Hexagonal Superlattice Pattern Research Articles

High-temperature Brown-Zak oscillations in graphene/hBN moiré field effect transistor fabricated using molecular beam epitaxy

Graphene placed on hexagonal boron nitride (hBN) has received significant interest due to its excellent electrical performance and physics phenomena, such as superlattice Dirac points. Direct molecular beam epitaxy growth of graphene on hBN offers an alternative fabrication route for hBN/graphene devices. Here, we investigate the electronic transport of moiré field effect transistors (FETs) in which the conducting channel is monolayer graphene grown on hexagonal boron nitride by high temperature molecular beam epitaxy (HT-MBE). Alignment between hBN and HT-MBE graphene crystal lattices gives rise to a moiré-fringed hexagonal superlattice pattern. Its electronic band structure takes the form of a “Hofstadter butterfly”. When a strong magnetic field B is applied perpendicular to the graphene layer, the electrical conductance displays magneto-oscillations, periodic in B−1, over a wide range of gate voltages and temperatures up to 350 K. We attribute this behaviour to the quantisation of electronic charge and magnetic flux within each unit cell of the superlattice, which gives rise to so-called Brown-Zak oscillations, previously reported only in high-mobility exfoliated graphene. Thus, this HT-MBE graphene/hBN heterostructure provides a platform for observation of room temperature quantum effects and device applications.

Formation of honeycomb-Kagome hexagonal superlattice pattern with dark discharges in dielectric barrier discharge

A honeycomb-Kagome hexagonal superlattice pattern with dark discharges is observed in a dielectric barrier discharge system for the first time. The spatiotemporal structure of the honeycomb-Kagome hexagonal superlattice pattern with dark discharges is investigated by an intensified charge-coupled device and the photomultipliers show that it is an interleaving of three different sub-lattices, which are bright-spot, invisible honeycomb lattice, and Kagome lattice with invisible frameworks and dim-spots, respectively. The invisible honeycomb lattices and Kagome lattices are actually composed of dark discharges. By using the optical emission spectra method, it is found that the plasma parameters of the three different sub-lattices are different. The influence of the dark discharges on pattern formation is discussed. The results may have significance for the investigation of the dark discharges and will accelerate the development of self-organized pattern dynamics.

Erratum: “The interaction between volume discharges and surface discharges in spot-line white-eye hexagonal superlattice pattern in dielectric barrier discharge” [Phys. Plasmas 26, 023507 (2019)

Erratum: “The interaction between volume discharges and surface discharges in spot-line white-eye hexagonal superlattice pattern in dielectric barrier discharge” [Phys. Plasmas <b>26</b>, 023507 (2019)

Formation of kagome-white-eye-honeycomb hexagonal superlattice pattern in dielectric barrier discharge.

A kagome-white-eye-honeycomb hexagonal superlattice pattern is observed in dielectric barrier discharge and studied by two photomultipliers, an intensified charge-coupled device, and a spectrograph. It consists of four sublattices, which are kagome structure, halos of white-eye hexagon, honeycomb frame, and central spots hexagon. As an unconventional symmetry sublattice, the kagome structure results in amazing sublattice discharge order. Based on the consideration that any discharge is related to all previous discharges, a mapping matrix which governs self-organization of the pattern is proposed. These results will promote the development of the pattern dynamics.

The interaction between volume discharges and surface discharges in spot-line white-eye hexagonal superlattice pattern in dielectric barrier discharge

We report on the interaction between surface discharges (SDs) and volume discharges (VDs) in the spot-line white-eye hexagonal superlattice pattern in dielectric barrier discharge using an intensified charge-coupled device camera, a high-speed video camera, and a spectrograph. The small spot-lines and halos discharge in the first pulse and the second pulse at the rising edge of the voltage, respectively. The central spots discharge at the falling edge of voltage. The small spots are VDs whose discharge time is incompletely simultaneous. The lines are direction-selective SDs induced by small spots. It is found that the above phenomena result from the interaction between SDs and VDs. The incompletely simultaneous discharge of the small spots is due to the different quantities of wall charges transported by the SDs induced by small spots. The directional selectivity of the SDs results from that the SDs are extinguished when they are close to halos due to the neutralization of the wall charge of halos (VDs) and the wall charge of SDs, while they can stretch to other small spots.

Study on bright-dim hollow hexagonal superlattice pattern in dielectric barrier discharge

We report on the investigation of the bright-dim hollow hexagonal superlattice pattern (BDHHSP) in dielectric barrier discharge (DBD) for the first time. It bifurcates from a hexagon pattern as the applied voltage increases. The spatiotemporal structure investigated by using an intensified charge device and a lens-aperture photomultiplier tube system shows that the BDHHSP is an interleaving of three different sub-lattices, which are bright spots, dim spots, and halos, respectively, and dim spots are located at the center of the triangle formed by three bright spots. But not all the centers of each triangle have a dim spot. The formation mechanism of the phenomenon called selectively insert discharge is discussed. The results have significance for the selective mechanism of discharge position in the DBD system.

Study on moving filaments in honeycomb pattern in dielectric barrier discharge

We report on the study of moving filaments in a honeycomb pattern in a dielectric barrier discharge system using photomultipliers, a high-speed video camera, and a spectrometer. The honeycomb pattern bifurcates from the hexagonal super-lattice pattern with increasing voltage. It is found that the honeycomb framework is composed of filaments with irregular reciprocating motion, which indicates that the honeycomb framework results from statistical self-organization. The spatiotemporal dynamics show that the pattern consists of three different sub-lattices. The plasma parameters (molecular vibrational temperature and electron density) of the pattern, determined from the optical emission spectra, show that different sub-lattices are in different plasma states. Based on these measurements, the mechanism of the movement of filaments is analyzed briefly.

Study on hexagonal super-lattice pattern with surface discharges in dielectric barrier discharge

The hexagonal super-lattice pattern with surface discharges (SDs) in dielectric barrier discharge is investigated by intensified charge-coupled device. The pattern is composed of the bright spot and the dim spot which is located at the centroid of surrounding other three bright spots. The phase diagram of the pattern as a function of the gas pressure and the argon concentration is given. The instantaneous images indicate that the bright spot emerging at the front of the current pulse is formed by the volume discharge (VD), and dim spot occurring at the tail of the current pulse is formed by the SD. The above result shows that the SD is induced by the VD. The simulation of the electric fields of wall charges accumulated by VDs confirms that the dim spot is formed by the confluences of the SDs of surrounding other three bright spots. By using optical emission spectrum method, both the molecule vibration temperature and electron density of the SD are larger than that of the VD.

Investigation on motional characteristics of paired filaments in a dielectric barrier discharge by a high-speed framing camera

Motional characteristics of paired filaments in a hexagonal superlattice pattern in a dielectric barrier discharge are investigated by a high-speed framing camera. Through images correlated with successive current pulse phases, the change in position of the paired filaments is observed, and the time-reversed sequence of the appearance of the paired filaments is determined. Generally, the first ignited spot moves closer to their centre, while the second ignited spot moves further from it, and the distance between the two spots does not change significantly. Sometimes only one filament has obvious changes in position, leading to the variation of distance and orientation of the pair. Based on the appearance sequence, the change in position of the paired filaments is explained by the interaction of internal fields induced by surface charges. The statistics of the variations of the distance D between the paired filaments are investigated within successive discharges.

Investigation on collisions of filament pairs in dielectric barrier discharge

Collisions of filament pairs in a hexagonal superlattice pattern in dielectric barrier discharge are investigated on different timescales. In the evolution of the pattern, the space scale of each hexagon cell decreases with the increasing voltage. The duration of one collision is seven half voltage cycles at least. Two stable orientations of a pair are approximately perpendicular to each other and the orientational changes occurring during the entire colliding process should be a multiple of 30°. The time interval between two consecutive collisions decreases with the increasing voltage. The distance between the paired spots decreases nonmonotonically. Based on the discharge order of the pattern, it is inferred that the collision should be the interaction between a discharging filament and the surface charges deposited by another discharged filament, and the nonmonotonic decrease of distance D is explained.

Pattern formation based on the triple-layer coupling mechanism

We report on the first investigation of the triple-layer coupling pattern formation in a dielectric barrier discharge system. The pattern basically consists of one discharge subpattern ignited in the gas gap and two surface-charge subpatterns deposited on the dielectric surfaces. The coupling of the three subpatterns (layers) is presented by analyzing the time-resolved discharge sequence of a white-eye hexagonal super lattice pattern (WEHSP). A triple-layer coupling reaction-diffusion regime is also established to conduct simulations and the simulated WEHSP agrees well with the experiment. This paper will provide a deeper understanding for the layer coupling mechanism in pattern formation.

Motion of rotating pairs in a hexagonal superlattice pattern within dielectric barrier discharge

Stochastic rotation of rotating pairs in a hexagonal superlattice pattern is observed in a dielectric barrier discharge system. It is found that the pairs rotate with orientation and diameter randomly changing by observing a series of frames recorded by a high speed video camera. Frames recorded by a high speed framing camera with an exposure time corresponding to current pulse phases in one half cycle of the applied voltage show that one rotating spot, six small spots, and another rotating spot in one cell discharge successively. Based on this discharging sequence, forces exerted on a rotating spot are analyzed at different discharging stages in a half voltage cycle. A resultant force on a rotating spot with both magnitude and direction varied leads to the stochastic rotation.

Hexagonal superlattice pattern consisting of colliding filament pairs in a dielectric barrier discharge

Colliding-pairs hexagonal superlattice pattern (CPHSP) is studied in a dielectric barrier discharge system. The evolution of CPHSP bifurcating from a hexagonal pattern to chaos is shown. The phase diagrams of CPHSP as a function of discharge parameters are given. From a series of pictures taken by a high speed video camera, collisions between two spots are observed and the superposition of many collisions results in each big spot presenting four small spots on long time scales. Measurements of the correlation between filaments indicate that the pattern is an interleaving of four different transient hexagonal sublattices. Depending on the discharging sequence, the forces exerted on one colliding spot are discussed briefly.

Collision Between Two Spots in a Hexagonal Superlattice Pattern in Dielectric Barrier Discharge

The collision between two spots in a hexagonal superlattice pattern in a dielectric barrier discharge is studied by a fast intensified camera. The hexagonal superlattice pattern is composed of small and big spots. In the amplified pictures, each big spot appears as four small spots at long exposure time, while it presents a pair of spots at short exposure time. A series of images, which arc taken by a fast intensified camera, displays that two spots collide continually and the orientation of two spots changes about 90° after each collision. The superposition of a lot of collisions between two spots appears as four small spots.

Study of composition of big spots in a hexagonal superlattice pattern by image analysis

Study of composition of big spots in a hexagonal superlattice pattern by image analysis

Harmonic hexagonal superlattice pattern in a dielectric barrier discharge at atmospheric pressure

We report a harmonic hexagonal superlattice pattern in a dielectric barrier discharge in air/argon mixture at atmospheric pressure. The bifurcation scenario of harmonic hexagonal superlattice pattern with the applied voltage increasing is given. The phase diagram of the pattern types as a function of the applied voltage and the air-concentration is obtained. The hysteresis of pattern transitions at the upward and downward stage of the applied voltage is observed. The correlation measurements indicate that harmonic hexagonal superlattice pattern is an interleaving of two different transient sublattices. The spatial power spectrum demonstrates that harmonic hexagonal superlattice pattern has two separate wave vectors. Both small wave vector qh and big wave vector Kh belong to the harmonic mode, and they obey a triad resonant interaction qh1 + qh2 =kh.

Experimental study on self-organized hexagonal superlattice pattern in dielectric barrier discharge in argon/air

A new type of hexagonal superlattice pattern is observed under three different boundary conditions by using a dielectric barrier discharge device with water electrode. The power spectrum of hexagonal superlattice pattern and its angular distributions are shown. The phase diagram of the hexagonal superlattice pattern as a function of air concentration and applied voltage is obtained. The correlation measurements indicate that the hexagonal superlattice pattern is an interllacing of two different transient sublattices. The selection of pattern formation in quadrangular boundary with different area is studied. It is found that the hexagonal superlattice pattern is a typical type of nonlinear self-organized pattern, and the formation of square superlattice pattern is dependent upon the boundary conditions.

Self-Organized Gas-Discharge Patterns in a Dielectric-Barrier Discharge System

A rich variety of gas-discharge patterns have been observed in a specially designed dielectric-barrier discharge system with two liquid electrodes. The patterns presented here include square-lattice pattern, square-texture pattern, square-superlattice pattern, hexagonal superlattice state, multiarmed-spiral pattern, hollow-hexagonal pattern, and rotating-wheels pattern.