Time-periodic Potential Research Articles

Dual-heterodyne Kelvin probe force microscopy.

We present a new open-loop implementation of Kelvin probe force microscopy (KPFM) that provides access to the Fourier spectrum of the time-periodic surface electrostatic potential generated under optical (or electrical) pumping with an atomic force microscope. The modulus and phase coefficients are probed by exploiting a double heterodyne frequency mixing effect between the mechanical oscillation of the cantilever, modulated components of the time-periodic electrostatic potential at harmonic frequencies of the pump, and an ac bias modulation signal. Each harmonic can be selectively transferred to the second cantilever eigenmode. We show how phase coherent sideband generation and signal demodulation at the second eigenmode can be achieved by using two numerical lock-in amplifiers configured in cascade. Dual-heterodyne KPFM (DHe-KPFM) can be used to map any harmonic (amplitude/phase) of the time-periodic surface potential at a standard scanning speed. The Fourier spectrum (series of harmonics) can also be recorded in spectroscopic mode (DHe-KPFM spectroscopy), and 2D dynamic images can be acquired in data cube mode. The capabilities of DHe-KPFM in terms of time-resolved measurements, surface photovoltage (SPV) imaging, and detection of weak SPV signals are demonstrated through a series of experiments on difference surfaces: a reference substrate, a bulk organic photovoltaic heterojunction thin film, and an optoelectronic interface obtained by depositing caesium lead bromide perovskite nanosheets on a graphite surface. The conclusion provides perspectives for future improvements and applications.

Optimum transport in systems with time-dependent drive and short-ranged interactions.

We consider a one-dimensional lattice gas model of hardcore particles with nearest-neighbor interaction in presence of a time-periodic external potential. We investigate how attractive or repulsive interaction affects particle transport and determine the conditions for optimum transport, i.e., the conditions for which the maximum dc particle current is achieved in the system. We find that the attractive interaction in fact hinders the transport, while the repulsive interaction generally enhances it. The net dc current is a result of the competition between the current induced by the periodic external drive and the diffusive current present in the system. When the diffusive current is negligible, particle transport in the limit of low particle density is optimized for the strongest possible repulsion. But when the particle density is large, very strong repulsion makes particle movement difficult in an overcrowded environment and, in that case, the optimal transport is obtained for somewhat weaker repulsive interaction. Our numerical simulations show reasonable agreement with our mean-field calculations. When the diffusive current is significantly large, the particle transport is still facilitated by repulsive interaction, but the conditions for optimality change. Our numerical simulations show that the optimal transport occurs at the strongest repulsive interaction for large particle density and at a weaker repulsion for small particle density.

Spin-valley-dependent transport in a monolayer MoS2 under strain and time-oscillating potential

The effect of the external strain and time-periodic potential on the spin/valley transmission probability are studied theoretically in the monolayer MoS2. It is found that, the probability of transmission shows oscillatory pattern with strain strength. Also, the probability of transmission strongly depends on the direction of the strain, incident electron angle, amplitude of the oscillating potential, and sideband orders. By increasing the order of the sideband, the transmission probability decreases. Therefore, the higher order of the sidebands have a smaller contribution to the probability of transmission. Remarkably, when the time-dependent potential is applied to the monolayer MoS2 under armchair direction strain, unlike the strain in the zigzag direction, the transmission probability will be an even function in terms of the incident electron angle. Our results provides a new structure, which can be useful to future spintronic, valleytronic and electronic devices.

Transport properties in a monolayer MoS2 with time-periodic potential

Transport properties in a monolayer MoS2 with time-periodic potential

Growth of Sobolev norms in linear Schrödinger equations as a dispersive phenomenon

In this paper we consider linear, time dependent Schrödinger equations of the form i∂tψ=K0ψ+V(t)ψ, where K0 is a strictly positive selfadjoint operator with discrete spectrum and constant spectral gaps, and V(t) a smooth in time periodic potential. We give sufficient conditions on V(t) ensuring that K0+V(t) generates unbounded orbits. The main condition is that the resonant average of V(t), namely the average with respect to the flow of K0, has a nonempty absolutely continuous spectrum and fulfills a Mourre estimate. These conditions are stable under perturbations. The proof combines pseudodifferential normal form with dispersive estimates in the form of local energy decay.We apply our abstract construction to the Harmonic oscillator on R and to the half-wave equation on T; in each case, we provide large classes of potentials which are transporters.

Stochastic model of translocation of knotted proteins.

Knotted proteins, when forced through the pores, can get stuck if the knots in their backbone tighten under force. Alternatively, the knot can slide off the chain, making translocation possible. We construct a simple energy landscape model of this process with a time-periodic potential that mimics the action of a molecular motor. We calculate the translocation time as a function of the period of the pulling force, discuss the asymptotic limits and biological relevance of the results.

Transport properties in MoS2 quantum dot under time-oscillating potential

We report a theoretical study of transport properties in a circular MoS2 quantum dot under spin-orbit coupling and time-periodic potential. It is shown that the scattering coefficient depends on the frequency () and the amplitude of the time-periodic potential () as well as the radius of the quantum dot (R), and has an oscillatory behavior with respect to and R. Also, the scattering coefficient is dependent on the order of the sideband as well as the sign of the sideband. Results show that for (), the scattering is negligible for the large frequency values. Interestingly, the magnitude of radial reflected current can be efficiently controlled by the quantum dot coordinates. Thus, a circular MoS2 quantum dot with a time-oscillating potential can temporarily trap electrons. These results clarify that a circular MoS2 quantum dot can be useful for the design of novel electronic devices.

Pseudospin-one particles in the time-periodic dice lattice: a new approach to transport control

The controlling of the transmission in the pseudospin-one Dirac–Weyl systems offers a rich tool to study new concepts of massive Dirac electron tunneling by means of a time-dependent potential. The time-periodic potential is one of the experimental techniques to have more control over the tunneling effect. In this paper, we study the transmission coefficient for different sidebands to obtain total transmission. We show how the super Klein tunneling under special conditions is independent of the incidence angle, oscillation amplitude, frequency, and barrier width. We consider a band gap opening with different locations of the flat band and modulate the resonances by tuning free parameters in our system.

Electron scattering in silicene quantum dot with a time-periodic potential

We investigate the scattering problem for electrons in a circular silicene quantum dot with a time-periodic potential and intrinsic spin-orbit coupling. Our results demonstrate that the scattering coefficient depends on the radius of the quantum dot (R), the amplitude , and the frequency of the time-periodic potential as well as the order of the sideband. For the zero bias, unlike the finite bias, the scattering coefficient is independent of the sign of n for the n-th sideband. We also find that the scattering increases with R. Also, for smaller values of R, there is not any scattering in the silicene quantum dot for both the zero bias and the finite bias. For n > 1, the scattering is significant only for the small frequency values. Interestingly, a circular silicene quantum dot can temporarily trap electrons.

Transport properties through graphene with sequence of alternative magnetic barriers and wells in the presence of time-periodic scalar potential

We investigate the electronic transport properties of a graphene sheet under the magnetic barriers and wells through the oscillating scalar potential combined with the static scalar potential barrier having two types of uniform and alternative profiles. We compute the total sideband transmission of the system by additional sidebands at energy, in presence of oscillating potential, V_1, using the transfer-matrix formalism and the Floquet sidebands series. The oscillating potential, generally, suppresses the Klein tunneling and the confinement of the charge carriers. In the absence of V_1, both profiles show the wave vector filtering effect for the carriers by controlling the energy E relative to the potential barrier height, V_0. The (N-1)-fold resonance splittings are observed through a region around E=V_0 with reduction of the transmission. The transmission vanishes in this region upon increasing the number of magnetic blocks N, strength of the magnetic field B in both configurations. We present an estimate relation for the width of the reduction region expressed in terms of E, V_0, B and the angle of incidence of the quasiparticles. We observe, in the second profile, (N-1)-fold resonances in the transmission for special values of E=V_0 with a separation depending on the width of the magnetic blocks. The magnetic field and the width of the magnetic blocks have critical values, where the transmission reduces to zero. All the features observed in the transmission reflect to the conductance. In both configurations, there are some peaks in the conductance corresponding to the resonances of the transmission. The oscillations of the conductance are obtained which was observed in the experimental results. We, also, find the possibility for switching the transport properties of the system by changing the characteristic parameters of the magnetic system.

Anomalous Floquet tunneling in uniaxially strained graphene

The interplay of strain engineering and photon-assisted tunneling of electrons in graphene is considered for giving rise to atypical transport phenomena. The combination of uniaxial strain and a time-periodic potential barrier helps to control the particle transmission for a wide range of tunable parameters. With the use of the tight-biding approach, the elasticity theory, and the Floquet scattering, we found an angular shift of the maximum transmission in the sidebands for uniaxial strains breaking the mirror symmetry with respect to the normal incidence, which is called anomalous Floquet tunneling. We show that electron tunneling depends strongly on the barrier width, incident angle, uniaxial strain, and the tuning of the time-periodic potential parameters. An adequate modulation of the barrier width and oscillation amplitude serves to select the transmission in the sidebands. These findings can be useful for controlling the electron current through the photon-assisted tunneling being used in multiple nanotechnological applications.

Dynamics of one-dimensional quantum many-body systems in time-periodic linear potentials

We study a system of one-dimensional interacting quantum particles subjected to a time-periodic potential linear in space. After discussing the cases of driven one- and two-particles systems, we derive the analogous results for the many-particles case in presence of a general interaction two-body potential and the corresponding Floquet Hamiltonian. When the undriven model is integrable, the Floquet Hamitlonian is shown to be integrable too. We determine the micro-motion operator and the expression for a generic time evolved state of the system. We discuss various aspects of the dynamics of the system both at stroboscopic and intermediate times, in particular the motion of the center of mass of a generic wavepacket and its spreading over time. We also discuss the case of accelerated motion of the center of mass, obtained when the integral of the coeffcient strenght of the linear potential on a time period is non-vanishing, and we show that the Floquet Hamiltonian gets in this case an additional static linear potential. We also discuss the application of the obtained results to the Lieb-Liniger model.

Spin dependent group delay time in graphene with a time-periodic potential

The spin-dependent group delay time and the Hartman effect in the ferromagnetic monolayer graphene electrostatic barrier are theoretically studied with a time-dependent oscillating potential. It was found that the spin-dependent group delay time could be controlled by adjusting the amplitude of the oscillating potential. The results showed that for an electron beam at an oblique angle of incidence, unlike the normal angle, the spin-dependent group delay time depends on the sign of n for the nth sideband. Interestingly, for the central band, the Hartman effect can be observed for all angles of incidence. Whereas, for the sidebands, this phenomenon can only occur when the angle of incidence is larger than the critical angle (φ≥π/6).

Nearly pure spin-valley sideband tunneling in silicene: Effect of interplay of time periodic potential barrier and spin-valley-dependent Dirac mass

We study massive Dirac fermion tunneling through time periodic potential in a silicene-based N-TP-N junction, where Ns are normal silicene regions and TP is the time periodic potential barrier. The fermions would absorb or emit photons due to the presence of the Floquet sidebands created in the TP. The nearly perfect spin-valley-sideband filtering is predicted. Applying only the exchange field leads to just only the electron absorbing a single photon almost purely allowed to tunnel through the junction for the large electric field. Reversing direction of electric field can select spin of the allowed electron. In the case of applying only off-resonant circularly polarized light, just only the electron absorbing a single photon with spin up, is almost purely allowed to tunnel through the junction. The valley is also selected by reversing direction of the electric field. The controllable sideband channel may be applicable for sideband-based spin-valleytronics.

Berry‐Phase in a Periodically Driven Single Molecule Magnet Transistor

The electron transport through a single molecule magnet transistor in the presence of a local transverse magnetic field and ac‐driven gate voltage has been considered. The conductance has been calculated as a function of the electron energy and transverse magnetic field by using the Floquet and Landauer formalism. It is shown that the time periodic potential causes zero transmission resonances that oscillate as a function of the transverse magnetic field due to the Berry phase interference associated with two quantum tunneling paths. It has been found that these Berry phase oscillations can be detected in the conductance as a function of the transverse magnetic field for an incoming electron with a specific energy.

Analytical study of AC electroosmotic mixing in 2-dimensional microchannel with time periodic surface potential.

This work reported an analytic study of AC electroosmotic flows with a view to control the degree of mixing in a rectangular microchannel. Only with spatially non-uniform zeta potential distribution, fluid particles travel back and forth along a vortical flow field developed inside a microchannel. Although complex patterns of electroosmotic vortical flows can be obtained by various types of non-uniform zeta potential distributions, fluid particles always follow regular paths due to a laminar flow limit. To further facilitate the mixing of sample fluid, we propose a scheme that the zeta potential distribution was temporally non-uniform as well. General solutions for both the double layer potential distribution and the AC electroosmotic flow field are analytically determined by solving the unsteady Stokes equation with an electrostatic body force. As an illustrative example, we consider a case where two different types of non-uniform zeta potential distributions alternate with each other and the effects of both the AC frequency and the frequency of the alternation of the two zeta potential distributions on flow characteristics are examined using the Poincaré sections. Conclusively, one can either enhance or prevent mixing compared to a static electroosmotic flow, which is in line with previously demonstrated experimental works. Thus, the results presented would be an effective mean for controllable electroosmotic flow in a microfluidic platform.

On the Nonlinear Wave Equation with Time-periodic Potential

Abstract It is known that for some time-periodic potentials $q(t, x) \geq 0$ having compact support with respect to $x$ some solutions of the Cauchy problem for the wave equation $\partial _t^2 u - \Delta _x u + q(t,x)u = 0$ have exponentially increasing energy as $t \to \infty $. We show that if one adds a nonlinear defocusing interaction $|u|^ru, 2\leq r < 4,$ then the solution of the nonlinear wave equation exists for all $t \in{\mathbb R}$, and its energy is polynomially bounded as $t \to \infty $ for every choice of $q$. Moreover, we prove that the zero solution of the nonlinear wave equation is instable if the corresponding linear equation has the property mentioned above.

Bloch oscillation of Weyl metal along synthetic dimensions**Project supported by the National Natural Science Foundation of China (Grant No. 11774177).

Synthetic dimensions in time (Sambe space) can be utilized in a periodic time-dependent system. By subjecting the system into a time-periodic potential and measuring the physical quantities at distinct time in one period,one is able to simulate the models in higher dimension. To verify this approach, we show that the Bloch oscillation of wave packets along the magnetic field in a three-dimensional (3D) Weyl metal can be simulated on a two-dimensional (2D) insulator. Different from the chiral anomaly, this Bloch oscillation is anisotropic when the initial wave packet is noton the 0-th Landau level.

Floquet topological polaritons in semiconductor microcavities

We propose and model Floquet topological polaritons in semiconductor microcavities, using the interference of frequency detuned coherent fields to provide a time periodic potential. For arbitrarily weak field strength, where the Floquet frequency is larger than the relevant bandwidth of the system, a Chern insulator is obtained. As the field strength is increased, a topological phase transition is observed with an unpaired Dirac cone proclaiming the anomalous Floquet topological insulator. As the relevant bandwidth increases even further, an exotic Chern insulator with flat band is observed with unpaired Dirac cone at the second critical point. Considering the polariton spin degree of freedom, we find that the choice of field polarization allows oppositely polarized polaritons to either co-propagate or counter-propagate in chiral edge states.

Impenetrability in Floquet Scattering in One Dimension

We study the scattering off a time-periodic zero-range potential in one spatial dimension. We focus on the parameter regions that lead to zero-transmission probability (ZTP). For static potentials, ZTP leads to fermionization of distinguishable equal-mass particles. For time-periodic potentials, fermionization is prevented by the formation of evanescent waves.