Electron dynamics in crystalline semiconductors

Electron dynamics in crystalline semiconductors is described by distinguishing between an instantaneous velocity related to electron's momentum and an average velocity related to its quasi-momentum in a periodic potential. It is shown that the electron velocity used in the theory of electron transport and free-carrier optics is the average electron velocity, not the instantaneous velocity. An effective mass of charge carriers in solids is considered and it is demonstrated that, in contrast to the "acceleration" mass introduced in textbooks, it is a "velocity" mass relating carrier velocity to its quasi-momentum that is a much more useful physical quantity. Among other advantages, the velocity mass is a scalar for spherical but nonparabolic energy bands $\epsilon(k)$, whereas the acceleration mass is not a scalar. Important applications of the velocity mass are indicated. A two-band {\bm k}\cdot {\bm \hp} model is introduced as the simplest example of a band structure that still keeps track of the periodic lattice potential. It is remarked that the two-band model, adequately describing narrow-gap semiconductors (including zero-gap graphene), strongly resembles the special theory of relativity. Instructive examples of the "semi-relativistic" analogy are given. The presentation has both scientific and pedagogical aspects.Comment: 7 pages; 1 figur

Transitional labour markets in a transitional economy: Could they work? The example of Poland

The prospects for successful implementation of the TLM approach in Poland depend on numerous factors, and it is important to remember that the impact of these factors will rarely be one-dimensional. TLMs would entail a series of both advantages and disadvantages for employers, employees, the self-employed, non-paid workers, the unemployed, trainees and older workers facing retirement. Moreover, the unique mix of economic, social, technological and demographic changes found in Poland will have a substantial impact on the prospects for implementing TLMs. There is no conclusive answer to the question formulated in the title. A number of arguments suggest that the reply might be positive: the prospect of social and political approval for TLMs, EU membership, the need to combat widespread unemployment and illicit employment, the rising level of education, the high rate of economic growth, and many others. There are also, however, many potential obstacles: the poor level of agreement between the social partners, the lack of funds for ALMP, inadequate links between different employment statuses on the labour market, the scale of poverty, inadequate mobility, structural reforms, poor implementation of labour law, etc. -- Es gibt eine Vielzahl von Faktoren, die die Chancen einer effizienten Implementierung des Konzepts der Übergangsarbeitsmärkte (ÜAM) in Polen beeinflussen und die sich zudem selten in nur eine Richtung auswirken. ÜAM würden eine Reihe von Vor- wie Nachteilen für Arbeitgeber, Arbeitnehmer, Selbständige, Unbezahlte, Arbeitslose, Auszubildende und ältere Beschäftigte vor dem Ruhestand mit sich bringen. Darüber hinaus werden die Perspektiven für die Realisierung von ÜAM in Polen auch stark von den Besonderheiten des ökonomischen, gesellschaftlichen, technologischen und demographischen Wandels in diesem Lande bestimmt. Die im Titel formulierte Frage lässt sich nicht endgültig bejahen oder verneinen. Etliche Argumente sprechen für eine positive Antwort: die Aussicht auf gesellschaftliche und politische Zustimmung zu ÜAM, die EUMitgliedschaft, die Notwendigkeit, die hohe Arbeitslosigkeit und die weit verbreitete Schwarzarbeit zu bekämpfen, das steigende Bildungsniveau, das hohe Wirtschaftswachstum und vieles mehr. Es existieren jedoch auch viele potentielle Hindernisse: fehlendes Einvernehmen zwischen den Sozialpartnern, mangelnde finanzielle Mittel für aktive arbeitsmarktpolitische Maßnahmen, keine adäquaten Brücken für Übergänge in eine andere Erwerbsform, Armut, zu geringe Mobilität, Strukturreformen, schlechte Umsetzung des Arbeitsrechts usw.

Transient Zitterbewegung of charge carriers in graphene and carbon nanotubes

Observable effects due to trembling motion (Zitterbewegung, ZB) of charge carriers in bilayer graphene, monolayer graphene and carbon nanotubes are calculated. It is shown that, when the charge carriers are prepared in the form of gaussian wave packets, the ZB has a transient character with the decay time of femtoseconds in graphene and picoseconds in nanotubes. Analytical results for bilayer graphene allow us to investigate phenomena which accompany the trembling motion. In particular, it is shown that the transient character of ZB in graphene is due to the fact that wave subpackets related to positive and negative electron energies move in opposite directions, so their overlap diminishes with time. This behavior is analogous to that of the wave packets representing relativistic electrons in a vacuum.Comment: 7 pages, 3 figures, augmented versio

Spin-flip reflection of electrons from a potential barrier in heterostructures

Spin-conserving and spin-flip opaque reflections of electrons from a potential barrier in heterostructures are described. An electric field of the barrier is considered to be the only source of energy spin splitting in the presence of spin-orbit interaction and its form is calculated in the three-level {\kp} model for a nontrival case of unbound electrons. Reflection angles and amplitudes are calculated for oblique incoming directions. It is shown that the system can serve as a source or filter of spin-polarized electron beams. Two unexpected possibilities are pointed out: a) non attenuated electron propagation in the barrier whose height exceeds the energies of incoming electrons, b) total reflection of electrons whose energies exceed barrier's height.Comment: 10 pages, 3 figure

Nature of electron Zitterbewegung in crystalline solids

We demonstrate both classically and quantum mechanically that the Zitterbewegung (ZB, the trembling motion) of electrons in crystalline solids is nothing else, but oscillations of velocity assuring the energy conservation when the electron moves in a periodic potential. This means that the nature of electron ZB in a solid is completely different from that of relativistic electrons in a vacuum, as proposed by Schrodinger. Still, we show that the two-band {\bf k.p} model of electronic band structure, formally similar to the Dirac equation for electrons in a vacuum, gives a very good description of ZB in solids. Our results indicate unambiguously that the trembling motion of electrons in solids should be observable.Comment: 5 pages, 3 figure