Single-layer and bilayer graphene superlattices: collimation, additional Dirac points and Dirac lines

We review the energy spectrum and transport properties of several types of one- dimensional superlattices (SLs) on single-layer and bilayer graphene. In single-layer graphene, for certain SL parameters an electron beam incident on a SL is highly collimated. On the other hand there are extra Dirac points generated for other SL parameters. Using rectangular barriers allows us to find analytic expressions for the location of new Dirac points in the spectrum and for the renormalization of the electron velocities. The influence of these extra Dirac points on the conductivity is investigated. In the limit of {\delta}-function barriers, the transmission T through, conductance G of a finite number of barriers as well as the energy spectra of SLs are periodic functions of the dimensionless strength P of the barriers, P{\delta}(x) ~ V (x). For a Kronig-Penney SL with alternating sign of the height of the barriers the Dirac point becomes a Dirac line for P = {\pi}/2 + n{\pi} with n an integer. In bilayer graphene, with an appropriate bias applied to the barriers and wells, we show that several new types of SLs are produced and two of them are similar to type I and type II semiconductor SLs. Similar as in single-layer graphene extra "Dirac" points are found. Non-ballistic transport is also considered.Comment: 26 pages, 17 figure

Extra Dirac points in the energy spectrum for superlattices on single-layer graphene

We investigate the emergence of extra Dirac points in the electronic structure of a periodically spaced barrier system, i.e., a superlattice, on single-layer graphene, using a Dirac-type Hamiltonian. Using square barriers allows us to find analytic expressions for the occurrence and location of these new Dirac points in k-space and for the renormalization of the electron velocity near them in the low-energy range. In the general case of unequal barrier and well widths the new Dirac points move away from the Fermi level and for given heights of the potential barriers there is a minimum and maximum barrier width outside of which the new Dirac points disappear. The effect of these extra Dirac points on the density of states and on the conductivity is investigated.Comment: 7 pages, 8 figures, accepted for publication in Phys. Rev.

Dirac electrons in a Kronig-Penney potential: dispersion relation and transmission periodic in the strength of the barriers

The transmission T and conductance G through one or multiple one-dimensional, delta-function barriers of two-dimensional fermions with a linear energy spectrum are studied. T and G are periodic functions of the strength P of the delta-function barrier V(x,y) / hbar v_F = P delta(x). The dispersion relation of a Kronig-Penney (KP) model of a superlattice is also a periodic function of P and causes collimation of an incident electron beam for P = 2 pi n and n integer. For a KP superlattice with alternating sign of the height of the barriers the Dirac point becomes a Dirac line for P = (n + 1/2) pi.Comment: 5 pages, 6 figure

KINEMATIC AND DYNAMIC ANALYSIS OF THE ROWER'S GESTURE ON CONCEPT II ERGOMETER

INTRODUCTION : Biomechanics Studies of rowing, remain most of the time global and consider the gesture as an indivisible whole (classification in style(DAL MONTE 89), coefficient of efficiency(ZATSIORSKY 91), peak of force on the handle (HARTMANN 93)). We plan to consider the gesture as the result of an elementary movements succession(movement of legs, movement of the trunk, movement of arms). Therefore the evaluation of the gesture efficiency depends on the study organization of these movements. The method used was the morphological analysis of kinematic and dynamic variable. An original experimental device has been elaborated. It consists of an optoelectronic system and a Concept II ergometer with of force and torque transducers. The population was a group of three rowers : a beginner, a regional level rower and a female rower of French team. After a period of warming of few minutes, the experimentation consisted in rowing during 20 minutes. The order was to row the furthest possible. The acquisition has been carried out for the first 5minutes.RESULTS : The first results show, for the three subjects, that the developed force on the handle cancels each other out before the end of the propulsion. This corresponds to a inefficiency phase of the gesture of the rower. A thorough morphological analysis shows that this phase is synchronized with a fall of the speed of the handle. Nevertheless, during this phase, the elbow angular speed is maximal. Consequently. During this phase, the contribution of arm is inefficient. The rower does not manageto increase the speed of the handle anymore. In addition, a comparative analysis between the three rowers is presented. It is based on inter-limb angular variable study and on effort delivered by the feet and the hands. The angular variable analysis shows a movement stereotyped for skilled rower. This confirmed that the expert's gestures are an automatism. Moreover, the increase of the force, applied on the feet strechers, carried out by the female rower, during the recovery, was delated, comparatively with the others rowers. The female rower controls her recovery. As this force does not make the boat further, the analysis of this variable shows as inefficient phase for the beginner and the regional rower. CONCLUSION : Kinematic and dynamic analysis of the rower gesture allowed to find 2 ineffective phases : the first during the end of the propulsion and the second during the end of the recovery. REFERENCES :DAL MONTE 89 : Dal Monte A,, Komor A.,Rowing and Sculling Mechanics, Article, Biomechanics of sport, Vaughan C.L.,ISBN : 0-8493-6820-0, 1989ZATSIORSKY 91 : Zatsiorsky V., YakuninN., Mechanics and Biomechanics of Rowing : TO review, International Newspaper of sport biomechanics, p229-281, 1991HARTMANN 93 : Hartmann U., Mader A.,Wasser K., Klauer I., Peak Forces,Velocity, and Power During Five and Maximal Ten Rowing Ergometer Strokesby World Class Female and Pain Rowers, Int J. Sport Med, Flight 14, Supl.1, p 42-545,199

EXPERIMENTAL DEVICE FOR THE ANALYSIS OF THE CYCLER'S MOVEMENT

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