Vsevolod F. Gantmakher

Carrier Scattering in Metals and Semiconductors

Preface. 1. Quasi-particles in an ideal crystal. 2. Scattering. 3. Electron-phonon interaction. 4. Scattering by long-wavelength phonons in a simple band. 5. Scattering by phonons in an anisotropic electron band. 6. Electron-electron scattering and the electron temperature. 7. Relaxation characteristics of kinetic effects. 8. Two-phonon processes. 9. Scattering by impurities. 10. Scattering by dislocations. 11. Scattering by a crystal surface. 12. Scattering in a degenerate band and in a multiband model. 13. Spin-flip induced by spin-orbit interaction. 14. The effect of a magnetic field on scattering. 15. Exchange and spin interaction. Appendix. References. Author index. Subject index. Materials index. Cumulative index.

The experimental study of electron-phonon scattering in metals

The review is devoted to low temperature methods of the study of electron scattering on phonons in metals. The basic emphasis is put on those experiments or those aspects of experiments which are governed by or can yield information about the electron-phonon scattering anisotropy, i.e. the dependence of scattering probability on the electron position on the Fermi surface.

Localized – delocalized electron quantum phase transitions

Metal--insulator transitions and transitions between different quantum Hall liquids are used to describe the physical ideas forming the basis of quantum phase transitions and the methods of application of theoretical results in processing experimental data. The following two theoretical schemes are discussed and compared: the general theory of quantum phase transitions, which has been developed according to the theory of thermodynamic phase transitions and relies on the concept of a partition function, and a theory which is based on a scaling hypothesis and the renormalization-group concept borrowed from quantum electrodynamics, with the results formulated in terms of flow diagrams.

Destruction of localized electron pairs above the magnetic-field-driven superconductor-insulator transition in amorphous In-O films

We have investigated the field-induced superconductivity-destroying quantum transition in amorphous indium oxide films at low temperatures down to 30 mK. It has been found that, on the high-field side of the transition, the magnetoresistance reaches a maximum and the phase can be insulating as well as metallic. With further increasing magnetic field the film resistance drops and approaches in the high-field limit the resistance value at transition point so that at high fields the metallic phase occurs for both cases. We give a qualitative account of this behavior in terms of field-induced destruction of localized electron pairs.The field-induced superconductivity-destroying quantum transition in amorphous indium oxide films are investigated at low temperatures down to 30 mK. It is found that, on the high-field side of the transition, the magnetoresistance reaches a maximum and the phase can be insulating as well as metallic. With further increase of the magnetic field the resistance of the film drops and in the high-field limit approaches the resistance value at the transition point, so that at high fields the metallic phase occurs for both cases. We give a qualitative account of this behavior in terms of field-induced destruction of localized electron pairs.

Scaling Analysis of the Magnetic Field-Tuned Quantum Transition in Superconducting Amorphous In-O Films 1

We studied the magnetic field-tuned superconductor-insulator transition (SIT) in amorphous In-O films with different oxygen contents and, hence, different electron densities. Whereas the two-dimensional scaling behavior was confirmed for the states of the film near the zero-field SIT, the SIT scenario changed for the deeper states in the superconducting phase; in addition to the scaling function describing the conductivity of the fluctuation-induced Cooper pairs, the temperature-dependent contribution to the film resistance emerged. This contribution can originate from the conductivity of normal electrons.We have studied the magnetic-field-tuned superconductor-insulator quantum transition (SIT) in amorphous In-O films with different oxygen content and, hence, different electron density. While for states of the film near the zero-field SIT the two-dimensional scaling behaviour is confirmed, for deeper states in the superconducting phase the SIT scenario changes: in addition to the scaling function that describes the conductivity of fluctuation-induced Cooper pairs, there emerges a temperature-dependent contribution to the film resistance. This contribution can originate from the conductivity of normal electrons.

Observation of the parallel-magnetic-field-induced superconductor-insulator transition in thin amorphous InO films

We study the response of a thin superconducting amorphous InO film with variable oxygen content to a parallel magnetic field. A field-induced superconductor-insulator transition (SIT) is observed that is very similar to the one in normal magnetic fields. As the boson-vortex duality, which is the key-stone of the theory of the field-induced SIT, is obviously absent in the parallel configuration, we have to draw conclusion about the theory insufficiency.We study the response of a thin superconducting amorphous InO film with variable oxygen content to a magnetic field. A field-induced superconductor-insulator transition (SIT) is observed that is very similar to the one in normal magnetic fields. As the boson-vortex duality, which is the keystone of the theory of the field-induced SIT, is obviously absent in the parallel configuration, we have to draw a conclusion about the theory’s insufficiency.

Superconductor–insulator transitions and insulators with localized pairs

Two experiments are described which are related to the problem of localized Cooper pairs. Magnetic-field-tuned superconductor-insulator transition was studied in amorphous In--O films with onset of the superconducting transition in zero field near 2 K. Experiments performed in the temperature range T>0.3 K indicate that at the critical field, B=B_c, the first derivative of the resistance dR/dT is non-zero at T=0 and hence the scaling relations should be written in more general form. Study of the magnetotransport of high-resistance metastable alloy Cd-Sb on the insulating side of the superconductor-insulator transition revealed below 0.1 K a shunting condiction mechanism in addition to usual one-particle hopping. Possibility of pair hopping is discussed.

Superconductor–insulator transition in amorphous In–O films

Abstract From experiments with amorphous InOx films, three conclusions are made: (i) The pattern of the superconductor–insulator transition (SIT) seen before for 2D electron gas in normal magnetic field can be reproduced under different experimental conditions, with field parallel to the film; (ii) The negative magnetoresistance (NMr) observed in high fields is due to breaking of localized pairs and transformation of bosons into fermions, the latter having higher mobility; hence, NMr is a confirmation of the conception of localized pairs.; (iii) Assumption of existence near the SIN of two complementary groups of electrons, paired, i.e. bosons with density nb, and unpaired fermions with density nf (2nb+nf=n, the total density), can explain the nonuniversality of the critical resistance Rc0 seen before and its temperature dependence which we found in films with comparatively high n.

Mooij rule and weak localization

It has been shown that the observed correlation between the resistivity ρ of high-resistivity metallic alloys and the sign of the temperature derivative of their resistivity can be explained by taking into account the weak localization effect. This correlation is as follows: the derivative dρ/dT is negative for alloys with resistivity in the range of 150–300 μΩ cm, which corresponds to the mean free path of electrons about the interatomic distance; however, this derivative is positive for alloys with lower resistivities (Mooij rule).

Suppression of 2D superconductivity by the magnetic field: Quantum corrections vs. The superconductor-insulator transition

Magnetotransport of superconducting Nd2−xCexCuO4+y(NdCeCuO) films is studied in the temperature interval 0.3–30 K. The microscopic theory of the quantum corrections to conductivity, both in the Cooper and in the diffusion channels, qualitatively describes the main features of the experiment, including the negative magnetoresistance in the high-field limit. Comparison with the model of the field-induced superconductor-insulator transition is included and a crossover between these two theoretical approaches is discussed.Magnetotransport of superconducting Nd_{2-x}Ce_xCuO_{4+y} (NdCeCuO) films is studied in the temperature interval 0.3-30 K. The microscopic theory of the quantum corrections to conductivity, both in the Cooper and in the diffusion channels, qualitatively describes the main features of the experiment including the negative magnetoresistance in the high field limit. Comparison with the model of the field-induced superconductor-insulator transition (SIT) is included and a crossover between these two theoretical approaches is discussed.