Real-space Trajectories Research Articles

Hexagonal warping effects on Bloch oscillations in proximitized Rashba systems

Bloch oscillations (BOs) in Rashba systems, taking into account the effects of hexagonal warping and proximity-induced band gap, are reported. We find that in addition to real-space trajectories, the group and Berry velocities of Bloch electrons exhibit novel BOs which strongly depend on the crystal momentum. This oscillatory motion is affected significantly by variations in the strength of hexagonal warping and the proximity-induced band gap, originating from the substantial changes in the energy spectrum induced by these factors. In addition, it is shown that the Bloch oscillations are modified considerably under the influence of applied uniform in-plane electric and transverse magnetic fields, which allow for a geometric visualization of the Bloch dynamics. Interestingly, when the system is subjected to these fields simultaneously, it undergoes a dynamic phase transition between confined and de-confined states. This phase transition is tuned by the relative strength of the applied fields and is further influenced by variations in the strength of hexagonal warping and proximity-induced band gap. The appearance of such a transition is attributed to the interplay between the external fields and the intrinsic properties of the crystal lattice. Moreover, we find that the direct-current drift velocity shows negative differential conductivity, which is a characteristic feature of the BO regime.

Bloch oscillations probed quantum phases in HgTe quantum wells

The semiconductor quantum well based on mercury telluride is characterized by two distinct phases: conventional insulating phase and topological insulating phase with helical edge states. The system undergoes a topological quantum phase transition from one phase to the other, tuned by the critical geometric parameters of the quantum well. It is shown that the quantum states in each phase exhibit distinct flavors of Bloch oscillations, depending strongly on the geometric parameters and crystal momentum of the system. In particular, the group and Berry velocities and the real-space trajectories exhibit pronounced Bloch oscillations. Interestingly, the x- and y-components of the group velocity are interchanged by interchanging their corresponding components of the crystal momentum. In addition, a Gaussian wave packet undergoes distinct time evolution in each quantum phase of the HgTe quantum well. Moreover, the effects of applied in-plane electric and transverse magnetic fields are determined within the framework of Newtonian mechanics, leading to the geometric visualization of such an oscillatory motion. We find that in the presence of both applied in-plane electric and transverse magnetic fields simultaneously, the system undergoes a dynamic phase transition between confined and de-confined states, tuned by the relative strength of the fields. It is argued that the distinct Bloch oscillations originate from the peculiar band structure of HgTe quantum wells in each quantum phase. Furthermore, we find that the direct-current drift velocity in each quantum phase exhibits negative differential conductivity, a hallmark of the Bloch oscillation regime.

Brownian dynamics of Dirac fermions in twisted bilayer graphene

Brownian dynamics of Dirac fermions in twisted bilayer graphene is investigated within the framework of semiclassical relativistic Langevin equations. We find that under the influence of orthogonal, commensurate ac drives in the periodic ratchet potential of a substrate, the charge carriers in the system exhibit pronounced random dynamics, tuned by the twist angle, making twisted bilayer graphene distinct from monolayer graphene. It is shown that as threshold twist angle matches the optimal angle, deterministic running states appear in the limit of weak thermal noise where the diffusion rate is enhanced significantly compared to bare thermal diffusion. Analysis of the real space trajectories and diffusion coefficient illustrates the significant role of thermal noise in the random motion of Dirac fermions. In addition, we find that the Brownian particle shows remarkable ratchet effect as a net current.

Bloch oscillations in moiré flat band systems

Bloch oscillations of wave packets in moiré flat band systems are investigated. We find that the real space trajectories and group velocity of wave packet undergo Bloch oscillations in the moiré flat band. It is shown that the Bloch dynamics is affected significantly by the magnitude and orientation of an applied in-plane electric field. In the presence of both external perpendicular magnetic field and in-plane electric field, confinement and de-confinement of cyclotron orbits occur which strongly depend on the relative strength of the applied fields.

Rotating bi-electron in two-dimensional systems with mexican-hat single-electron energy dispersion

A number of novel two-dimensional materials and nanostructures demonstrate complex single-electron energy dispersion, which is called the mexican-hat dispersion. In this paper, we analyze interaction of a pair of electrons with such an energy dispersion. We show that relative motion of the electron pair is of a very peculiar character. For example, the real space trajectories corresponding to electron-electron scattering can have three reversal points, reversal points at non-zero radial momentum and other unusual features. Despite the repulsive Coulomb interaction, two electrons can be coupled forming a composite quasi-particle – the bi-electron. The bi-electron corresponds to excited states of the two-electron system. Because the bi-electron coupled states exist in continuum of extended (free) states of the electron pair, these states are quasi-resonant and have finite times of life. We found that rotating bi-electron is a long-living composite quasi-particle. The rotating bi-electrons can be in motion. For slowly moving bi-electrons, we have determined the kinetic energy and the effective mass. Due to strongly nonparabolic energy dispersion, the translational motion of the bi-electron is coupled to its internal motion. This results in effective masses dependent on quantum states of the bi-electron. In the paper, properties of the bi-electron have been illustrated for the example of bigraphene in a transverse electric field. We have suggested that investigation of rotating bi-electrons at the mexican-hat single-electron energy dispersion may bring new interesting effects in low-dimensional and low-temperature physics.

Stochastic-field approach to the quench dynamics of the one-dimensional Bose polaron

We consider the dynamics of a quantum impurity after a sudden interaction quench into a one-dimensional degenerate Bose gas. We use the Keldysh path integral formalism to derive a truncated Wigner like approach that takes the back action of the impurity onto the condensate into account already on the mean-field level and further incorporates thermal and quantum effects up to one-loop accuracy. This framework enables us not only to calculate the real space trajectory of the impurity but also the absorption spectrum. We find that quantum corrections and thermal effects play a crucial role for the impurity momentum at weak to intermediate impurity-bath couplings.Furthermore, we see the broadening of the absorption spectrum with increasing temperature.

Analytic solutions to compact binary inspirals with leading order spin-orbit contribution using the dynamical renormalization group

We calculate the real-space trajectory and spin precession of a generic spinning compact binary inspiral at any time instant using the dynamical renormalization group formalism. This method leads to closed-form analytic solutions to the binary motion through treating radiation reaction as perturbations and resumming the secular growth of perturbative terms. We consider the spin-orbit effects at leading order and the 2.5PN radiation reaction without orbit averaging or precession averaging for arbitrary individual masses and spin magnitudes and orientations. The solutions are written in a moving reference frame, with the orbital angular momentum and binary radial directions aligned along two of the axes. The resummed solutions show improved accuracy compared to adiabatic solutions while also being an order of magnitude faster computationally compared to numerical integration methods.

Complex-valued derivative propagation method with approximate Bohmian trajectories: Application to electronic nonadiabatic dynamics

The coupled complex quantum Hamilton-Jacobi equations for electronic nonadiabatic transitions are approximately solved by propagating individual quantum trajectories in real space. Equations of motion are derived through use of the derivative propagation method for the complex actions and their spatial derivatives for wave packets moving on each of the coupled electronic potential surfaces. These equations for two surfaces are converted into the moving frame with the same grid point velocities. Excellent wave functions can be obtained by making use of the superposition principle even when nodes develop in wave packet scattering.

Atomic-like high-harmonic generation from two-dimensional materials.

The generation of high-order harmonics from atomic and molecular gases enables the production of high-energy photons and ultrashort isolated pulses. Obtaining efficiently similar photon energy from solid-state systems could lead, for instance, to more compact extreme ultraviolet and soft x-ray sources. We demonstrate from ab initio simulations that it is possible to generate high-order harmonics from free-standing monolayer materials, with an energy cutoff similar to that of atomic and molecular gases. In the limit in which electrons are driven by the pump laser perpendicularly to the monolayer, they behave qualitatively the same as the electrons responsible for high-harmonic generation (HHG) in atoms, where their trajectories are described by the widely used semiclassical model, and exhibit real-space trajectories similar to those of the atomic case. Despite the similarities, the first and last steps of the well-established three-step model for atomic HHG are remarkably different in the two-dimensional materials from gases. Moreover, we show that the electron-electron interaction plays an important role in harmonic generation from monolayer materials because of strong local-field effects, which modify how the material is ionized. The recombination of the accelerated electron wave packet is also found to be modified because of the infinite extension of the material in the monolayer plane, thus leading to a more favorable wavelength scaling of the harmonic yield than in atomic HHG. Our results establish a novel and efficient way of generating high-order harmonics based on a solid-state device, with an energy cutoff and a more favorable wavelength scaling of the harmonic yield similar to those of atomic and molecular gases. Two-dimensional materials offer a unique platform where both bulk and atomic HHG can be investigated, depending on the angle of incidence. Devices based on two-dimensional materials can extend the limit of existing sources.

Hybridization effects on wave packet dynamics in topological insulator thin films

Theoretical study of electron wave packet dynamics in topological insulator (TI) thin films is presented. We have investigated real space trajectories and spin dynamics of electron wave packets in TI thin films. Our focus is on the role of hybridization between the electronic states of the two surfaces. This allows us to access the crossover regime of a thick film with no hybridization to a thin film with finite hybridization. We show that the electron wave packet undergoes side-jump motion in addition to zitterbewegung. The oscillation frequency of zitterbewegung can be tuned by the strength of hybridization, which in turn can be tuned by the thickness of the film. We find that the spin expectations also exhibit zitterbewegung tunable by hybridization. We also show that it is possible to obtain persistent zitterbewegung, oscillations which do not decay, in both the real space trajectories as well as spin dynamics. The zitterbewegung oscillation frequency in TI thin films falls in a parameter regime where it might be possible to observe these effects using present day experimental techniques.

Deriving analytic solutions for compact binary inspirals without recourse to adiabatic approximations

We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is $v^5 \nu \Omega(t-t_0)$ where $t_0$ is the initial time, $t$ is the time elapsed, and $\Omega$ and $v$ are the angular orbital frequency and initial speed, respectively, and $\nu$ is the binary's symmetric mass ratio. We demonstrate how to apply the renormalization group method to resum solutions beyond leading order in two ways. First, we calculate the second order corrections of the leading radiation reaction force, which involves highly non-trivial checks of the formalism (i.e. its renormalizability). Second, we show how to systematically include post-Newtonian corrections to the radiation reaction force. By avoiding orbit averaging we gain predictive power and eliminate ambiguities in the initial conditions. Finally, we discuss how this methodology can be used to find analytic solutions to the spin equations of motion that are valid over long times.

Graphene Nanobubbles as Valley Filters and Beam Splitters.

The energy band structure of graphene has two inequivalent valleys at the K and K^{'} points of the Brillouin zone. The possibility to manipulate this valley degree of freedom defines the field of valleytronics, the valley analogue of spintronics. A key requirement for valleytronic devices is the ability to break the valley degeneracy by filtering and spatially splitting valleys to generate valley polarized currents. Here, we suggest a way to obtain valley polarization using strain-induced inhomogeneous pseudomagnetic fields (PMFs) that act oppositely on the two valleys. Notably, the suggested method does not involve external magnetic fields, or magnetic materials, unlike previous proposals. In our proposal the strain is due to experimentally feasible nanobubbles, whose associated PMFs lead to different real space trajectories for K and K^{'} electrons, thus allowing the two valleys to be addressed individually. In this way, graphene nanobubbles can be exploited in both valley filtering and valley splitting devices, and our simulations reveal that a number of different functionalities are possible depending on the deformation field.

Complex-valued derivative propagation method with approximate Bohmian trajectories for quantum barrier scattering

The complex quantum Hamilton–Jacobi equation for the complex action is approximately solved by propagating individual Bohmian trajectories in real space. Equations of motion for the complex action and its spatial derivatives are derived through use of the derivative propagation method. We transform these equations into the arbitrary Lagrangian–Eulerian version with the grid velocity matching the flow velocity of the probability fluid. Setting higher-order derivatives equal to zero, we obtain a truncated system of equations of motion describing the rate of change in the complex action and its spatial derivatives transported along approximate Bohmian trajectories. A set of test trajectories is propagated to determine appropriate initial positions for transmitted trajectories. Computational results for transmitted wave packets and transmission probabilities are presented and analyzed for a one-dimensional Eckart barrier and a two-dimensional system involving either a thick or thin Eckart barrier along the reaction coordinate coupled to a harmonic oscillator.

Gilbert damping and critical real-space trajectory of L10-ordered FePt films investigated by magnetic-field-induction and all-optical methods

The magnetization dynamics of perpendicularly magnetized FePt films is studied using both magnetic-field-induction and all-optical methods. A critically damped trajectory was observed in this system, where the precession ended within subnanoseconds after a single large oscillation. Using the Landau–Lifshitz–Gilbert (LLG) calculation with an experimental configuration, the effective anisotropy and damping constant were obtained. A damping constant of approximately 0.2 was determined after both a magnetic field and a laser pulse were used. The laser-induced real-space trajectory was well explained by the modified LLG calculation taking into account the demagnetization and time-dependent anisotropy.

Complex quantum Hamilton–Jacobi equation with Bohmian trajectories for wave packet dynamics

The complex quantum Hamilton–Jacobi equation (CQHJE) for the action function is integrated by propagating correlated Bohmian trajectories in real space. We transform the CQHJE into the arbitrary Lagrangian–Eulerian (ALE) version with the grid velocity matching the flow velocity of the probability fluid. The ALE version describes the rate of change in the complex action transported along Bohmian trajectories. The spatial derivatives of the complex action required for the integration of the CQHJE are evaluated with a moving least squares algorithm. The method is applied to a squeezed state in the harmonic potential and to a two-dimensional barrier scattering problem.

Dynamics of a deformable active particle under shear flow

The motion of a deformable active particle in linear shear flow is explored theoretically. Based on symmetry considerations, we propose coupled nonlinear dynamical equations for the particle position, velocity, deformation, and rotation. In our model, both, passive rotations induced by the shear flow as well as active spinning motions, are taken into account. Our equations reduce to known models in the two limits of vanishing shear flow and vanishing particle deformability. For varied shear rate and particle propulsion speed, we solve the equations numerically in two spatial dimensions and obtain a manifold of different dynamical modes including active straight motion, periodic motions, motions on undulated cycloids, winding motions, as well as quasi-periodic and chaotic motions induced at high shear rates. The types of motion are distinguished by different characteristics in the real-space trajectories and in the dynamical behavior of the particle orientation and its deformation. Our predictions can be verified in experiments on self-propelled droplets exposed to a linear shear flow.

Simulation of “Ab Initio” Quantum Confinement Scattering in UTB MOSFETs Using Three-Dimensional Ensemble Monte Carlo

In this paper, we report a 3-D Monte Carlo (MC) simulation methodology that includes complex quantum confinement effects captured through the introduction of robust and efficient density gradient (DG) quantum corrections (QCs), which has been used to introduce “ab initio ” scattering from quantum confinement fluctuations in ultrathin body silicon-on-insulator metal-oxide-semiconductor field-effect transistors (MOSFETs) through the real space trajectories of the particles driven by the DG effective quantum potential and to study the enhanced current variability due to the corresponding transport variations. A “frozen field” approximation, where neither the field nor the QCs are updated, has been used to examine the dependence of mobility on silicon thickness in large self-averaging devices. This approximation, along with the MC simulations that are self-consistent with Poisson's equation, is applied to study the variability of on-current due to random body thickness fluctuations in thin-body MOSFETs at low and high drain biases.

Three-dimensional magnetization evolution and the role of anisotropies in thin Fe/MgO films: Static and dynamic measurements

We have quantitatively characterized the real-space components of the magnetization vector M in thin epitaxial Fe(001)/MgO(001) films through an experimental set-up based on the magneto-optical Kerr effect. The capabilities of the method permit to investigate the magnetization reversal under the effect of an applied field directly on the real-space trajectories of M, providing a straightforward interpretation of the magnetization switching mechanisms in terms of magnetic anisotropies and domains formation. Using the pump-probe technique we also studied the three-dimensional precession dynamics of the magnetization vector triggered by a femtosecond laser pulse, revealing how the anisotropy fields (magnetocrystalline and shape) affect the observed features of the precessional dynamics, i.e., the frequency and the amplitude of motion. Our quantitative approach permits a deeper understanding of the basic mechanisms underlying spin dynamics and it can be successfully applied to a large class of magnetic thin layers.

Random-Dopant-Induced Drain Current Variation in Nano-MOSFETs: A Three-Dimensional Self-Consistent Monte Carlo Simulation Study Using “Ab Initio” Ionized Impurity Scattering

A comprehensive simulation study of random-dopant-induced drain current variability is presented for a series of well-scaled <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> -channel MOSFETs representative of the 90-, 65-, 45-, 35-, and 22-nm technology nodes. Simulations are performed at low and high drain biases using both 3-D drift diffusion (DD) and 3-D Monte Carlo (MC). The ensemble MC simulator incorporates an ldquo <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ab</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">initio</i> rdquo treatment of ionized impurity scattering through the real-space trajectories of the carriers in the Coulomb potential of the random discrete impurities. When compared with DD simulations, the MC simulations reveal a significant increase in the drain current variability as a result of additional transport variations due to position-dependent Coulomb scattering that is not captured within the DD mobility model. Such transport variations are in addition to the electrostatic variation in carrier density that is alone captured within the DD approach. Through comparison of the DD and MC results, we estimate the relative importance of electrostatic and transport-induced variability at different drain bias conditions.

Real Space Trajectory of the Ultrafast Magnetization Dynamics in Ferromagnetic Metals

We have measured the real space trajectory of the ultrafast magnetization dynamics in ferromagnetic metals induced by femtosecond optical pulses. Our approach allows the observation of the initial change of the modulus and orientation of the magnetization, occurring within a few hundreds of femtoseconds, as well as its subsequent precession and damping around the effective field. The role of the magnetocrystalline anisotropy shows up in the magnetization reorientation occurring during the electron-lattice relaxation. In addition, we propose a model which takes into account the initial demagnetization in the Bloch formalism describing the magnetization dynamics.