The single-particle electronic structure of a two-dimensional electron gas in a nonuniform magnetic field B consists of states that propagate perpendicularly to the field gradient \B and have a remarkable time-reversal asymmetry. In one of the allowed directions the propagation has free-electron character and is confined to a narrow one-dimensional channel localized about the region where \B\ is minimum. In the opposite direction, the Landau states propagate throughout the rest of the sample with a velocity proportional to |V#| I/2 . PACS numbers: 72.15.Gd, 72.20.My, 73.20.DxThe electrical behavior of a two-dimensional electron gas (2DEG) subjected to a uniform magnetic field has been studied recently in much detail [1,2]. In the ballistic regime, the system is characterized by stationary Landau states, which do not propagate and yield no contribution to its conductance. The charge flow observed in finite samples was shown to be due to edge states localized at the boundary of the 2DEG [3]. This Letter discusses the situation in which the magnetic field in the interior of the sample is not uniform. In this case the Landau states are no longer stationary but propagate perpendicularly to the field gradient and exhibit a remarkable time-reversal asymmetry. In one of the allowed directions the propagation has free-electron character, and it is confined to a narrow one-dimensional region localized near the line where the magnitude of the magnetic field is minimum. In the opposite direction the Landau states propagate throughout the rest of the sample with a velocity which depends on the field gradient.The asymmetric propagation of electrons in a nonuniform magnetic field can be understood by the following classical argument illustrated in Fig. 1. Consider a 2DEG constrained by rigid walls to -£/2 :<>>:< L/2, but infinite along the x axis, and subjected to a magnetic field with a component perpendicular to the x-y plane, given bysuch that it changes sign at the line >>=0 [4]. The trajectory of a classical electron moving in the plane has an instantaneous radius of curvature given by r =cp/eB, where p is the momentum of the electron, and B the local magnitude of the magnetic field [5]. This means that the part of the trajectory that scans larger (smaller) values of the magnetic field will have a smaller (larger) radius, giving rise to an open orbit that drifts perpendicularly to the field gradient, as illustrated by the drift (d) trajectories in Fig. 1. For the case of a sufficiently small field gradient, VZ?=#iy, a straightforward classical calculation shows that the magnitude of the drift velocity is given by [5] v=er 2 B\/2mc. (2) Near the boundaries of the sample, collisions against the rigid walls force the electrons into skipping orbits as illustrated by the edge (e) trajectories in Fig. 1, which propagate in the same direction as the d trajectories. On the other hand, in the region where B-0 the electrons scan magnetic fields with alternating positive and negative signs, giving rise to the s trajectory, that propa...

No abstract

H20/Pt(lll)-interface 12D-structure I Phase transition I Scanning tunneling microscopy The H20-adsorption on Pt(l 11) at 120 K-140 is investigated by temperature-variable scanning tunneling microscopy. At 140 the adsorption kinetics of the first bilayer is determined by heterogeneous nucleation at the upper side and the lower side of step edges as well as by homogeneous island nucleation on the terraces. Depending on the preparation conditions the bilayer exhibits three different phases. Phase I can be characterized as an ideal ice bilayer rotated ±7°with respect to the (112)-direction of the Pt(lll)-surface. As a result the STM-images show a Moirée pattern. The second phase, Unauthenticated Download Date | 6/27/16 11:48 AM anomalie des Wassers in drei Dimensionen. Unterhalb von 135findet Nukleation in der zweiten Lage statt. Sie beginnt an ausgezeichneten Stellen der darunterliegenden Überstruktur und fiihrt zu einem regelmá-Bigen Muster kleiner Cluster. Die Dichte der Cluster in der zweiten Lage ist nahezu drei GröBenordnungen gröBer als die Inseldichte in der ersten Doppellage.Aufgrund einer Analyse des, die Abbildung von H20 auf Pt(lll) ermöglichenden Kontrastmechanismus, konnten wir schlieBen, daB die , -Lage auf der Pt( 111 )-Oberflache im Gegensatz zu 3D-Wasser eine metallische Leitfahigkeit besitzt. Dies kann für die Beschreibung von Elektronentransferprozessen in Experimenten der Elektrochemie von Bedeutung sein.

No abstract

No abstract