons from a normal-metal (or semimetal)/superconductor interface, which involves an unusual phenomenon called Andreev reflection, in which the signs of both the charge and mass change. Also described are TEF studies of scattering of light-excited electrons from an intercrystalline boundary and recent TEF measurements of q for scattering from the boundary of the two-dimensional electron gas. The authors conclude with a list of future TEF studies of conduction-electron/interface interactions that they believe to be interesting and important.

On the question of short-period oscillations of the collector voltage during transverse electron focusing

Giant short-period oscillations during transverse electron focusing at high emitter voltages have been observed in bismuth samples with a superlattice on the surface. A model is proposed which explains the onset of the oscillations, their position on the magnetic-field scale, and their intensification and shift along the magnetic-field scale with increasing current (this shift depending on the direction of current flow) and which can also account for the absence of oscillations in fields which are multiples of the field of the first oscillation. In this model the oscillations are attributed to the appearance of resonant surface (edge) states and their contribution to the electron transport.