Dirac fermions in strong electric field and quantum transport in graphene

Stochastic equations of the hydrodynamic theory of plasma are presented in relation to strong external fields. It is shown that the use of these stochastic equations makes it possible to obtain new theoretical solutions for plasma as a result of its heating in a strong external electric field. Theoretical solutions for the conductivity of turbulent plasma when heated in an external electric field of 100 V/cm are considered. Calculated values for the electron drift velocity, electron mobility, electron collision frequency, and the Coulomb logarithm in the region of strong electric fields are obtained. Here we consider experiments on turbulent heating of hydrogen plasma in the range of electric field strength of 100 < E < 1000. The calculated dependences of plasma conductivity are in satisfactory agreement with experimental data for heating plasma in a strong electric field. It is shown that the plasma turbulence in the region of strong electric fields E ~1000 V/cm is close to 100%. For the first time, it is confirmed that the derived dependences for collision frequency, drift velocity, and other values include the degree of turbulence of plasma, which makes it possible to correctly describe experimental data for heating plasma even with strong electric fields. In addition, it was determined that the scatter of experimental data may be associated with the variability of the function in the expression for the heat flux density. For the first time, it is shown theoretically that the experimentally determined fact of the possibility of the existence of an approximate constancy of plasma conductivity in the region E = 100–1000 V/cm can occur with an error of ~30%. The results show significant advantages of the stochastic hydrodynamic plasma theory over other methods that are not yet able to satisfactorily as well as qualitatively and quantitatively predict long-known experimental data while taking into account the degree of turbulence.

We give the general results for spontaneous and photon-induced pair production in strong, constant parallel electric and magnetic fields. For photons propagating exactly parallel to the constant fields there is no effect. For photons propagating at right angles to the constant fields the vacuum behaves in a birefringent manner. These results generalize earlier work in the field by others who did not include a constant electric field. Some numerical estimates are given for both the spontaneous and photon-induced pair production rates using numbers currently thought to obtain near the surface of a pulsar-which is believed to possess not only a strong magnetic field but also a strong electric field.

This work focuses on the numerical study of electrohydrodynamic multiphase fluid flow problems. Liquid bodies experience deformations caused by strong external electric fields. These deformations can be used in industrial applications to accurately control the motion of single droplets. In the limiting case, strong electric fields can force atomisation of fine microdroplets from much larger liquid bulks. Due to differences in the electrical properties of the different fluid phases, the flow affects in turn the electric field distribution. The analysis of such coupled flows requires numerical modelling of the interdependent hydrodynamic and electrodynamic problems. Since most liquids exhibit some conductivity due to intrinsic ionic species and dissolved impurities, the electrodynamic problem must be modelled by an electroquasistatic model taking into account capacitive, resistive and convective electrical currents. This electroquasistatic problem is coupled to an incompressible fluid flow problem described by the Navier-Stokes equations. Both problems are solved on the same computational grid, using the finite volume method. The fluid-fluid interface is modelled using the volume of fluid method. The resulting diffuse interface captures the motion of the phase boundaries while efficiently handling topology changes. The motion of contact lines is furthermore modelled using a dynamic contact angle model including hysteresis effects. Pinned contact lines and stick-slip contact line motion in transient problems can therefore be represented. The developed solver is readily applicable to a large range of electrohydrodynamic flow problems. This work investigates electrohydrodynamic flows occurring in three technical applications. First, the dynamics of sessile droplets subjected to an AC electric field on the surface of an insulator are considered. The dynamics of the oscillating droplets are compared with experimental data. Partial discharge inception fields are then estimated for similar configurations. Secondly, the detachment dynamics of two liquids in an on-demand droplet generator, where droplet detachment is enforced by electric fields, are considered and compared to experimental data. The different conductivities of the liquids are shown to lead to substantially different detachment dynamics. Relevant parameters in the detachment dynamics are extracted from the simulations. Finally, transient electrosprays in the cone-jet mode are characterised for a number of liquids with different electromechanical properties. The charge-radius correlations of the first ejections are found to obey the scaling laws reported in the literature. Moreover, additional scaling laws are found for the subsequent ejections.

We present a calculation of the effective geometry-induced quantum potential for the carriers in graphene shaped as a helicoidal nanoribbon. In this geometry the twist of the nanoribbon plays the role of an effective transverse electric field in graphene and this is reminiscent of the Hall effect. However, this effective electric field has a different sign for the two iso-spin states and translates into a mechanism to separate the two chiral species on the opposing rims of the nanoribbon. Iso-spin transitions are expected with the emission or absorption of microwave radiation which could be adjusted to be in the THz region.

The results of a linear analysis for the stability of a homogeneous dielectric liquid with respect to density perturbations in a uniform electric field are presented. The electric field increases the instability increment for the stratification along the field and decreases this increment in the transverse direction. Thus, a strong electric field can induce anisotropic decay into liquid and vapor phases for a fluid that is initially both in a labile state and in a metastable or stable state. Theoretical calculations are confirmed by the results of numerical modeling of the fluid dynamics. The new regions of a low-density phase have the form of narrow cylindrical channels oriented along the field. This new mechanism of gas phase formation in strong local electric fields probably plays a key role in the inception and ultra-fast propagation of streamers during the breakdown in dielectric liquids in a nanosecond range.

This chapter contains sections titled: Introduction Previous Treatments of the Nonlinear Dielectric and Birefringence Relaxation Orientational Relaxation Processes in the Presence of Strong Electric Fields: The Rotational Diffusion Model Nonlinear Transients in Dielectric Relaxation and Dynamic Kerr Effect Arising from Sudden Changes of a Strong dc Electric Field Steady-State Response Arising fom a Weak ac Field Superimposed on a Strong dc Bias field Nonlinear stationary Respones in Strong ac and dc Electric Fields Effects Due to Hyperpolarizabilities of Molecules on Kerr Effect Relaction Intertial Effects in Dielectric and Birefringence Relaction in a Strong sc ElectricField: Linear response Application to Related Relaxation Phenomena Conclusion

In this paper, we present a new fabrication method for the whispering gallery mode (WGM) micro-sphere based electric field sensor that which allows for longer time periods of sensitivity. Recently, a WGM-based photonic electric field sensor was proposed using a coupled dielectric microsphere-beam. The external electric field imposes an electrtrostriction force on the dielectric beam, deflecting it. The beam, in turn compresses the sphere causing a shift in its WGM. As part of the fabrication process, the PDMS micro-beams and the spheres are curied at high-temperature (100oC) and subsequently poled by exposing to strong external electric field (~8 MV/m) for two hours. The poling process allows for the deposition of surface charges thereby increasing the electrostriction effect. This methodology is called curing-then-poling (CTP). Although the sensors do become sufficiently sensitive to electric field, they start de-poling after a short period (within ~ 10 minutes) after poling, hence losing sensitivity. In an attempt to mitigate this problem and to lock the polarization for a longer period, we use an alternate methodology whereby the beam is poled and cured simultaneously (curing-while-poling or CWP). The new fabrication method allows for the retention of polarization (and hence, sensitivity to electric field) longer (~ 1500 minutes). An analysis is carried out along with preliminary experiments. Results show that electric fields as small as ~ 100 V/m can be detected with a 300 μm diameter sphere sensor a day after poling.

We investigated ultrafast dynamics of Dirac electrons under a high electric field in graphene combining strong THz pulses and ultrafast transient absorption spectroscopy. Comparison with semi-classical Boltzmann equation clarifies efficient impact ionization process.

The graphene surface with the unpaired π electrons presents an ideal two‐dimensional electron system. Although the effective massless Dirac fermions are important, they are not the only carriers that describe the quantum transport in graphene. Above zero energy, the current carrying carriers in graphene are the usual electrons. This electron density may vary depending on the surface defects and π–σ interaction, and this may lead to a possible Wigner crystallization on the surface of graphene. Calculations for nonmagnetic, ferromagnetic, and antiferromagnetic Wigner crystals are carried out based on the Koster–Kohn variational principle for direct calculation of Wannier functions. The effect of positive background due to the carbon ions is suitably treated. From our results, we find that Wigner crystallization is possible in grapheme, if we consider the electrons on the surface, which obey quadratic dispersion relation. The electron crystal with ferromagnetic phase and face centered square lattice structure has the lowest energy. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

The effect of bias electric field on the nonlinear stress–strain response of a lead zirconate–lead titanate piezoelectric ceramic is studied. The material is subjected to various compressive stress amplitudes (25–300 MPa) under constant electric field (from −0.5 to 2.0 MV/m) along the original poling direction. Application of a positive electric-field bias results in closed stress–strain hysteresis loops absorbing significant amounts of mechanical energy. Increasing the positive electric field increases the specific damping and decreases the elastic modulus. The trend is reversed when the electric field becomes sufficiently high to inhibit the domain-wall motion by the mechanical stresses. Measured specific damping values vary from 0.18 to 0.46 depending on the stress amplitude and bias electric field. The corresponding secant modulus varies from 79 to 24 GPa. The coercive stress is found to approach zero as the negative electric-field bias approaches the coercive field value. The coercive stress increases with increasing positive electric field as expected from the balance of mechanical and electrical energies. The physics of the observed phenomena is explained in terms of non-180° domain-wall motion.

Pair production in a constant electric field is closely analogous to bubble nucleation in a false vacuum. The classical trajectories of the pairs are Lorentz invariant, but it appears that this invariance should be broken by the nucleation process. Here, we use a model detector, consisting of other particles interacting with the pairs, to investigate how pair production is seen by different Lorentzian observers. We focus on the idealized situation where a constant external electric field is present for an infinitely long time, and we consider the in-vacuum state for a charged scalar field that describes the nucleating pairs. The in-vacuum is defined in terms of modes which are positive frequency in the remote past. Even though the construction uses a particular reference frame and a gauge where the vector potential is time dependent, we show explicitly that the resulting quantum state is Lorentz invariant. We then introduce a ``detector'' particle which interacts with the nucleated pairs, and show that all Lorentzian observers will see the particles and antiparticles nucleating preferentially at rest in the detector's rest frame. Similar conclusions are expected to apply to bubble nucleation in a sufficiently long lived vacuum. We also comment on certain unphysical aspects of the Lorentz invariant in-vacuum, associated with the fact that it contains an infinite density of particles. This can be easily remedied by considering Lorentz breaking initial conditions.

Vacuum bubbles nucleate at rest with a certain critical size and subsequently expand. But what selects the rest frame of nucleation? This question has been recently addressed in [1] in the context of Schwinger pair production in 1+1 dimensions, by using a model detector in order to probe the nucleated pairs. The analysis in [1] showed that, for a constant external electric field, the adiabatic ``in" vacuum of charged particles is Lorentz invariant, {and in this} case pairs tend to nucleate preferentially at rest with respect to the detector. Here, we sharpen this picture by showing that the typical relative velocity between the frame of nucleation and that of the detector is at most of order Δv ∼ SE−1/3 << 1. Here, SE >> 1 is the action of the instanton describing pair creation. The bound Δv coincides with the minimum uncertainty in the velocity of a non-relativistic charged particle embedded in a constant electric field. A velocity of order Δv is reached after a time interval of order Δt ∼ SE−1/3r0 << r0 past the turning point in the semiclassical trajectory, where r0 is the size of the instanton. If the interaction takes place in the vicinity of the turning point, the semiclassical description of collision does not apply. Nonetheless, we find that even in this case there is still a strong asymmetry in the momentum transferred from the nucleated particles to the detector, in the direction of expansion after the turning point. We conclude that the correlation between the rest frame of nucleation and that of the detector is exceedingly sharp.

The effect of a pulsed (with a duration on the order of 1 ms) and of a constant external electric field on plasma-chemical processes in the lower ionosphere at altitudes of 70–100 km above the Earth’s surface is considered. Interest in these externally stimulated physical settings is associated with traditional radiophysical research and problems of radio-chemical atmospheric physics, which has been actively in recent years due to its various scientific and technical applications. A new page in this field of science (unlike the use of spurious radio signals) opens up the possibility of the purposeful field impact on a GPS receiver on the improvement of work and the further development of satellite navigation systems, which, undoubtedly, has not been discussed previously in the literature. In this work, on the basis of the numerical simulation, the concentrations of the main charged particles and the electron temperature in the presence of a strong external electric field have been calculated at an altitude of 100 km.

The photochemical conversion of CO 2 into valuable fuels faces challenges of low efficiency and poor selectivity. Hydrated electrons (e aq − ), with their extremely negative reduction potential, are promising CO 2 -reducing agents, yet their short lifetime limits selectivity and high-energy-density product formation. Herein, we show that microdroplet interfaces with strong electric fields (10 9 volts per meter) substantially extend the lifespan of e aq − generated from industrial sulfite pollutants (SO 3 2− ), lowering energy barriers in the CO 2 reduction reaction and enabling targeted product formation. The machine learning strategy identified microdroplet size as the key parameter controlling electric field strength, product yield, and selectivity. In our lab-based scaled-up system, microdroplets &lt;10 micrometers improved performance by four to seven orders of magnitude over bulk-phase systems, achieving ~99% methanol selectivity. Strong interfacial electric fields stabilize intermediates and modulate carbon-oxygen bond lengths, directing pathways to high-value products. This approach enables sustainable CO 2 utilization via microdroplets, potentially producing fuels from waste.

The effects of a static, homogeneous, and strong electric field on the radiative and steric properties of the LiCs molecule in its $^{1}\ensuremath{\Sigma}^{+}$ electronic ground state are investigated. Combining discretization and basis-set methods, the rovibrational Schr\odinger equation is solved and dipole transition rates are calculated. Spontaneous emission decay rates and radiative lifetimes of rovibrationally excited states have been studied extensively and particularly in the presence of the external homogeneous electric field. The intriguing possibility to control the alignment and orientation by applying a sufficiently strong field while switching between different configurations via absorption and emission processes is demonstrated.