Renormalization-convolution approach to the electronic transport in two-dimensional aperiodic lattices

A novel method combining the renormalization and convolution techniques is developed for the Kubo-Greenwood formula. Using this method, the dc and ac conductance at zero temperature in two-dimensional (2D) quasiperiodic systems are studied. The results show that the ac conductance of quasiperiodic systems could be significantly modified by the presence of periodic leads, which are usually employed as the measurement connections. Furthermore, when the system is periodic along the applied electrical field, a quantized dc conductance spectrum is observed at zero temperature and this quantized spectrum is destroyed when an oscillating electrical field is introduced. However, when the electric field is applied along a quasiperiodic direction of the system, the ac conductance spectrum shows a non-Drude behaviour, in good agreement with experiment results.     

Wave propagation in two-dimensional periodic lattices

Plane wave propagation in infinite two-dimensional periodic lattices is investigated using Floquet-Bloch principles. Frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies: hexagonal honeycomb, Kagomé lattice, triangular honeycomb, and the square honeycomb. These topologies exhibit dramatic differences in their long-wavelength deformation properties. Long-wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices. The slenderness ratio of the constituent beams of the lattice (or relative density) has a significant influence on the band structure. The techniques developed in this work can be used to design lattices with a desired band structure. The observed spatial filtering effects due to anisotropy at high frequencies (short wavelengths) of wave propagation are consistent with the lattice symmetries.     

Quantum droplets in two-dimensional optical lattices

We study the stability of zero-vorticity and vortex lattice quantum droplets (LQDs), which are described by a two-dimensional (2D) Gross–Pitaevskii (GP) equation with a periodic potential and Lee– Huang–Yang (LHY) term. The LQDs are divided in two types: onsite-centered and offsite-centered LQDs, the centers of which are located at the minimum and the maximum of the potential, respectively. The stability areas of these two types of LQDs with different number of sites for zero-vorticity and vorticity with S = 1 are given. We found that the μ–N relationship of the stable LQDs with a fixed number of sites can violate the Vakhitov–Kolokolov (VK) criterion, which is a necessary stability condition for nonlinear modes with an attractive interaction. Moreover, the μ–N relationship shows that two types of vortex LQDs with the same number of sites are degenerated, while the zero-vorticity LQDs are not degenerated. It is worth mentioning that the offsite-centered LQDs with zero-vorticity and vortex LQDs with S = 1 are heterogeneous.     

Reduced-symmetry two-dimensional solitons in photonic lattices

We demonstrate theoretically and experimentally a novel type of localized beam supported by the combined effects of total internal and Bragg reflection in nonlinear two-dimensional square periodic structures. Such localized states exhibit strong anisotropy in their mobility properties, being highly mobile in one direction and trapped in the other, making them promising candidates for optical routing in nonlinear lattices.     

Disordered quantum walks in two-dimensional lattices

The properties of the two-dimensional quantum walk with point,line,and circle disorders in phase are reported.Localization is observed in the two-dimensional quantum walk with certain phase disorder and specific initial coin states.We give an explanation of the localization behavior via the localized stationary states of the unitary operator of the walker+coin system and the overlap between the initial state of the whole system and the localized stationary states.     

Studies of two-dimensional lattices using ferrofluid

By exerting a magnetic filed H normal to a ferrofluid layer, a triangular lattice of droplets is formed when H exceeds a characteristic critical field. The lattice may be “heated” by reducing H and the effects of dislocations and disclinations may be studied. This offers a new experimental system for direct visual observations of phenomena related to two-dimensional melting.     

Spatiotemporal surface solitons in two-dimensional photonic lattices

We analyze spatiotemporal light localization in truncated two-dimensional photonic lattices and demonstrate the existence of two-dimensional surface light bullets localized in the lattice corners or the edges. We study the families of the spatiotemporal surface solitons and their properties such as bistability and compare them with the modes located deep inside the photonic lattice.     

Periodic electron oscillation in coupled two-dimensional lattices

We study the time evolution of electron wavepacket in the coupled two-dimensional(2D) lattices with mirror symmetry, utilizing the tight-binding Hamiltonian framework. We show analytically that the wavepacket of an electron initially located on one atomic layer in the coupled 2D square lattices exhibits a periodic oscillation in both the transverse and longitudinal directions. The frequency of this oscillation is determined by the strength of the interlayer hopping. Additionally, we provide nume...     

Self-localized single-anharmonic vibrational modes in two-dimensional lattices

Many stationary forms of self-localized modes exist in a simple square and hexagonal lattice. They consist of a certain number of an elementary self-localized anharmonic mode (SLAM). This has several shapes depending on the uniform power of the nearest-neighbour interaction. By comparing SLAMs of the same vibrational frequency a binding energy can be derived for each stationary aggregated SLAM. Also infinite chains and whole lattices of elementary SLAMs are obtained. They have to be distinguished from standing waves of single-anharmonic phonons.     

Soliton stripes in two-dimensional nonlinear photonic lattices

We study experimentally the interaction of a soliton with a nonlinear lattice. We observe the formation of a novel type of composite soliton created by strong coupling of mutually incoherent periodic and localized beam components. By imposing an initial transverse momentum on the soliton stripe, we observe the effect of lattice compression and deformation.     

Theory of electronic transport in two-dimensional systems in the presence of magnetic fields

Three parts of the paper [Czech. J. Phys.41 (1991) 620,7 are focused on the Landauer-Büttiker approach to the study of transport in two-dimensional electron systems, with particular attention to the influence of an external magnetic field. In the previous parts the Landauer formalism was generalized for two-dimensional systems in quantizing magnetic fields. In the present part we applied the formalism to an analysis of magnetoresistance measurements. The two-dimensional electron gas preserved in the non-dissipative quantum Hall regime acts as the ideal leads necessary in the Landauer-Büttiker approach. The voltage, applied to the gate, forms a scattering region in the gated part of the sample, in between of its undisturbed parts (ideal leads). The dependence of the resistance on the gate voltage and the number of available channels within the ideal leads are discussed.The author wishes to thank to Professor P. Steda for cooperation and to Professor L. Smrka for his encouragement and support. Dr. R. J. Haug should be acknowledged for providing his experimental results.     

Theory of electronic transport in two-dimensional systems in the presence of magnetic fields

The paper of three parts is focused on the Landauer-Büttiker approach to the study of transport in two-dimensional electron systems, with particular attention to the influence of an external magnetic field. In the previous part the total conductance of such a system was shown to be proportional to the transmission current. In the present part we give a detailed proof, based on the linear response theory, to the last statement. The value of the magnetic field may be arbitrary and possible inhomogeneity of the electric field is also considered.The author wishes to thank to Professor P. Steda and Professor L. Smrka for discussions and encouragement.