Super Bloch oscillations in the Peyrard-Bishop-Holstein model

Recently, polarons in the Peyrard-Bishop-Holstein model under DC electric fields were established to perform Bloch oscillations, provided the charge-lattice coupling is not large. In this work, we study this model when the charge is subjected to an applied field with both DC and AC components. Similarly to what happens in the rigid lattice, we find that the carrier undergoes a directed motion or coherent oscillations when the AC field is resonant or detuned with respect to the Bloch frequency, respectively. The electric density current and its Fourier spectrum are also studied to reveal the frequencies involved in the polaron dynamics.     

Symmetry theory of the flexomagnetoelectric effect in the Bloch lines

It was shown that there are 48 magnetic point groups of the Bloch lines including 22 (11 time-invariant and 11 time-noninvariant) enantiomorphic and 26 non-enantiomorphic groups. The Bloch lines with the time-noninvariant enantiomorphism have identical types (parities) of the magnetization and polarization dependences. The list of soliton-like Bloch lines is derived from the symmetry classification. The tip electrode method of the creation of these Bloch lines is suggested for the potential applications in the magnetoelectric memory devices. The method of the experimental determination of the flexomagnetoelectric properties of the Bloch lines carried by the Bloch domain wall has been suggested. New type of the flexomagnetoelectric coupling, which is determined by the spatial derivatives of the electric polarization, can be found in the vicinity of the Curie temperature or compensation point of the ferrimagnets. The multi-state Bloch line magnetoelectric/multiferroic memory is proposed. It can be considered as a concept of the magnetoelectric enhancement of existing Bloch line memory invention.     

Dynamics of domain walls with drifting Bloch lines in single crystals of yttrium iron garnet

Induction and magnetic methods are used to study the effect of drifting Bloch lines on the wall velocity in a single crystal sample of yttrium iron garnet cut in the form of a long prism with only one 180-degree domain wall. A sharp increase in the velocity and in resonance bending vibrations of the wall are observed when Bloch line drift is initiated. The character of the wall motion is investigated under these conditions. An analysis of the experimental data shows that the effective reduction in the influence of drifting Bloch lines on the characteristics of the wall motion may be related to a magnetic aftereffect phenomenon. Zh. éksp. Teor. Fiz. 115, 1377–1385 (April 1999)     

Bloch oscillations and Wannier-Stark ladder in the coupled LC circuits

We present a new scheme for realizing Bloch oscillations and Wannier-Stark ladder based on a lattice of coupled LC circuits. By converting the second order dynamical ODEs of the system into a first order Schrödinger-like equation, we propose an equivalent tight binding Hamiltonian to describe the circuit. We show that a synthesized electric field is produced by introducing a frequency mismatch into the resonant frequency of the adjacent LC resonators. The Wannier-Stark modes are the normal modes of the circuit and the Bloch oscillations can be observed in a coupled LC lattice. By addition of coupling capacitors between nodes of the circuit, we study the Bloch oscillation in the presence of long-range couplings. We also show that the circuit converts to a transmission line simulating synthetic electric fields in the continuum limit. The coupled LC circuit is, in some sense, amongst the simplest physical systems exhibiting Bloch oscillation and Wannier-Stark Ladder.     

Spectrum of flexural oscillations of a domain wall with drifting Bloch lines

It is observed that in single-crystalline yttrium iron garnet the amplitude of characteristic flexural oscillations of a 180° domain wall containing Bloch lines increases sharply when drift of the Bloch lines is excited. The resonance frequencies of these oscillations are virtually identical to those of flexural oscillations of a monopolar wall. It is shown experimentally that this phenomenon is most likely caused by a magnetic aftereffect. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 1, 72–75 (10 January 1998)     

Transient Dynamics of Super Bloch Oscillations of a 1D Holstein Polaron under the Influence of an External AC Electric Field

Theoretical formalism for DC‐field polaron dynamics is extended to the dynamics of a 1D Holstein polaron in an external AC electric field using multiple Davydov trial states. Effects of carrier–phonon coupling on detuned and resonant scenarios are investigated for both phase and nonzero phase. For slightly off‐resonant or detuned cases, a beat between the usual Bloch oscillations and an AC driving force results in super Bloch oscillations, that is, rescaled Bloch oscillations in both the spatial and the temporal dimension. Super Bloch oscillations are damped by carrier–phonon coupling. For resonant cases, if the carrier is created on two nearest‐neighboring sites, the carrier wave packet spreads with small‐amplitude oscillations. Adding carrier–phonon coupling localizes the carrier wave packet. If an initial broad Gaussian wave packet is adopted, the centroid of the carrier wave packet moves with a certain velocity and with its shape unchanged. Adding carrier–phonon coupling broadens the carrier wave packet and slows down the carrier movement. Our findings may help provide guiding principles on how to manipulate the dynamics of the super Bloch oscillations of carriers in semiconductor superlattice and optical lattices by modifying DC and AC field strengths, AC phases, and detuning parameters.     

Generation of 1D interference patterns of Bloch surface waves

Interference patterns of Bloch surface waves with a period that is significantly less than the wavelength of incident radiation are formed using dielectric diffraction gratings located on the surface of photonic crystal. The simulation based on electromagnetic diffraction theory is used to demonstrate the possibility of high-quality interference patterns due to resonant enhancement of higher evanescent diffraction orders related to the excitation of the Bloch surface waves. The contrast of the interference patterns is close to unity, and the period is less than the period of the diffraction structure by an order of magnitude.     

Resonant delocalization and Bloch oscillations in modulated lattices

We study the propagation of light in Bloch waveguide arrays exhibiting periodic coupling interactions. Intriguing wave packet revival patterns as well as beating Bloch oscillations are demonstrated. A new resonant delocalization phase transition is also predicted.     

On the existence and detection of Bloch oscillations in superlattices

While many predicted superlattice behaviors depend on the presence of Bloch oscillations, the existence of such oscillations remains problematical. Here, we consider procedures by which their existence within a superlattice could be detected. We first set upper and lower bounds on the necessary fields. We then demonstrate that while a negative differential mobility is expected, no resonant peak occurs in this mobility at the Bloch frequency. However, we provide two ways of directly observing Bloch oscillations. In the first, we note the existence of structures in the dc velocity-field characteristic when an externally applied RF field has a frequency which is harmonically related to the Bloch frequency. The second approach is to measure the velocity fluctuation noise spectra, which should have a peak at the field-tunable Bloch frequency.     

Microscopic observations and simulations of Bloch walls in nematic thin films

We study Bloch wall defects formed by quenching nematic thin films from planar anchoring to homeotropic anchoring through a temperature-driven anchoring transition. The director profiles of the walls are directly visualized using fluorescence confocal polarizing microscopy, and shown to agree well with the simulation based on the Frank elasticity theory. A pure twist wall exists if the ratio of sample thickness to surface extrapolation length p is smaller than or close to 1; while a diffuse Bloch wall is obtained if p is much greater than 1.     

Anharmonic Bloch Oscillation of Electrons in Biased Superlattices

The oscillatory motion of electrons in a periodic potential under a constant applied electric field, known as Bloch oscillations (BO), is one of the most striking and intriguing quantum effects and was predicted more than eighty years ago. Oscillating electrons emit electromagnetic radiation and here we consider this BO effect for emission in the THz region. To date, it has been assumed that the Bloch oscillation of an electron is anharmonic oscillation, therefore with radiation emitted at the single Bloch frequency. We analyze scenarios when Bloch oscillations can be accompanied by the emission of radiation not only at the Bloch frequency but also with double and triple Bloch frequencies. The first scenario means that electrons could jump over neighboring Stark states. The second scenario of anharmonic emission is coupled to an opening of the minigap in the miniband.     

Quantum tunneling of a Bloch line in the domain wall of a cylindrical magnetic domain

Tunneling through a vertical Bloch line (BL) defect in the domain wall of a cylindrical magnetic domain is considered. It is shown that the BL tunneling probability and the corresponding crossover temperature are determined by the vibrational spectrum of the domain. The parameters characterizing this effect are estimated for a state of the domain close to the elliptical instability state.     

Optical Bloch oscillation and resonant Zener tunneling in one-dimensional quasi-period structures containing single negative materials

We studied the optical Bloch oscillation and resonant Zener tunneling in macroscopic quasi-period structures of alternatively stratified single negative and dielectric slabs. By a decrease in the thicknesses of the dielectric slabs, the electronic potential of crystals subjected to external dc electric fields is mimicked and the optical Wannier-Stark ladder (WSL) is realized. Both scattering states and the time-resolved transmission of a short pulse are provided to show the existence of the optical analogue of electronic Bloch oscillation. At a critical gradient, the resonant photon Zener tunneling is demonstrated both from the amplitude and the time delay in the transmitted signal of a short pulse.     

Rabi oscillations between dissipative Bloch bands

Within a two-band tight-binding model driven by DC–AC electric fields, we investigate the dynamics of electrons with Markoffian dephasing. We find that Rabi oscillations between the Bloch bands under the resonant condition may be destroyed by scattering from lattice imperfections. Through a perturbative calculation, we also obtain the effective decay time for the approach to equal Bloch band populations under conditions of small interband coupling and in the long-time limit. The decay rate shows characteristic sharp peaks at values of the parameters that give a signature of Rabi oscillations, and quasienergy spectra display avoided crossings at the same time.     

Influence of the demagnetizing field on the structure of a Bloch wall in a (001) plate of a magnetically ordered cubic crystal

The planar Bloch wall is considered in an infinite (001) plate of a cubic crystal with a negative first magnetic anisotropy constant for various values of the ratio between the magnetocrystalline-anisotropy and demagnetization energy densities of the sample. The energy and structure of the Bloch wall are shown to depend on this ratio and on the orientation of a vector equal to the difference between the magnetization vectors of the neighboring domains.     

Shear Surface Wave on a Moving Bloch Wall

Using Galileo's transformation for moving to the rest frame of the Bloch wall in the exchange-free magnetostatic approximation, we obtain the dispersion relation for a shear surface wave guided by a moving 180-degree domain boundary of a ferromagnetic crystal. It is found that the motion of the domain boundary has the orienting action on the wave normal of the shear surface wave and significantly changes the spectrum of forward-propagating waves in the frequency band below the scattered-field ferromagnetic resonance.     

Spectral properties of reduced Bloch Hamiltonians

Bloch Hamiltonians are defined, and the existence of bands is proven for a large class of periodic operators. The results are strong enough to include most of the reasonable physical models of a single electron in crystals. A notable exception is the Dirac Bloch Hamiltonian for a Coulombic crystal with high charge. Properties of the Bloch waves are briefly described and it is shown that “simple” Bloch Hamiltonians do not have Bloch waves with a finite number of Fourier coefficients. The asymptotic distribution of the bands is determined, and it is shown that for a large class of Hamiltonians, it is determined by the kinetic energy alone.     

Photonic Bloch oscillations of correlated particles

A photonic realization of Bloch oscillations (BOs) of two correlated electrons that move on a one-dimensional periodic lattice, based on spatial light transport in a square waveguide array with a defect line, is theoretically proposed. The signature of correlated BOs, such as frequency doubling of the oscillation frequency induced by particle interaction, can be simply visualized by monitoring the spatial path followed by an optical beam that excites the array near the defect line.     

Drift of vertical Bloch lines in a domain wall with a noninterchangeable spectrum in perpendicularly magnetized films

The dynamics of vertical Bloch lines in variable external magnetic fields is examined with allowance for the magnetostatic noninterchangeability of the spectrum of the domain wall. The drift velocity of the translational motion of vertical Bloch lines is calculated and is found to be nonzero in second order in the weak oscillating field. Zh. éksp. Teor. Fiz. 112, 2169–2177 (December 1997)