Semiclassical Boltzmann Equations Research Articles

Magnetism and magnetotransport in the kagome antiferromagnet Mn3Ge

We perform classical Monte Carlo and stochastic Landau-Lifshitz-Gilbert simulations to study the temperature-dependent magnetism of the kagome antiferromagnet Weyl metal ${\text{Mn}}_{3}\text{Ge}$, and we find that a long-range chiral order sets in at a transition temperature well below the N\'eel temperature (${T}_{N}$). Based on the crystalline symmetries imposed by the chiral magnetic order, we argue for the presence of multiple isoenergetic Weyl nodes (nodes that are at the same energy and with a congruent Fermi surface around them) near the chemical potential. Using the semiclassical Boltzmann equations, we show that the combined contribution to the net longitudinal magnetoconductance (LMC) and the planar Hall conductance (PHC) from tilted Weyl nodes can lead to signatures that are qualitatively distinct from that of a single pair of Weyl nodes. In particular, we show that magnetic orders with different chiralities can give rise to different periods in LMC and PHC as a function of the in-plane magnetic field direction. This is ultimately related to differences in the symmetry-imposed constraints on the Weyl nodes.

CP-violating transport theory for electroweak baryogenesis with thermal corrections

We derive CP-violating transport equations for fermions for electroweak baryogenesis from the CTP-formalism including thermal corrections at the one-loop level. We consider both the VEV-insertion approximation (VIA) and the semiclassical (SC) formalism. We show that the VIA-method is based on an assumption that leads to an ill-defined source term containing a pinch singularity, whose regularisation by thermal effects leads to ambiguities including spurious ultraviolet and infrared divergences.We then carefully review the derivation of the semiclassical formalism and extend it to include thermal corrections. We present the semiclassical Boltzmann equations for thermal WKB-quasiparticles with source terms up to the second order in gradients that contain both dispersive and finite width corrections. We also show that the SC-method reproduces the current divergence equations and that a correct implementation of the Fick's law captures the semiclassical source term even with conserved total current ∂μ j μ = 0. Our results show that the VIA-source term is not just ambiguous, but that it does not exist. Finally, we show that the collisional source terms reported earlier in the semiclassical literature are also spurious, and vanish in a consistent calculation.

An Efficient GFET Structure

A graphene field effect transistor, where the active area is made of monolayer large-area graphene, is simulated including a full 2D Poisson equation and a drift-diffusion model with mobilities deduced by a direct numerical solution of the semiclassical Boltzmann equations for charge transport by a suitable discontinuous Galerkin approach. The critical issue in a graphene field effect transistor is the difficulty of fixing the off state which requires an accurate calibration of the gate voltages. In the present paper we propose and simulate a graphene field effect transistor structure which has well-behaved characteristic curves similar to those of conventional (with gap) semiconductor materials. The introduced device has a clear off region and can be the prototype of devices suited for post-silicon nanoscale electron technology. The specific geometry overcomes the problems of triggering the minority charge current and gives a viable way for the design of electron devices based on large area monolayer graphene as substitute of standard semiconductors in the active area. The good field effect transistor behavior of the current versus the gate voltage makes the simulated device very promising and a challenging case for experimentalists.

Temperature Dependent Resistivity of Chiral Single-Walled Carbon Nanotubes in the Presence of Coherent Light Source

We have studied the axial resistivity of chiral single-walled carbon nanotubes (SWCNTs) in the presence of a combined direct current and high frequency alternating fields. We employed semiclassical Boltzmann equations approach and compared our results with a similar study that examined the circumferential resistivity of these unique materials. Our work shows that these materials display similar resistivity for both axial and circumferential directions and this largely depends on temperature, intensities of the applied fields and material parameters such as chiral angle. Based on these low-temperature bidirectional conductivity responses, we propose chiral SWCNTs for design of efficient optoelectronic devices.

ULYSSES: Universal LeptogeneSiS Equation Solver

ULYSSES is a python package that calculates the baryon asymmetry produced from leptogenesis in the context of a type-I seesaw mechanism. The code solves the semi-classical Boltzmann equations for points in the model parameter space as specified by the user. We provide a selection of predefined Boltzmann equations as well as a plugin mechanism for externally provided models of leptogenesis. Furthermore, the ULYSSES code provides tools for multi-dimensional parameter space exploration. The emphasis of the code is on user flexibility and rapid evaluation. It is publicly available at https://github.com/earlyuniverse/ulysses. Program summaryProgram Title: ULYSSESCPC Library link to program files:https://doi.org/10.17632/rzd24f34h2.1Developer’s repository link:github.com/earlyuniverse/ulyssesLicensing provisions: MITProgramming language: python3Nature of problem: Solving semi-classical momentum averaged Boltzmann equations for leptogenesis in the context of a type-I seesaw mechanism.Solution method: Numerically solving coupled differential equations that can be complex.

Acoustomagnetoelectric effect in two-dimensional materials: Geometric resonances and Weiss oscillations

We study electron transport in two-dimensional materials with parabolic and linear (graphene) dispersions of the carriers in the presence of surface acoustic waves and an external magnetic field using semiclassical Boltzmann equations approach. We observe an oscillatory behavior of both the longitudinal and Hall electric currents as functions of the surface acoustic wave frequency at a fixed magnetic field and as functions of the inverse magnetic field at a fixed frequency of the acoustic wave. We explain the former by the phenomenon of geometric resonances, while we relate the latter to the Weiss-like oscillations in the presence of the dynamic superlattice created by the acoustic wave. Thus we demonstrate the dual nature of the acoustomagnetoelectric effect in two-dimensional electron gas.

A full coupled drift-diffusion-Poisson simulation of a GFET

A graphene field effect transistor (GFET), where the active area is made of monolayer large-area graphene, is simulated including a full 2D Poisson equation and a drift-diffusion model with mobilities deduced by a direct numerical solution of the semiclassical Boltzmann equations for charge transport by a suitable discontinuous Galerkin approach Romano et al. (2015), Coco et al. (2017), Coco et al. (2019), Majorana et al. (2019), Coco and Nastasi (2020)[1–5]. The results are qualitatively in agreement with experimental data and other simulations known in the literature and based on compact models where some heuristics is present (see for example Jiménez and Moldovan (2011), Upadhyay et al. (2018)[6,7]).The critical issue in a GFET is the difficulty of fixing the off state which requires an accurate calibration of the gate voltages. In the present paper we have further confirmation of this feature which makes GFET not the optimal device for post-silicon nanoscale electron technology.

Simulation of bipolar charge transport in graphene on h-BN

Purpose The purpose of this paper is to simulate charge transport in monolayer graphene on a substrate made of hexagonal boron nitride (h-BN). This choice is motivated by the fact that h-BN is one of the most promising substrates on account of the reduced degradation of the velocity due to the remote impurities. Design/methodology/approach The semiclassical Boltzmann equations for electrons in the monolayer graphene are numerically solved by an approach based on a discontinuous Galerkin (DG) method. Both the conduction and valence bands are included, and the inter-band scatterings are taken into account as well. Findings The importance of the inter-band scatterings is accurately evaluated for several values of the Fermi energy, addressing the issue related to the validity of neglecting the generation-recombination terms. It is found out that the inclusion of the inter-band scatterings produces sizable variations in the average values, like the current density, at zero Fermi energy, whereas, as expected, the effect of the inter-band scattering becomes negligible by increasing the absolute value of the Fermi energy. Research limitations/implications The correct evaluation of the influence of the inter-band scatterings on the electronic performances is deeply important not only from a theoretical point of view but also for the applications. In particular, it will be shown that the time necessary to reach the steady state is greatly affected by the inter-band scatterings, with not negligible consequences on the switching on/off processes of realistic devices. As a limitation of the present work, the proposed approach refers to the spatially homogeneous case. For the simulation of electron devices, non-homogenous numerical solutions are required. This last case will be tackled in a forthcoming paper. Originality/value As observed in Majorana et al. (2019), the use of a Direct Simulation Monte Carlo (DSMC) approach, which properly describes the inter-band scatterings, is computationally very expensive because the valence band is highly populated and a huge number of particles is needed. Even by simulating holes instead of electrons does not overcome the problem because there is a certain degree of ambiguity in the generation and recombination terms of electron-hole pairs. The DG approach, used in this paper, does not suffer from the previous drawbacks and requires a reasonable computing effort.

Improved mobility models for charge transport in graphene

Abstract Charge transport in graphene is crucial for the design of a new generation of nanoscale electron devices. A reasonable model is represented by the semiclassical Boltzmann equations for electrons in the valence and conduction bands. As shown by Romano et al. (J. Comput. Phys., 2015), the discontinuous Galerkin methods are a viable way to tackle the problem of the numerical integration of these equations, even if efficient DSMC with a proper inclusion of the Pauli principle have been also devised. One of the advantages of the solutions obtained with deterministic approach is of course the absence of statistical noise. This fact is crucial for an accurate estimation of the low field mobility as proved by Majorana et al. (J. Math. Industry, 2016) in the case of a unipolar charge transport in a suspended graphene sheet under a constant electric field. The mobility expressions are essential for the drift-diffusion equations which constitute the most adopted models for charge transport in CAD. Here the analysis by Majorana et al. (J. Math. Industry, 2016) is improved in two ways: by including the charge transport both in the valence and conduction bands; by taking into account the presence of an oxide as substrate for the graphene sheet. New models of mobility are obtained and, in particular, relevant improvements of the low field mobility are achieved.

Effect of halogens doping on transparent conducting properties of SnO2 rutile: an ab initio investigation

We discuss the fundamental transparent conducting properties of halogens doped SnO2 rutile systems include the structural, electronic structure, optical and electrical properties. Within this study, we employ the first-principles calculation of the full potential linearized augmented plane wave (FP-LAPW) method based on the density function theory and semiclassical Boltzmann equations. It is found that the halogens substitutional doping cause an expansion of SnO2 lattice constants and low thermodynamic perturbation. The dopants act as shallow donors by creating impurity states at the bottom of the conduction band that lead to blue-shift in the optical transparency. Moreover, the electrical conductivity of SnO2 Rutile is significantly improving by halogens doping. In fact, these results could stimulate the future experimental works for elaborating new generations of the transparent conducting oxides in an optimal way.

Exploration of thermoelectricity in ScRhTe and ZrPtPb Half Heusler compounds: A first principle study

Motivated by the results of other well known Half Heusler compounds, the structural, electronic, phonon and thermoelectric properties of two novel Half Heusler compounds ScRhTe and ZrPtPb are thoroughly investigated with the frame work of first principle calculations and semi classical Boltzmann equations with constant relaxation time approximation. These materials show direct band semiconductors nature with band gap 0.43 eV (ScRhTe) and 0.83 eV (ZrPtPb) respectively. The phonon dispersion curves indicate that these compounds are thermodynamically stable. The Seebeck coefficient, electrical conductivity, electronic thermal conductivity and power factor as function of chemical potential are evaluated in this report. These materials have high power factor for n-type doping. The lattice thermal conductivity of these materials decreases with increase in temperature. The calculated results divulge that these materials are potential candidates for thermoelectric applications.

Emergence of thermoelectricity in Half Heusler topological semimetals with strain

The band structure and thermoelectric properties of Half Heusler topological materials XPtBi (X = Sc,Y, Lu) have been investigated using density functional theory and semi-classical Boltzmann equations. At 5% strain, the band gap opens in all the materials but maximum band opens in LuPtBi and acts as thermoelectric materials. We have calculated the Seebeck coefficient, electrical conductivity, electronic thermal conductivity and lattice thermal conductivity of these materials. Thermoelectric properties at high temperature and lattice thermal conductivity of these materials are studied first time in this work. The thermoelectric performance of LuPtBi is high because of low lattice thermal conductivity as compared to ScPtBi and YPtBi.

New potential dopants for BaSnO3-based transparent conducting oxides

In this paper, we present ab initio calculations to evaluate the potential of alternative dopants for mono-doping BaSnO3 in order to develop new BaSnO3-based transparent conducting oxides. The calculations have been carried out using the density functional theory and semi-classical Boltzmann equations to investigate the structural, electronic structure, optical and electrical transport properties of doped BaSnO3 systems. The results would help to plan the future experimental works.

Nonlocal Drag of Magnons in a Ferromagnetic Bilayer

Quantized spin waves, or magnons, in a magnetic insulator are assumed to interact weakly with the surroundings, and to flow with little dissipation or drag, producing exceptionally long diffusion lengths and relaxation times. In analogy to Coulomb drag in bilayer two-dimensional electron gases, in which the contribution of the Coulomb interaction to the electric resistivity is studied by measuring the interlayer resistivity (transresistivity), we predict a nonlocal drag of magnons in a ferromagnetic bilayer structure based on semiclassical Boltzmann equations. Nonlocal magnon drag depends on magnetic dipolar interactions between the layers and manifests in the magnon current transresistivity and the magnon thermal transresistivity, whereby a magnon current in one layer induces a chemical potential gradient and/or a temperature gradient in the other layer. The largest drag effect occurs when the magnon current flows parallel to the magnetization; however, for oblique magnon currents a large transverse current of magnons emerges. We examine the effect for practical parameters, and find that the predicted induced temperature gradient is readily observable.

Dynamics of the energy relaxation in a parabolic quantum well laser

We explore two parabolic quantum well (PQW) samples, with and without Bragg mirrors, in order to optimise the building blocks of a Bosonic Cascade Laser. The photoluminescence spectra of a PQW microcavity sample is compared against that of a conventional microcavity with embedded quantum wells (QWs) to demonstrate that the weak coupling lasing in a PQW sample can be achieved. The relaxation dynamics in a conventional QW microcavity and in the PQW microcavity was studied by a non-resonant pump-pump excitation method. Strong difference in the relaxation characteristics between the two samples was found. The semi-classical Boltzmann equations were adapted to reproduce the evolution of excitonic populations within the PQW as a function of the pump power and the output intensity evolution as a function of the pump-pump pulse delay. Fitting the PQW data confirms the anticipated cascade relaxation, paving the way for such a system to produce terahertz radiation.

First-principles and Boltzmann equation studies of the Cl-doped ZnO transparent conducting oxide

The density functional theory and semiclassical Boltzmann equations were employed to study the electronic, optical, and electrical properties Cl-doped ZnO. As results, the substitution Cl-dopants in O site lead to increase the optical band and blue-shift. Additionally, the Cl-dopant creates shallow donor derived mainly from Cl-3s states. The transmittance is somewhat wakened in the visible and IR regions, while it is significantly improved in UV region. The electrical conductivity is enhanced as result of Cl doping.

Spin-dependent Seebeck effect and huge growth of thermoelectric parameters at band edges in H- and F-doped graphene, free-standing and deposited on 4H-SiC(0001) C-face

Graphene halfly doped with H or F possesses local magnetization at the undoped C sites. Thus the Seebeck coefficient is different for each spin channel and its sign also changes depending on the spin polarization. Deposition of doped graphene on the C-face 4H-SiC(0001) with two buffer layers substantially varies the electronic and thermoelectric properties. These properties are efficiently calculated from the semiclassical Boltzmann equations, using the maximally-localized Wannier-functions interpolation of the band structures obtained with the density-functional theory. Our results indicate large growth of the thermopower and the ZT efficiency at the band edges. We show in the model discussion that this phenomenon is more general and applies also to other systems than graphene. It gives prospect for developing new spintronic devices working in the band-edge regime.

Electrically-controlled nonlinear terahertz optical properties of graphene

In this paper, we present a detailed theoretical study of nonlinear terahertz optical properties of graphene in the presence of electric field and terahertz radiation field. The optical current is computed and investigated on the basis of quantum theory and semi-classical Boltzmann equations. It shows a large nonlinear terahertz response and the nonlinearity becomes larger with increasing electric field or decreasing terahertz frequencies. Moreover, it is found that the optical nonlinearity can be modified and controlled by electric fields.

Anomalous Hall effects of light and chiral edge modes on the Kagomé lattice

We theoretically investigate a photonic Kagom\'e lattice which can be realized in microwave cavity arrays using current technology. The Kagom\'e lattice exhibits an exotic band structure with three bands, one of which can be made completely flat. The presence of artificial gauge fields makes it possible to emulate topological phases and induce chiral edge modes which can coexist inside the energy gap with the flat band that is topologically trivial. By tuning the artificial fluxes or in the presence of disorder, the flat band can also acquire a bandwidth in energy allowing the coexistence between chiral edge modes and bulk extended states; in this case the chiral modes become fragile towards scattering into the bulk. The photonic system then exhibits equivalents of both a quantum Hall effect without Landau levels and an anomalous Hall effect characterized by a nonquantized Chern number. We discuss experimental observables such as local density of states and edge currents. We show how synthetic uniform magnetic fields can be engineered, which allows an experimental probe of Landau levels in the photonic Kagom\'e lattice. We then draw on semiclassical Boltzmann equations for transport to devise a method to measure Berry's phases around loops in the Brillouin zone. The method is based solely on wave-packet interference and can be used to determine band Chern numbers or the photonic equivalent of the anomalous Hall response. We demonstrate the robustness of these measurements towards on-site and gauge-field disorder. We also show the stability of the anomalous quantum Hall phase for nonlinear cavities and for (artificial) atom-photon interactions.

Generic picture of the emission properties of III-nitride polariton laser diodes: Steady state and current modulation response

The main emission characteristics of electrically driven polariton lasers based on planar GaN microcavities with embedded InGaN quantum wells are studied theoretically. The polariton emission dependence on pump current density is first modeled using a set of semiclassical Boltzmann equations for the exciton polaritons that are coupled to the rate equation describing the electron-hole plasma population. Two experimentally relevant pumping geometries are considered, namely the direct injection of electrons and holes into the strongly coupled microcavity region and intracavity optical pumping via an embedded light-emitting diode. The theoretical framework allows the determination of the minimum threshold current density J(thr),(min) as a function of lattice temperature and exciton-cavity photon detuning for the two pumping schemes. A J(thr, min) value of 5 and 6 A cm(-2) is derived for the direct injection scheme and for the intracavity optical pumping one, respectively, at room temperature at the optimum detuning. Then an approximate quasianalytical model is introduced to derive solutions for both the steady-state and high-speed current modulation. This analysis makes it possible to show that the exciton population, which acts as a reservoir for the stimulated relaxation process, gets clamped once the condensation threshold is crossed, a behavior analogous to what happens in conventional laser diodes with the carrier density above threshold. Finally, the modulation transfer function is calculated for both pumping geometries and the corresponding cutoff frequency is determined.