Energy Dispersion Of Electrons Research Articles

Synthetic dimensions in optical cavities and their analogies to two-dimensional materials

A method to produce synthetic dimensions in an optical cavity is presented. The system is obtained by coupling two one-dimensional optical cavities by means of a moving mirror. Its translation generates a new synthetic dimension resulting in a transmittance pattern that corresponds to the energy dispersion of electrons in a two-dimensional lattice: in this case a strained triangular lattice. We elucidate the analogy between these two systems by relating the distribution of transmittances of the optical cavity to the density of states of the two-dimensional lattice and the Bragg diffraction modes to the Van Hove singularities. Our mapping makes the coupled optical cavity a simulator for lattice Hamiltonians found in solid-state physics, providing an easier alternative platform to access some of their properties, as for example, the electronic conductivity, which is found here using the Boltzmann formula. Moreover, it is proved that the truly synthetic behavior appears only when the two cavities have an irrational length ratio as modes resonant on one cavity are never resonant in the other. Mathematically, wave phase differences act independently as they are given by a function that behaves as a pseudorandom number generator. This provides an elegant way to study synthetic dimensions without the need to move the central mirror, i.e., in a single, fixed geometry device. Thus, our work establishes a bridge between the fields of optical cavities, synthetic dimensions, and two-dimensional materials.

Quasiparticle focusing of bound states in two-dimensional s -wave superconductors

A magnetic impurity on a superconducting substrate induces in-gap Yu-Shiba-Rusinov (YSR) bound states, whose intricate spatial structure crucially influences the possibilities of engineering collective impurity states. By means of a saddle-point approximation, we study the scattering processes giving rise to YSR states in gapped, two-dimensional superconductors. Further, we develop a theory, which relates through a simple analytical expression, an arbitrary energy dispersion of normal electrons in a two-dimensional host to the spatial features of the YSR states. Namely, we find that flatter segments of the Fermi surface with large Fermi velocity enhance the local density of states (LDOS) around the impurity. Our analytical approximation is quantitatively accurate against tight-binding calculations on various lattices with different Fermi surfaces, and it allows to predict the shape and orientation of YSR states observed in scanning tunneling spectroscopy experiments. We illustrate our results with a model of ${\mathrm{NbSe}}_{2}$.

Theory of Seebeck ratchet in a noncentrosymmetric electron-phonon coupled system

A thermoelectric effect of the noncentrosymmetric electron-phonon coupled system is proposed, in which a temperature difference between electrons and phonons, instead of a spatial temperature gradient, induces an electric current. This is a realization of Seebeck ratchet in solids with the asymmetric energy dispersion of electrons, and the dynamical phonons act as the fluctuation of the scalar potential and induce the dc current. Possible realizations of this mechanism are also discussed.

Graphene-based Saturable Absorber for Pulsed Fiber Laser Generation

Recently, graphene has been considered as great candidate to be applied as the saturable absorber (SA) with its brilliant optical characteristics such as ultrafast recovery time and ultra-wideband absorption due to its zero bandgap energy and linear dispersion of Dirac electrons. This paper focuses on reviewing the generation of short pulses from passive mode-locked fiber lasers that employ graphene-based saturable absorber (GBSA). Various parameters that make it excellent for generation ultra-short pulsed including modulation depth, nonlinearity, saturation intensity, self-amplitude modulation, its crystal lattice structure, band gap energy distribution are discuss in details. Furthermore, comparison between single layers and multilayer GBSA is made to explain the effect of layers number on the behaviour of SA in ring cavity fiber lasers.

Origin of the Flat Band in Heavily Cs-Doped Graphene.

A flat energy dispersion of electrons at the Fermi level of a material leads to instabilities in the electronic system and can drive phase transitions. Here we show that the flat band in graphene can be achieved by sandwiching a graphene monolayer by two cesium (Cs) layers. We investigate the flat band by a combination of angle-resolved photoemission spectroscopy experiment and the calculations. Our work highlights that charge transfer, zone folding of graphene bands, and the covalent bonding between C and Cs atoms are the origin of the flat energy band formation. Analysis of the Stoner criterion for the flat band suggests the presence of a ferromagnetic instability. The presented approach is an alternative route for obtaining flat band materials to twisting bilayer graphene which yields thermodynamically stable flat band materials in large areas.

Simultaneous Remote Observations of Intense Reconnection Effects by DMSP and MMS Spacecraft During a Storm Time Substorm.

During a magnetic storm on 23 June 2015, several very intense substorms took place, with signatures observed by multiple spacecraft including DMSP and Magnetospheric Multiscale (MMS). At the time of interest, DMSP F18 crossed inbound through a poleward expanding auroral bulge boundary at 23.5 h magnetic local time (MLT), while MMS was located duskward of 22 h MLT during an inward crossing of the expanding plasma sheet boundary. The two spacecraft observed a consistent set of signatures as they simultaneously crossed the reconnection separatrix layer during this very intense reconnection event. These include (1) energy dispersion of the energetic ions and electrons traveling earthward, accompanied with high electron energies in the vicinity of the separatrix; (2) energy dispersion of polar rain electrons, with a high‐energy cutoff; and (3) intense inward convection of the magnetic field lines at the MMS location. The high temporal resolution measurements by MMS provide unprecedented observations of the outermost electron boundary layer. We discuss the relevance of the energy dispersion of the electrons, and their pitch angle distribution, to the spatial and temporal evolution of the boundary layer. The results indicate that the underlying magnetotail magnetic reconnection process was an intrinsically impulsive and the active X‐line was located relatively close to the Earth, approximately at 16–18 RE.

Quantum theory of the third-order nonlinear electrodynamic effects of graphene

The linear energy dispersion of graphene electrons leads to a strongly nonlinear electromagnetic response of this material. We develop a general quantum theory of the third-order nonlinear local dynamic conductivity of graphene $\sigma_{\alpha\beta\gamma\delta}(\omega_1,\omega_2,\omega_3)$, which describes its nonlinear response to a uniform electromagnetic radiation. The derived analytical formulas describe a large number of different nonlinear phenomena such as the third harmonic generation, the four wave mixing, the saturable absorption, the second harmonic generation stimulated by a dc electric current, etc., which may be used in different terahertz and optoelectronic devices.

Active-matrix nanocrystalline Si electron emitter array with a function of electronic aberration correction for massively parallel electron beam direct-write lithography: Electron emission and pattern transfer characteristics

A planar nanocrystalline silicon (nc-Si) electron emitter array compatible with an active-matrix large-scale integrated (LSI) driving circuit has been developed for massively parallel electron beam direct-write lithography. The electron-emitting part of the device consists of a 50-μm-pitch and 200 × 200 arrays of nc-Si dots fabricated on a Si substrate, and via-first-processed through-silicon-via (TSV) plugs of poly-Si connected with the dots from behind the substrate. Tapered emitter-array etching and electrochemical-oxidation with subsequent annealing and super-critical rinsing and drying processes significantly enhanced the electron emission current by improving and stabilizing uniformity and reducing the process temperature. When the emitter array was driven, electrons were effectively injected into the nc-Si layer through the TSV plugs and quasiballistically emitted through the gold surface electrode. The nc-Si emitter responded to the input signal within times of 0.1 μs or less. A 1:1 pattern transfer experiment demonstrated that 5 × 5 subset square patterns selected from the emitter array can be reproduced on an e-beam resist without any distortions or fluctuations, showing that the energy dispersion of the emitted electrons is quite small. The basic concept of electronic aberration correction performed by an active-matrix LSI driving circuit is also discussed.

Energy-momentum dispersion relation of plasmarons in bilayer graphene

The relation between the energy and momentum of plasmarons in bilayer graphene is investigated within the Overhauser approach, where the electron-plasmon interaction is described as a field theoretical problem. We find that the Dirac-like spectrum is shifted by $\Delta E(\mathbf{k})\sim 100\div150\,{\rm meV}$ depending on the electron concentration $n_{e}$ and electron momentum. The shift increases with electron concentration as the energy of plasmons becomes larger. The dispersion of plasmarons is more pronounced than in the case of single layer graphene, which is explained by the fact that the energy dispersion of electrons is quadratic and not linear. We expect that these predictions can be verified using angle-resolved photoemission spectroscopy (ARPES).

Fourier-transform scanning tunneling microscopy investigation of the energy versus wave vector dispersion of electrons at the Au(111) surface

We have investigated the contributions of surface-state electrons and bulk state electrons to the spatially oscillating local density of states (LDOS) of the Au(111) surface by scanning tunneling microscopy and spectroscopy at low temperatures. Based on the Fourier-transform images of LDOS maps obtained at various energies, we were able to determine the dispersion of the surface-state electrons in a broad range of energies, up to 3 eV. The energy versus wave vector dispersion relation was found to clearly deviate from the parabolic free-electron-like behavior at higher energies above 1 eV. Moreover, relying on two-dimensional Fourier-transform analysis, we develop an original approach to determine the dispersion behavior of bulk state electrons that are scattered at (sub)surface defects in the top atomic layers of the Au(111) surface. This ``additional set'' of electrons is found to exhibit a dispersion for the occupied states that is consistent with the calculated band structure of bulk Au and previous photoemission experiments. On the other hand, an anomalous bulk state dispersion behavior occurs in the empty state regime, where the wavelength of the spatial oscillations of the LDOS is observed to remain constant for the investigated energy range. This behavior is inconsistent with previous band-structure calculations and requires further theoretical investigation that takes into account the influence of inelastic electron scattering.

Effects of multi-band mixing on the spin-polarized transport in quasi-one-dimensional electron waveguides

We present numerical calculations of the energy dispersion of spin-polarized electrons in quasi-one-dimensional electronic waveguides in the presence of Rashba spin–orbit interaction (SOI), by using an efficient expanded basis method. Within this model, the general mixing between any two subbands is taken into account. We investigate the properties of spin-polarized transport in the nonuniform SOI system. It is found that the multi-band mixing brings significant effects on the properties of multiple subbands transport in the regime of high energy, especially for the cases of the wide waveguide, the strong SOI and the long extension of the SOI region.

Thermopower of an infinite Luttinger liquid

The thermopower of a Luttinger liquid (LL), originating from the energy dispersion of electrons at the Fermi level and/or from the backscattering of electrons by impurities, is analytically evaluated. It is shown that in both cases the thermopower is described by a corresponding Fermi-liquid formula renormalized by an interaction-dependent factor. For an infinite LL the renormalization coefficients decrease with an increase of the electron-electron interaction. In a realistic situation, when a LL wire is connected to leads of noninteracting electrons, the dispersion-induced thermopower in the limit of strong repulsive interaction is strongly suppressed, ${S}_{W}^{(d)}\ensuremath{\sim}{g}^{2}{S}_{0}^{(d)}\ensuremath{\ll}{S}_{0}^{(d)}$ (here ${S}_{0}^{(d)}$ is the corresponding Fermi-liquid value for the thermopower and $g\ensuremath{\ll}1$ is the LL correlation parameter), while the impurity-induced thermopower ${S}_{W}^{(i)}\ensuremath{\sim}{S}_{0}^{(i)}/g$ is enhanced by the interelectron interaction.

VELOX: a new VLF/ELF receiver in Antarctica for the Global Geospace Science mission

VELOX (VLF/ELF Logger Experiment), a new facility for systematically studying the characteristics of magnetospherically generated ELF/VLF radio noise received at a high-latitude ground station (Halley, Antarctica, 76°S, 26°W, L = 4.3), measures continuously at 1 s resolution the absolute power (peak, mean, and minimum), arrival azimuth, and polarisation ellipticity in 8 logarithmically spaced frequency bands ranging from 500 Hz to 9.3 kHz. All filtering etc. is done in real time using Digital Signal Processing (DSP) techniques. Key parameters (1 kHz and 3 kHz power channels only, at 1-minute intervals) for each day are extracted and regularly transferred to the Global Geospace Study Central Data Handling Facility. Data from the first year of operation (1992) show that, whilst the upper channels (6 kHz and 9.3 kHz) are dominated by thunderstorm (spheric) noise, which is strongest at night and repeatable from day to day, magnetospheric chorus and hiss emissions are more important in the 1–4 kHz range of high attenuation in the Earth-ionosphere waveguide. They are highly variable in intensity from below system noise level (15–20 dB above the reference level 10 −33 T 2 Hz −1) up to a maximum of 60–70 dB. Three classes of event are usually observed during specific local time sectors: substorm-related chorus events in the midnight-dawn sector, dawn chorus, and hiss-like events in the afternoon; all may occasionally be completely absent on quiet days. The substorm chorus events are shorter (typically 10–20 minutes) and more narrow-band than dawn chorus. Both upper and lower cut-off frequencies rise rapidly (∼ 100 Hz/min), consistent with the energy dispersion of resonant electrons as they drift eastward from injection near midnight, and with the inward drift, driven by substorm-enhanced electric fields, of whistler ducts which support propagation to the ground. Afternoon emission events are often punctuated by sudden deep fading, to noise level within 1–2 minutes, usually followed by complete recovery after a few minutes. All frequencies in the emission band are affected simultaneously. The explanation for this effect is unknown, though it could be a cut-off of propagation through the ionosphere to the ground by irregularities or gradients tilting the wave-normals out of the transmission cone. A similar system to VELOX will be deployed on a network of Automatic Geophysical Observatories extending to higher latitudes, south of Halley.

Energy dispersion of Auger electrons in resonant excitation of the Mo 2p3/2 orbital in Mo and Li2MoO4

The Mo L3M4.5M4.5 Auger electron spectra have been measured with tubbable synchrotron radiation in the vicinity of the Mo 2p32/ absorption edge. It has been found that the L3M44d.5M4.5 Auger lines shift to a higher kinetic energy with increasing photon energy, about 4 eV for Mo and about 12 eV for Li2MoO4. It is also shown that the L3M4.5M4.5 Auger lines of Li2MoO4 are split into two-peak structures just above the resonant Mo 2p3/2 to 4d(5s) excitation, which are assigned as the spectator and normal Auger transitions. The peculiarities in the Li2MoO4 case are interpreted in terms of the Auger resonant Raman scattering of the incident photons and band-like structures of the unoccupied molecular orbitals in the insulating solid.

Energy Gaps and Electrical Resistivity Associated with Screw-Type Spin Arrangements

Discontinuities in the energy dispersion of conduction electrons which appear in consequence of the screw-type ordering of the 4ƒ spins in rare-earth metals through the s-ƒ interaction are investigated theoretically. Light absorption with the electronic transition across the energy gap is discussed. The anomalous temperature dependence of electrical resistivity due to the appearance of the gaps is calculated. The result of a semi-quantitative calculation for erbium is compared with an experimental result, giving a rather good agreement.