Semiclassical Monte Carlo Simulation Research Articles

Vapor-liquid equilibrium and thermodynamic properties of saturated argon and krypton from Monte Carlo simulations using abinitio potentials.

Vapor-liquid equilibria and thermodynamic properties of saturated argon and krypton were calculated by semi-classical Monte Carlo simulations with the NpT + test particle method using abinitio potentials for the two-body and nonadditive three-body interactions. The NpT + test particle method was extended to the calculation of second-order thermodynamic properties, such as the isochoric and isobaric heat capacities or the speed of sound, of the saturated liquid and vapor by using our recently developed approach for the systematic calculation of arbitrary thermodynamic properties in the isothermal-isobaric ensemble. Generally, the results for all simulated properties agree well with experimental data and the current reference equations of state for argon and krypton. In particular, the results for the vapor pressure and for the density and speed of sound of the saturated liquid and vapor agree with the most accurate experimental data for both noble gases almost within the uncertainty of these data, a level of agreement unprecedented for many-particle simulations. This study demonstrates that the vapor-liquid equilibrium and thermodynamic properties at saturation of a pure fluid can be predicted by Monte Carlo simulations with high accuracy when the intermolecular interactions are described by state-of-the-art abinitio pair and nonadditive three-body potentials and quantum effects are accounted for.

Network of chiral one-dimensional channels and localized states emerging in a moiré system

Moiré systems provide a highly tunable platform for engineering band structures and exotic correlated phases. Here, we theoretically study a model for a single layer of graphene subject to a smooth moiré electrostatic potential, induced by an insulating substrate layer. For sufficiently large moiré unit cells, we find that ultra-flat bands coexist with a triangular network of chiral one-dimensional (1D) channels. These channels mediate an effective interaction between localized modes with spin-, orbital- and valley degrees of freedom emerging from the flat bands. The form of the interaction reflects the chirality and 1D nature of the network. We study this interacting model within an SU(4) mean-field theory, semi-classical Monte-Carlo simulations, and an SU(4) spin-wave theory, focusing on commensurate order stabilized by local two-site and chiral three-site interactions. By tuning a gate voltage, one can trigger a non-coplanar phase characterized by a peculiar coexistence of three different types of order: ferromagnetic spin order in one valley, non-coplanar chiral spin order in the other valley, and 120∘ order in the remaining spin and valley-mixed degrees of freedom. Quantum and classical fluctuations have qualitatively different effects on the observed phases and can, for example, create a finite spin-chirality purely via fluctuation effects.

Detection and Modeling of Hole Capture by Single Point Defects under Variable Electric Fields

Understanding carrier trapping in solids has proven key to semiconductor technologies, but observations thus far have relied on ensembles of point defects, where the impact of neighboring traps or carrier screening is often important. Here, we investigate the capture of photogenerated holes by an individual negatively charged nitrogen-vacancy (NV) center in diamond at room temperature. Using an externally gated potential to minimize space-charge effects, we find the capture probability under electric fields of variable sign and amplitude shows an asymmetric-bell-shaped response with maximum at zero voltage. To interpret these observations, we run semiclassical Monte Carlo simulations modeling carrier trapping through a cascade process of phonon emission and obtain electric-field-dependent capture probabilities in good agreement with experiment. Because the mechanisms at play are insensitive to the characteristics of the trap, we anticipate the capture cross sections we observe─largely exceeding those derived from ensemble measurements─may also be present in materials platforms other than diamond.

Heat transport in an optical lattice via Markovian feedback control

Ultracold atoms offer a unique opportunity to study many-body physics in a clean and well-controlled environment. However, the isolated nature of quantum gases makes it difficult to study transport properties of the system, which are among the key observables in condensed matter physics. In this work, we employ Markovian feedback control to synthesize two effective thermal baths that couple to the boundaries of a one-dimensional Bose–Hubbard chain. This allows for the realization of a heat-current-carrying state. We investigate the steady-state heat current, including its scaling with system size and its response to disorder. In order to study large systems, we use semi-classical Monte-Carlo simulation and kinetic theory. The numerical results from both approaches show, as expected, that for non- and weakly interacting systems with and without disorder one finds the same scaling of the heat current with respect to the system size as it is found for systems coupled to thermal baths. Finally, we propose and test a scheme for measuring the energy flow. Thus, we provide a route for the quantum simulation of heat-current-carrying steady states of matter in atomic quantum gases.

Thermodynamic properties of argon from Monte Carlo simulations using ab initio potentials.

Ten different thermodynamic properties of the noble gas argon in the liquid and supercritical regions were obtained from semiclassical Monte Carlo simulations in the isothermal-isobaric ensemble using ab initio potentials for the two-body and nonadditive three-body interactions. Our results for the density and speed of sound agree with the most accurate experimental data for argon almost within the uncertainty of these data, a level of agreement unprecedented for many-particle simulations. This demonstrates the high predictive but yet unexploited power of ab initio potentials in the field of molecular modeling and simulation for thermodynamic properties of fluids.

Characterization of the inner edge of the neutron star crust

The poorly known crustal equation of state plays a critical role in many observational phenomena associated with a neutron star. Using semi-classical Monte Carlo simulations, we explore the possible configurations of the inner edge of the neutron-star crust for a variety of baryon densities and proton fractions. Applying the Kirkwood--Buff theory to these two-component systems, we observe how the isothermal compressibility reaches a maximum when isolated non-symmetric clusters are formed in an extremely dilute neutron gas. To determine the neutron fraction, we suggest a geometrical model based on the behavior of the proton-neutron pair correlation function. Accordingly, the equation of state of the inner crust is calculated, illustrating that the nuclear energy in beta-equilibrium follows a power-law behavior with baryon density. As a possible astrophysical outcome of this study, our results could help refine the mass-radius relation. Finally, our results pave the way towards further investigations of the impact of the proton-neutron pair correlation function on transport properties within the neutron-star crust.

Monte Carlo analysis of the influence of surface charges on GaN asymmetric nanochannels: Bias and temperature dependence

In this paper, the occupancy of sidewall surface states having a clear signature in the performance of AlGaN/GaN-based self-switching diodes (SSDs) is analyzed using a semi-classical Monte Carlo (MC) simulator in a wide temperature (T) range, from 100 to 300 K. Experimental I–V curves show an unusual current decrease at low temperature attributed to surface trapping. The dependence on T of the negative surface charge density σ at the etched sidewalls of the SSDs is essential to explain the measurements. Two devices with different widths (80 and 150 nm) have been characterized and simulated in detail paying especial attention to the modeling of the surface states. At room temperature, MC simulations with a position-independent value of σ are able to qualitatively reproduce the I–V curves. However, a more complex approach is required to correctly replicate the values and shape of the DC experimental curves at low temperature, below 220 K. An algorithm where σ depends not only on T but also on the applied bias V is proposed to successfully fit the current values at every bias point. The model is able to explain the physics of the unexpected dependence of the resistance with the channel width and the sign change in the bowing coefficient, the parameters that govern the detection capabilities of the diodes.

Wertheim Model for Quantum Associating Hard Spheres

In this article we analyze the introduction of quantum effects in the modeling of a quantum fluid formed by hard spheres with an off-center square-well attractive site, a quantum associating hard-spheres (QAHS) system. Semiclassical Monte Carlo simulations for the QAHS fluid were performed in order to study the variation of the fraction of free monomers with the thermal de Broglie wavelength λB = h/(2πmkT)1/2, where T is the temperature, h and k are the Planck’s and Boltzmann’s constants, respectively, and m is the hard-spheres mass. We present a quantum extension of the Wertheim model by considering the effect of the quantum nature of the system using the Slater sum for quantum hard spheres. Excellent agreement is found between theory and simulation results for the case of a bulk fluid.

Quantum and Thermal Phase Transitions of the Triangular SU(3) Heisenberg Model under Magnetic Fields.

We study the quantum and thermal phase transition phenomena of the SU(3) Heisenberg model on triangular lattice in the presence of magnetic fields. Performing a scaling analysis on large-size cluster mean-field calculations endowed with a density-matrix renormalization-group solver, we reveal the quantum phases selected by quantum fluctuations from the massively degenerate classical ground-state manifold. The magnetization process up to saturation reflects three different magnetic phases. The low- and high-field phases have strong nematic nature, and especially the latter is found only via a nontrivial reconstruction of symmetry generators from the standard spin and quadrupolar description. We also perform a semiclassical MonteCarlo simulation to show that thermal fluctuations prefer the same three phases as well. Moreover, we find that exotic topological phase transitions driven by the binding-unbinding of fractional (half-)vortices take place, due to the nematicity of the low- and high-field phases. Possible experimental realization with alkaline-earth-like cold atoms is also discussed.

Thermal rectification optimization in nanoporous Si using Monte Carlo simulations

We investigate thermal rectification in nanoporous silicon using a semiclassical Monte Carlo simulation method. We consider geometrically asymmetric nanoporous structures and investigate the combined effects of porosity, interpore distance, and pore position relative to the device boundaries. Two basis geometries are considered, one in which the pores are arranged in rectangular arrays and ones in which they form triangular arrangements. We show that systems (i) with denser, compressed pore arrangements (i.e., with smaller interpore distances), (ii) with the pores positioned closer to the device edge/contact, and (iii) with the pores in a triangular arrangement can achieve rectification of over 55%. Introducing smaller pores into existing porous geometries in a hierarchical fashion increases rectification even further to over 60%. Importantly, for the structures we simulate, we show that sharp rectifying junctions, separating regions of long from short phonon mean-free-paths, are more beneficial for rectification than spreading the asymmetry throughout the material along the heat direction in a graded fashion.

Nanostructured potential well/barrier engineering for realizing unprecedentedly large thermoelectric power factors

This work describes, through the semi-classical Boltzmann transport theory and simulation, a novel nanostructured material design that can lead to unprecedentedly high thermoelectric power factors, with improvements of more than an order of magnitude compared to optimal bulk material power factors. The design is based on a specific grain/grain-boundary (potential well/barrier) engineering such that: i) carrier energy filtering is achieved using potential barriers, combined with ii) higher than usual doping operating conditions such that high carrier velocities and mean-free-paths are utilized, iii) minimal carrier energy relaxation is achieved after passing over the barriers to propagate the high Seebeck coefficient of the barriers into the potential wells, and, importantly, iv) an intermediate dopant-free (depleted) region is formed. Thus, the design consists of a ‘three-region geometry’, in which the high doping resides in the center/core of the potential well, with a dopant-depleted region separating the doped region from the potential barriers. It is shown that the filtering barriers are optimal when they mitigate the reduction in conductivity they introduce, and this can be done primarily when they are ‘clean’ from dopants during the process of filtering. The potential wells, on the other hand, are optimal when they mitigate the reduced Seebeck coefficient they introduce by: i) not allowing carrier energy relaxation, and ii) mitigating the reduction in mobility that the high concentration of dopant impurities causes. It is shown that dopant segregation, with ‘clean’ dopant-depletion regions around the potential barriers, serves this key purpose of improved mobility toward the phonon-limited mobility levels in the wells. Using quantum transport simulations based on the non-equilibrium Green's function method as well as semi-classical Monte Carlo simulations, we also verify the important ingredients and validate this ‘clean-filtering’ design.

Monte Carlo study of β-Ga2O3 conductivity

Using semiclassical Monte Carlo simulations a conductivity of β-Ga2O3 is investigated considering a scattering of charge carriers on acoustical phonons, polar optical phonons and charged impurities. Modelling takes into account 12 IR active polar optical phonons modes. Dependence of mean collision frequency on energy of charge carriers is examined. The results are compared with the conclusions of other groups of researchers.

Holographic interferences in photoelectron spectra: different approaches

We perform a theoretical study of the holographic structures in photoelectron spectra for ionization of hydrogen atoms induced by short laser pulses. To elucidate the nature of the holographic structures present in the momentum distributions of photoelectrons, we use several quantum approximations, such as the strong field and Coulomb–Volkov approximations up to second order, as well as semiclassical Monte Carlo simulations. In a single-cycle pulse, we eliminate the intracycle interference from the spectra isolating the holographic structure formed in the photoionization process. We probe the different approaches and analyze the role of electron–core interaction numerically by solving the time dependent Schrodinger equation. We show that the two-step semiclassical model of Shvetsov-Shilovski et al. [Phys. Rev. A 94, 013415 (2016)] fully considers the effect of the Coulomb potential on the electron dynamics and semiclassical phase reproducing the holographic structure in full quantum calculations. Contrarily, perturbative quantum (strong field and Coulomb–Volkov) and semiclassical (quantum trajectory Monte Carlo) methods account only partially for some of the characteristics of the holographic interference pattern.

Electron transport within the wurtzite and zinc-blende phases of gallium nitride and indium nitride

Wide energy gap semiconductors are broadly recognized as promising materials for novel electronic and opto-electronic device applications. As informed device design requires a firm grasp on the material properties of the underlying electronic materials, the electron transport that occurs within the wide energy gap semiconductors has been the focus of considerable study over the years. In an effort to provide some perspective on this rapidly evolving and burgeoning field of research, we review analyzes of the electron transport within some wide energy gap semiconductors of current interest in this paper. In order to narrow the scope of this review, we will primarily focus on the electron transport that occurs within the wurtzite and zinc-blende phases of gallium nitride and indium nitride in this review, these materials being of great current interest to the wide energy gap semiconductor community; indium nitride, while not a wide energy gap semiconductor in of itself, is included as it is often alloyed with other wide energy gap semiconductors, the resultant alloy often being a wide energy gap semiconductor itself. The electron transport that occurs within zinc-blende gallium arsenide will also be considered, albeit primarily for bench-marking purposes. Most of our discussion will focus on results obtained from our ensemble semi-classical three-valley Monte Carlo simulations of the electron transport within these materials, our results conforming with state-of-the-art wide energy gap semiconductor orthodoxy. A brief tutorial on the Monte Carlo electron transport simulation approach, this approach being used to generate the results presented herein, will also be provided. Steady-state and transient electron transport results are presented. The evolution of the field, a survey of the current literature, and some applications for the results presented herein, will also be featured. We conclude our review by presenting some recent developments on the electron transport within these materials. This review is the latest in a series of reviews that have been published on the electron transport processes that occur within the class of wide energy semiconductor materials. The results and references have been updated to include the latest developments in this rapidly evolving field of study.

Footprints of electron correlation in strong-field double ionization of Kr close to the sequential-ionization regime

By combining kinematically complete measurements and a semiclassical Monte Carlo simulation we study the correlated-electron dynamics in the strong-field double ionization of Kr. Interestingly, we find that, as we step into the sequential-ionization regime, there are still signatures of correlation in the two-electron joint momentum spectrum and, more intriguingly, the scaling law of the high-energy tail is completely different from early predictions on the low-$Z$ atom (He). These experimental observations are well reproduced by our generalized semiclassical model adapting a Green-Sellin-Zachor potential. It is revealed that the competition between the screening effect of inner-shell electrons and the Coulomb focusing of nuclei leads to a non-inverse-square central force, which twists the returned electron trajectory at the vicinity of the parent core and thus significantly increases the probability of hard recollisions between two electrons. Our results might have promising applications ranging from accurately retrieving atomic structures to simulating celestial phenomena in the laboratory.

Monte Carlo simulations of electron photoemission from cesium antimonide

We report on the results from semi-classical Monte Carlo simulations of electron photoemission (photoelectric emission) from cesium antimonide (Cs3Sb) and compare them with experimental results at 90 K and room temperature, with an emphasis on near-threshold photoemission properties. Interfacial effects, impurities, and electron-phonon coupling are central features of our Monte Carlo model. We use these simulations to predict photoemission properties at the ultracold cryogenic temperature of 20 K and to identify critical material parameters that need to be properly measured experimentally for reproducing the electron photoemission properties of Cs3Sb and other materials more accurately.

The sensitivity of the electron transport within bulk zinc-blende gallium nitride to variations in the crystal temperature, the doping concentration, and the non-parabolicity coefficient associated with the lowest energy conduction band valley

Within the framework of a semi-classical three-valley Monte Carlo simulation approach, we analyze the steady-state and transient electron transport that occurs within bulk zinc-blende gallium nitride. In particular, we examine how the steady-state and transient electron transport that occurs within this material changes in response to variations in the crystal temperature, the doping concentration, and the non-parabolicity coefficient associated with the lowest energy conduction band valley. These results are then contrasted with those corresponding to a number of other compound semiconductors of interest.

Spin relaxation in bilayer graphene: the role of electron–electron scattering

This paper investigates the influence of electron–electron scattering on spin relaxation length in bilayer graphene using semiclassical Monte Carlo simulation. Both D’yakonov–P’erel and Elliot–Yafet mechanisms are considered for spin relaxation. It is shown that spin relaxation length decreases by 17 % at 300 K on including electron–electron scattering. The reason of this variation in spin relaxation length is that the ensemble spin is modified upon an e–e collision, and also e–e scattering rate is greater than phonon scattering rate which causes change in spin transport profile.

A 2015 perspective on the nature of the steady-state and transient electron transport within the wurtzite phases of gallium nitride, aluminum nitride, indium nitride, and zinc oxide: a critical and retrospective review

Wide energy gap semiconductors are broadly recognized as promising materials for novel electronic and optoelectronic device applications. As informed device design requires a firm grasp of the material properties of the underlying electronic materials, the electron transport that occurs within the wide energy gap semiconductors has been the focus of considerable study over the years. In an effort to provide some perspective on this rapidly evolving and burgeoning field of research, we review analyzes of the electron transport within some wide energy gap semiconductors of current interest in this paper. In order to narrow the scope of this review, we will primarily focus on the electron transport that occurs within the wurtzite phases of gallium nitride, aluminum nitride, indium nitride, and zinc oxide in this review, these materials being of great current interest to the wide energy gap semiconductor community; indium nitride, while not a wide energy gap semiconductor in of itself, is included as it is often alloyed with other wide energy gap semiconductors, the resultant alloys being wide energy gap semiconductors themselves. The electron transport that occurs within zinc-blende gallium arsenide is also considered, albeit primarily for bench-marking purposes. Most of our discussion will focus on results obtained from our ensemble semi-classical three-valley Monte Carlo simulations of the electron transport within these materials, our results conforming with state-of-the-art wide energy gap semiconductor orthodoxy. A brief tutorial on the Monte Carlo electron transport simulation approach, this approach being used to generate the results presented herein, is also provided. Steady-state and transient electron transport results are presented. The evolution of the field, and a survey of the current literature, are also featured. We conclude our review by presenting some recent developments on the electron transport within these materials.

Infinite density for cold atoms in shallow optical lattices

Infinite densities are non-normalizable quasi-probability distributions that can describe the long-time properties of systems when ergodicity is broken and the equilibrium Boltzmann-Gibbs distribution fails. Their experimental observation has remained elusive so far. We here perform semiclassical Monte Carlo simulations of cold atoms in dissipative optical lattices with realistic parameters. We show that the momentum infinite density, as well as its scale invariance, should be observable in shallow potentials. We further evaluate the momentum autocorrelation function both in the stationary and nonstationary, aging regime.