Momentum Relaxation Research Articles

Thickness-dependent electron momentum relaxation times in iron films

Terahertz time-domain conductivity measurements in 2–100 nm thick iron films resolve the femtosecond time delay between the applied electric fields and the resulting currents. This current response time decreases from 29 fs for the thickest films to 7 fs for the thinnest films. The macroscopic response time is not strictly proportional to the conductivity. This excludes the existence of a single relaxation time universal for all conduction electrons. We must assume a distribution of microscopic momentum relaxation times. The macroscopic response time depends on the average and variation of this distribution; the observed deviation between the response time and conductivity scaling corresponds to the scaling of the variation. The variation of microscopic relaxation times depends on the film thickness because electrons with different relaxation times are affected differently by the confinement since they have different mean free paths.

Out-of-equilibrium chiral magnetic effect and momentum relaxation in holography

The authors study the chiral magnetic effect in out of equilibrium situations in a holographic setup describing a far from equilibrium evolution. They find that the anomaly induced response shows a late equilibration and suggest that this could be a universal feature of anomalous transport, which could provide an important lesson for observations in heavy ion collisions.

Magnetic impurities as the origin of the variability in spin relaxation rates in Cu-based spin transport devices

The Elliott-Yafet spin relaxation mechanism posits linear proportionality between spin and momentum lifetimes in low spin-orbit coupling nonmagnetic metals, and is widely accepted in spintronics. Accurate experimental determination of the Elliott-Yafet proportionality constants (${\ensuremath{\beta}}_{i}$) between the spin and momentum relaxation times for individual scattering sources is challenging, however. This is apparent from the literature on nonlocal spin transport in Cu, for example, where reported phonon (${\ensuremath{\beta}}_{\mathrm{ph}}$) and defect (${\ensuremath{\beta}}_{\mathrm{def}\phantom{\rule{4pt}{0ex}}}$) Elliott-Yafet constants vary by an order of magnitude. In recent work we discovered that even part-per-million-level magnetic impurity concentrations can substantially influence spin relaxation in Cu, via a spin transport analog of the Kondo effect. To clarify whether this could explain the reported variability in ${\ensuremath{\beta}}_{i}$, here we report on a comprehensive study of spin transport in Cu-based lateral nonlocal spin valves, varying the ferromagnetic contact material, interface structure, Cu thickness, and post-fabrication annealing conditions, resulting in widely varied microstructures and magnetic impurity concentrations. Quantifying the effects of magnetic impurities on charge and spin transport we demonstrate the dramatic, even dominant, effect these can have on spin relaxation rates, and thus extracted ${\ensuremath{\beta}}_{i}$. Minimization of magnetic impurity effects is achieved via Al interlayer insertion or moderate annealing, restoring the expected temperature dependence for phonon-mediated spin relaxation, and enabling more reliable determination of ${\ensuremath{\beta}}_{i}$ for phonons (740 \ifmmode\pm\else\textpm\fi{} 200), and nonmagnetic defects (240 \ifmmode\pm\else\textpm\fi{} 50). The latter contribution is shown to be dominated by grain boundaries in these polycrystalline Cu films. Cross-sectional transmission electron microscopy measurement of grain sizes in actual nonlocal spin valve devices then establishes a useful empirical relationship between average grain size and spin diffusion length. These measurements highlight the importance of magnetic impurities in metallic spin transport, explain the wide variability in reported ${\ensuremath{\beta}}_{\mathrm{ph}}$ and ${\ensuremath{\beta}}_{\mathrm{def}}$ in Cu, and elucidate the relationship between metallic spin transport and microstructure.

Ballistic and hydrodynamic magnetotransport in narrow channels

An increasing number of low carrier density materials exhibit a surprisingly large transport mean-free path due to inefficient momentum relaxation. Consequently, charge transport in these systems is markedly non-Ohmic but rather ballistic or hydrodynamic, features which can be explored by driving current through narrow channels. Using a kinetic equation approach, we theoretically investigate how a nonquantizing magnetic field discerns ballistic and hydrodynamic transport, in particular in the spatial dependence of the transverse electric field ${E}_{y}$: we find that ${E}_{y}$ is locally enhanced when the flow exhibits a sharp directional anisotropy in the nonequilibrium density. As a consequence, at weak magnetic fields, the curvature of ${E}_{y}$ has opposite signs in the ballistic and hydrodynamic regimes. Moreover, we find a robust signature of the onset of nonlocal correlations in the form of distinctive peaks of the transverse field, which are accessible by local measurements. Our results demonstrate that a purely hydrodynamic approach is insufficient in the Gurzhi regime once a magnetic field is introduced.

Spin-orbit torques in a Rashba honeycomb antiferromagnet

Recent experiments on switching antiferromagnetic domains by electric current pulses have attracted a lot of attention to spin-orbit torques in antiferromagnets. In this work, we employ the tight-binding model solver, kwant, to compute spin-orbit torques in a two-dimensional antiferromagnet on a honeycomb lattice with strong spin-orbit interaction of Rashba type. Our model combines spin-orbit interaction, local s-d-like exchange, and scattering of conduction electrons on on-site disorder potential to provide a microscopic mechanism for angular momentum relaxation. We consider two versions of the model: one with preserved and one with broken sublattice symmetry. A non-equilibrium staggered polarization, that is responsible for the so-called Neel spin-orbit torque, is shown to vanish identically in the symmetric model but may become finite if sublattice symmetry is broken. Similarly, anti-damping spin-orbit torques vanish in the symmetric model but become finite and anisotropic in a model with broken sublattice symmetry. As expected, anti-damping torques also reveal a sizable dependence on impurity concentration. Our numerical analysis also confirms symmetry classification of spin-orbit torques and strong torque anisotropy due to in-plane confinement of electron momenta.

Charge density response and fake plasmons in holographic models with strong translation symmetry breaking

We study the charge density response in holographic models with explicit trans- lation symmetry breaking which is relevant in IR. In particular, we focus on Q-lattices and the Bianchy VII helix. We show that the hydrodynamic sound mode is removed from the spectrum due to the strong momentum relaxation and therefore, the usual treatment of the plasmon as Coulomb-dressed zero sound does not apply. Furthermore, the dominant coherent modes in the longitudinal channel, which control the neutral density-density correlator, are the diffusive modes. We show these modes are strongly suppressed when the boundary Coulomb interaction is turned on. This renders the low frequency charge density response spectrum completely incoherent and featureless.At intermediate frequencies, we observe a broad feature — the fake plasmon — in the dressed correlator, which could be confused with an overdamped plasmon. However, its gap is set by the scale of translation symmetry breaking instead of the plasma frequency. This broad feature originates from the non-hydrodynamic sector of the holographic spectrum, and therefore, its behaviour, typical of strongly correlated quantum critical systems with holographic duals, deviates from the standard Fermi-liquid paradigm.

Excitation of unidirectionally propagating plasmon in the periodic graphene structure

The transformation of normally incident electromagnetic wave into propagating plasmon in periodical graphene structure with double grating gate is theoretically investigated. The most effective transformation appears in case of excitation plasmon modes with the wavevectors quantized with structure period. Blocking the reflection and the transmission of electromagnetic wave through the graphene structure by metal back gate and Fabry-Perot resonator are used. We found the 72% transformation of the incident wave radiation power into the power of unidirectionally-travelling plasmon for 1 ps momentum relaxation time in graphene.

Low Threshold Optical Bistability in Aperiodic PT-Symmetric Lattices Composited with Fibonacci Sequence Dielectrics and Graphene

We explore the optical bistability in aperiodic parity–time-symmetric (PT-symmetric) photonic lattices that are composed of Fibonacci sequence dielectrics and graphene at terahertz frequencies. Two Fibonacci sequence dielectrics, viz. aperiodic photonic lattices, are utilized for enhancing band-edge resonances and achieving the electric field localization that can enhance the nonlinearity of graphene. Modulating the gain-loss factor of dielectrics in the PT symmetry lattices further strengthens the nonlinearity effect and, consequently, low threshold bistability is realized. The interval between the upper and lower bistability thresholds enlarges as the momentum relaxation time of graphene changes. Moreover, we show that the bistability threshold can also be flexibly tuned by modulating the graphene chemical potential. The study might be applied in photomemories and optical switches.

Study of dephasing mechanisms on the potential profile of a nanowire FET

The objective of this work is to study the dephasing mechanisms in a channel of a nanowire FET. A self-consistent Non-Equilibrium Green’s function method is applied to model the channel current dephasing. The potential profile of the channel is obtained by varying the degree of phase and momentum relaxation independently. Studies are performed by invoking both phase and momentum relaxation mechanisms in the FET channel current. The dephasing strength is varied from 0.0003 eV2 to 0.3 eV2. The potential profile across the channel shows a linear behavior under very high value of dephasing strength. Also, the shape of the output characteristics of the nanowire FET gets changed due to dephasing mechanisms.

Quantization of the anomalous Hall conductance in a disordered magnetic Chern insulator

The intrinsic anomalous Hall conductance of a minimal model of the twodimensional disordered Chern insulator is investigated in the framework of Kubo quantum theory of linear response. The electron momentum relaxation is assumed to be due to electron scattering by Gaussian white-noise potential. The explicit expressions for the density of states and are obtained in the self-consistent Born approximation. The numerical analysis of these expressions at the different values of parameters of the considered model shows that calculated takes a quantized value e2/4πħ when the Fermi level lies within the energy gap. This gap is narrowed as disorder increases that leads to decreasing of the Hall plateau width.

Enhanced spin-to-charge current conversion at metal/oxide interfaces by lowering the temperature

We investigated the temperature dependence of the spin-to-charge current conversion at nonmagnetic metal (NM: Cu or Ag)/Bi2O3 interfaces with Rashba spin-splitting. Spin pumping induced inverse Edelstein effects are measured in the temperature range from 290 K to 10 K. Estimated conversion coefficients at the Cu(Ag)/Bi2O3 interfaces are increased by 40 (17)% at 10 K compared with those at 290 K. The conversion coefficient is found to be proportional to the conductivity of the NM layer, indicating that the momentum relaxation process in the metal layer dominates the spin-to-charge current conversion process at NM/Bi2O3 interfaces.

Impact of the scattering physics on the power factor of complex thermoelectric materials

We assess the impact of the scattering physics assumptions on the thermoelectric properties of five Co-based p-type half-Heusler alloys by considering full energy-dependent scattering times vs the commonly employed constant scattering time. For this, we employ density functional theory band structures and a full numerical scheme that uses Fermi's golden rule to extract the momentum relaxation times of each state at every energy, momentum, and band. We consider electron-phonon scattering (acoustic and optical), as well as ionized impurity scattering, and evaluate the qualitative and quantitative differences in the power factors of the materials compared to the case where the constant scattering time is employed. We show that the thermoelectric power factors extracted from the two different methods differ in terms of (i) their ranking between materials, (ii) the carrier density where the peak power factor appears, and (iii) their trends with temperature. We further show that the constant relaxation time approximation smoothens out the richness in the band structure features, thus limiting the possibilities of exploring this richness for material design and optimization. These details are more properly captured under full energy/momentum-dependent scattering time considerations. Finally, by mapping the conductivities extracted within the two schemes, we provide appropriate density-dependent constant relaxation times that could be employed as a fast first-order approximation for extracting charge transport properties in the half-Heuslers we consider.

Modeling Gain Mechanisms in Amorphous Silicon Due to Efficient Carrier Multiplication and Trap-Induced Junction Modulation

Amorphous materials have low mobility due to their nature of disorder. Surprisingly, some disordered materials showed photocurrent amplification not by conventional photoconductive gain. Recently, amorphous Silicon (a-Si) photodiodes with thin a-Si layer (∼40 nm) have shown a gain-bandwidth product of over 2 THz with very low excess noise and also have been used as a gain media in a cascaded system with single photon sensitivity. To unveil the true gain mechanism, we performed theoretical modeling and numerical analysis along with experimental data at different frequencies. We show evidence of highly effective carrier multiplication process within a-Si as the primary gain mechanism, especially at high frequency. We also show presence of trap-induced junction modulation at much lower frequency. We modeled the gain mechanism in a-Si by solving the transport equations including dynamics of defect states and carrier multiplication via the local field model. We further justified the application of local field model for thin a-Si, based on the property that in a-Si, the mean-free path for energy relaxation is orders of magnitude greater than the mean-free-path for momentum relaxation. The analysis further suggests that the carrier multiplication process in thin a-Si can be much more efficient than in thick a-Si, even stronger than single crystalline Si in some cases. Although seemingly counter intuitive, this is consistent with the proposed cycling excitation process where the localized states in the bandtails of disordered materials such as a-Si relax the k -selection rule and increase the rate of carrier multiplication.

Photon-Drag Effect in p-Type Tellurium

The paper suggests spectral and temperature dependences of the light absorption coefficient and photon-drag effect in p-type tellurium exposed to linear polarized light. The photon momentum is considered both in the law of conservation of energy and the matrix element of optical transition between subbands of tellurium valence band. Photoelectric current is measured as time approximation of the hole momentum relaxation.

Effect of Inertia on Linear Viscoelasticity of Harmonic Dumbbell Model

The overdamped (inertialess) dumbbell model is widely utilized to study rheological properties of polymers or other soft matters. In most cases, the effect of inertia is merely neglected because the momentum relaxation is much faster than the bond relaxation. We theoretically analyze the effect of inertia on the linear viscoelasticity of the harmonic dumbbell model. We show that the momentum and bond relaxation modes are kinetically coupled and the inertia can affect the bond relaxation if the momentum relaxation is not sufficiently fast. We derive an overdamped Langevin equation for the dumbbell model, which incorporates the weak inertia effect. Our model predicts the bond relaxation dynamics with the weak inertia effect correctly. We discuss how the weak inertia affects the linear viscoelasticity of a simple harmonic dumbbell model and the Rouse model.

Activation volume dominated diffusivity of Ni50Al50 melt under extreme conditions

In this work, ab initio molecular dynamic simulations investigate diffusivities of Ni and Al in Ni50Al50 melt under high pressures. While the tracer diffusion coefficients at the equilibrium state predicted by Green-Kubo and the Einstein equations follow the Arrhenius relationship and agree well with the experimental and theoretical results, a linear relationship between the logarithm of tracer diffusion coefficients and the external pressure is addressed in term of an activation volume modified Arrhenius relations. It is understood that the autocorrelation velocity functions (VACF) characterizes the capacity of an atom memorizing the velocity, which has also been considered as one of important approaches revealing thermodynamics, kinetics and structure relaxation dynamics of melts. The onset of the negative region of VACF is in line with the plateau of the meaning square displacement representing the cage effect of the system. The initial damping oscillations of VACFs are due to the momentum relaxation caused by the collision between the tagged atoms and its neighbor ones while the subsequent rises result from the energy relaxation. This work provides an insight into the physical factors controlling these dynamic behaviors under extreme conditions of Ni-Al, which could be extended to the other advanced materials.

Phase coherent transport in bilayer and trilayer MoS2

Bilayer MoS2 is a centrosymmetric semiconductor with degenerate spin states in the six valleys at the corners of the Brillouin zone. It has been proposed that breaking of this inversion symmetry by an out-of-plane electric field breaks this degeneracy, allowing for spin and valley lifetimes to be manipulated electrically in bilayer MoS2 with an electric field. In this work, we report phase-coherent transport properties of double-gated mono-, bi-, and tri-layer MoS2. We observe a similar crossover from weak localization to weak anti-localization, from which we extract the spin relaxation time as a function of both electric field and temperature. We find that the spin relaxation time is inversely proportional to momentum relaxation time, indicating that D'yakonov-Perel mechanism is dominant in all devices despite its centrosymmetry. Further, we found no evidence of electric-field induced changes in spin-orbit coupling strength. This suggests that the interlayer coupling is sufficiently weak and that electron-doped dichalcogenide multilayers behave electrically as decoupled monolayers.

(Invited) A New Analysis of the Dependence of Critical Electric Field on Semiconductor Bandgap

Recently there has been much interest in wide- and ultra-wide-bandgap (WBG/UWBG) semiconductors for power conversion, radio-frequency, and other applications. The benefits of these materials for high-power devices ultimately stems from the increase in critical electric field (EC) with increasing bandgap (EG). Most researchers cite the work of Hudgins et al. [IEEE Trans Power Elec. 18, 907 (2003)] which reported that EC ~ EG 2.0 for indirect-gap materials and EC ~ EG 2.5 for direct-gap materials. These dependencies are based on empirical power-law fits to reported experimental data. The exponent in the power-law is critical when predicting the performance of power devices composed of new UWBG materials, since the Unipolar Figure-of-Merit (UFOM) scales as EC 3. This work has re-analyzed old data and also analyzed new data, and has found EC ~ EG 1.8 with no difference between direct- and indirect-gap materials. A theory that explains this dependence has also been derived and shows good agreement with the experimental data. A key point is that the critical electric field is not a constant for a given material. Rather, EC depends on temperature and doping. Further, it is defined for a triangular field distribution, i.e. a non-punch-through (NPT) drift region, not a punch-through (PT) drift region with a trapezoidal field distribution. Careful examination of the literature revealed that critical electric field values have been reported for various doping levels, and that in general no distinction between values derived from PT and NPT structures has been made. Fortunately, in most cases values have been reported at room temperature, which is taken to be standard. As such, we have derived a procedure that allows EC values to be normalized to a fixed doping (1×1016 cm-3) and a NPT field distribution. The method equates the ionization integrals for the non-standard and standard configurations and backs out the values of EC normalized to the standard configuration. Using this algorithm, normalized values of EC for a variety of semiconductors were tabulated and plotted against bandgap. These data are shown in the attached Figure, where a power-law fit yielding an exponent of 1.8 for both direct- and indirect-gap semiconductors is also shown. The conventional semiconductors Ge, Si, InP, GaAs, and GaP are all included. The narrow-gap semiconductors InSb and InAs are not included, as it is believed that breakdown in these materials may have substantial contributions from tunneling, in addition to impact ionization. GaSb is also excluded due to experimental uncertainty. The wide-bandgap semiconductors SiC and GaN are included in the analysis, although considerable debate still exists concerning the critical field of GaN. For the UWBG semiconductors such as Ga2O3, AlN, and diamond, even more uncertainty exists, and only the critical electric field of diamond has been included in the analysis, which is nevertheless subject to large uncertainty. To explain the observed experimental data, a model based on the ionization integral has been derived. In this model, the ionization integral is transformed from an integral over space into an integral over electric field. The ionization rate as a function of field is then inserted into the integral. For this, the lucky-drift model of Ridley is used [J. Phys. C 16, 3373 (1983)]. This model is an extension of the more-commonly-cited lucky electron model first proposed by Shockley. In the extended model of Ridley, elastic momentum relaxation is considered in addition to energy relaxation. The model depends on three input parameters, which are the threshold energy required for ionization (Eth), the mean carrier relaxation length (l), and the ratio of the average energy lost per collision to the threshold energy (r). These parameters all depend on bandgap, with Eth ~ EG, l ~ EG -3/2, and r ~ EG -1. Inserting these dependencies into the ionization integral and numerically extracting the electric field at which avalanche occurs for a given bandgap yields a curve of EC versus EG, which closely matches the experimental EC ~ EG dependence. This work was partially supported by the Laboratory Directed Research and Development program at Sandia National Laboratories, a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly-owned subsidiary of Honeywell International Inc, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525. This material is also based upon work supported by the Assistant Secretary of Defense for Research and Engineering under Air Force Contract No. FA8702-15-D-0001. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the Assistant Secretary of Defense for Research and Engineering. Figure 1

The Effect of Elastic and Inelastic Scattering on Electronic Transport in Open Systems

Abstract The purpose of this study is to apply the distribution function formalism to the problem of electronic transport in open systems, and to numerically solve the kinetic equation with a dissipation term. This term is modeled within the relaxation time approximation and contains two parts, corresponding to elastic or inelastic processes. The collision operator is approximated as a sum of the semi-classical energy dissipation term and the momentum relaxation term, which randomizes the momentum but does not change the energy. As a result, the distribution of charge carriers changes due to the dissipation processes, which has a profound impact on the electronic transport through the simulated region discussed in terms of the current–voltage characteristics and their modification caused by the scattering. Measurements of the current–voltage characteristics for titanium dioxide thin layers are also presented, and compared with the results of numerical calculations.

Joule-Thomson expansion in AdS black holes with momentum relaxation

The inner structure of realistic materials make them exhibit momentum relaxation. In this paper we study the Joule-Thomson effect on AdS black holes in which translational invariance is broken by two methods: First by considering planar black holes in general relativity supported by scalar fields with a linear dependence on the horizon coordinates and secondly by considering black holes in massive gravity models in which momentum relaxation is obtained by breaking the bulk diffeomorphism invariance of the theory. In contrast with black holes studied so far, for both theories it is possible to obtain inversion curves with two branches reproducing the behavior of Van der Waals fluids. Moreover in the specific case of the massive gravity model we show that black holes can heat up when crossing the inversion curve.