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Language(s):
eng - English
Dates:
2008
Publication Status:
Issued
Pages:
VIII,268
Publishing info:
Berlin, Heidelberg, New York : Springer
Table of Contents:
{1}History of the Bernoulli potential}{1}
{1.1}Magneto-hydrodynamics}{1}
{1.2}Thermodynamical forces}{1}
{1.3}Surface dipole}{3}
{1.4}Non-local theory}{4}
{1.5}Field effect on the superconductivity}{4}
References
{2}Basic concepts}{7}
{2.1}Maxwell equations}{7}
{2.1.1}Electromagnetic potentials}{8}
{2.1.2}Coulomb gauge}{9}
{2.1.3}Equation of continuity}{10}
{2.2}Material relations in normal metals}{11}
{2.2.1}Ohm law}{9} {2.2.2}Hall effect}{11}
{2.2.3}Drift in crossed electric and magnetic fields}{14}
{2.3}Material relations in superconductors}{15}
{2.3.1}Magneto-hydrodynamical picture}{13}
{2.3.2}London theory}{18}
{2.3.3}London penetration depth}{20}
{3}Balance of forces}{21}
{3.1}Bernoulli potential}{21}
{3.1.1}Close to the charge neutrality}{22}
{3.1.2}Transient period}{23}
{3.2}Surface charge}{24}
(3.2.1}Diamagnetic current versus drift}{24}
{3.2.2}Surface charge}{25}
{3.2.3}Thomas-Fermi screening}{25}
{3.3}Finite temperatures}{29}
{3.3.1}London penetration depth}{29}
{3.3.2}Quasi-particle screening}{29}
{3.4}Lorentz force}{31}
{3.4.1}Magnetic pressure}{32}
{4}Thermodynamical correction}{35}
{4.1}Theory of Rickayzen}{35}
{4.1.1}Gibbs electro-chemical potential}{36}
{4.1.2}Local approximation of free energy}{37}
{4.1.3}Thermodynamical corrections}{39}
{4.2}Measurements of Bernoulli potential}{40}
{4.2.1}Standard Hall bar setup}{41}
{4.2.2}Kelvin capacitive pickup}{42}
{Bernoulli potential first observed}{44}
{High-precission measurements of the Bernoulli potential}{45}
{4.2.3}Charge transfer in the superconductor}{48}
{5}Phenomenological description}{51}
{5.1}Thermodynamic relations}{52}
{5.1.1}Free energy of a normal metal}{53}
{5.1.2}Free energy of a superconductor}{54}
{5.2}Two-fluid model}{55}
{5.3}Currents in the two-fluid model}{57}
{5.3.1}Extended London theory}{57}
{5.4}Electrostatic potential}{59}
{5.4.1}Free energy for the Coulomb interaction}{60}
{5.5}The two fluid model with the electric field}{61}
{5.5.1}Stability conditions alias Equations of motion}{61}
{5.5.2}Thomas-Fermi screening}{62}
{5.5.3}Thermodynamical correction of Rickayzen}{63}
{
{6}Non-local corrections}{67}
{6.1}Preliminary assumptions}{67}
{6.1.1}Intermediate states}{67}
{6.1.2}Magnetism of atoms}{69}
{Paramagnetic mechanism}{70}
{Diamagnetic mechanism}{70}
{Diamagnetic current}{71}
{6.2}Wave function for super-electrons}{72}
{6.2.1}Free energy with quantum features}{73}
{6.2.2}Neglect of surface free energy}{73}
{6.2.3}From kinetic energy to gradient corrections}{74}
{6.3}Free energy}{75}
{6.3.1}Original free energy of Ginzburg and Landau}{76}
{7}Extended Ginzburg-Landau theory}{79}
{7.1}Maxwell equations}{79}
{7.1.1}Poisson equations}{79}
{7.1.2}Ampere law}{80}
{7.2}Ginzburg-Landau equation}{81}
{7.2.1}Variation with complex variables}{81}
{7.2.2}Equation of Schr\"odinger type}{82}
{Quantum kinetic energy}{82}
{Equation for the wave function}{83}
{Boundary condition}{83}
{Effective potential for super-electrons}{84}
{7.3}Scalar potential}{86}
{8}Quasi-neutral limit}{89}
{8.1}Iterative treatment}{89}
{8.1.1}Zeroth order in the charge transfer}{89}
{8.1.2}Bernoulli potential in the first order}{90}
{8.1.3}Estimate of the charge density}{91}
{Scheme of iterations}{92}
{8.2}Continuity of super-current}{92}
{8.3}Anderson theorem}{93}
{8.4}Interaction with the magnetic field}{95}
{8.4.1}Phase transition in a very thin slab}{95}
{8.4.2}Little-Parks effect}{97}
{9}Diamagnetic current at surface}{103}
{9.1}Geometrical assumptions}{103}
{9.2}Low magnetic fields}{105}
{9.2.1}Zero magnetic field}{105}
{9.2.2}Linear order in the magnetic field}{106}
{9.3}Perturbations in the quadratic order}{106}
{9.3.1}GL wave function}{107}
{9.3.2}Bernoulli potential}{109}
{9.3.3}Surface charge}{110}
{9.3.4}Bernoulli potential at the surface}{111}
{9.3.5}Space profile of the Bernoulli potential}{112}
{9.3.6}Charge profile}{114}
{9.4}Strong magnetic field}{115}
{9.4.1}Magnetic field in third order response}{115}
{9.4.2}Magnetic field effect on the penetration depth}{116}
{9.5}Numerical results}{118}
{10}Surfaces}{123}
{10.1}Ground state energy for normal electrons}{124}
{10.1.1}Density of free electrons}{125}
{10.1.2}Kinetic energy of free electrons}{125}
{10.1.3}Gradient correction of Weizs\"acker}{126}
{10.1.4}Complete energy of the normal ground state}{127}
{10.2}Equations for charge profile}{128}
{10.2.1}Local approximation}{128}
{10.2.2}Screening in the local approximation}{129}
{10.2.3}Tunnelling into the vacuum}{130}
{10.2.4}Surface dipole}{131}
{10.3}Budd-Vannimenus theorem}{132}
{10.3.1}Identity for the surface potential}{133}
{10.3.2}Surface dipole of superconductor}{134}
{10.3.3}Magnetic field effect on the work function}{135}
{10.3.4}Electrostatic potential seen by capacitive pickup}{136}
{11}Matching of electrostatic potentials at surfaces}{139}
{11.1}Surface dipole on the intermediate scale}{139}
{11.2}Surface potential step in local approximations}{142}
{11.2.1}London theory}{142}
{11.2.2}Theory of van\nobreakspace {}Vijfeijken and Staas}{143}
{11.2.3}Theory of Rickayzen}{144}
{11.3}Matching for the Ginzburg-Landau theory in the quasi-neutral limit}{145}
{11.3.1}Integral of motion for the slab geometry}{146}
{11.3.2}Electrostatic potential at surface}{148}
{11.4}Matching for the Ginzburg-Landau theory}{148}
{11.4.1}Integral of motion for the slab geometry -- general case}{148}
{11.4.2}Gradient terms}{150}
{11.4.3}Electrostatic potential at the surface}{151}
{12}Diamagnetic currents deep in the bulk}{155}
{12.1}Nucleation of superconductivity}{156}
{12.1.1}Linearized GL theory}{156}
{12.1.2}Nucleation magnetic field $B_{\rm c2}$}{157}
{12.2}Vortex}{158}
{12.2.1}Vortex position}{160}
{12.2.2}Elementary magnetic flux}{161}
{12.3}Abrikosov vortex lattice}{161}
{12.3.1}Condensate and magnetic field}{162}
{12.3.2}Electrostatic potential}{165}
{12.3.3}Comparing forces on super-electrons}{166}
{12.3.4}Charge transfer}{167}
{13}Electrostatic potential above a surface with vortices}{171}
{13.1}Potential on the surface}{171}
{13.1.1}Comparing surface and bulk potentials}{174}
{13.1.2}Estimates of the surface potential}{175}
{13.2}Potential at finite distance from the surface}{176}
{13.2.1}Poisson equation and boundary conditions}{176}
{13.2.2}Potential above the Abrikosov lattice}{176}
{13.3}Charge transfer at the surface}{178}
{13.3.1}Surface charge}{178}
{13.3.2}Surface dipole}{179}
{13.4}Electric field above the Abrikosov vortex lattice}{180}
{14}Layered structures}{183}
{14.1}Cutting the space in slices}{184}
{14.1.1}Layer GL wave function}{185}
{14.1.2}Layer condensation energy}{185}
{14.1.3}In-layer kinetic energy}{186}
{14.1.4}Josephson coupling}{187}
{14.1.5}Electron free energy in the layered system}{188}
{14.1.6}Condition of stability}{188}
{14.2}Lawrence-Doniach model of YBa$_2$Cu$_3$O$_7$}{190}
{14.2.1}Condensation energy}{191}
{14.2.2}Kinetic energy}{191}
{14.2.3}Electromagnetic interaction}{192}
{14.3}Equations of motion}{193}
{14.3.1}Maxwell equation}{193}
{14.3.2}Lawrence-Doniach equations}{194}
{14.3.3}Electrostatic potential}{194}
{15}Charge transfer in layered structures}{197}
{15.1}Perpendicular magnetic field}{197}
{15.1.1}Ginzburg-Landau equations}{198}
{15.1.2}Effective Ginzburg-Landau equation}{198}
{15.1.3}Mapping on a metal}{199}
{15.2}Charge transfer in the YBa$_2$Cu$_3$O$_7$}{200}
{15.2.1}Electrostatic potential of a single layer}{201}
{15.2.2}Electrostatic potential of identically perturbed layers}{202}
{15.2.3}Charge transfer}{203}
{15.3}Close to the critical temperature}{204}
{15.3.1}Electrostatic potential}{204}
{15.3.2}Quasi-neutral approximation}{204}
{15.3.3}Beyond the quasi-neutrality}{206}
{15.4}Charge transfer effect on the nuclear resonance}{207}
{15.4.1}Energy levels of nucleon}{207}
{15.4.2}Frequencies of the nuclear magnetic resonance}{208}
{16}Effect of the electrostatic field on the superconductor}{211}
{16.1}Weakly screening materials}{211}
{16.1.1}Penetration of the electric field}{211}
{16.1.2}Weakly screened penetrating electrostatic potential}{212}
{16.1.3}Effect of the surface charge on superconductivity}{213}
{16.1.4}Increased temperature of the phase transition}{214}
{16.2}Strong screening}{216}
{16.2.1}Contribution of the surface dipole to the penetration depth}{216}
{16.2.2}Reduced charge perturbation behind the surface dipole}{217}
{16.2.3}Field effect on the GL wave function}{218}
{16.3}Effective boundary condition}{219}
{16.3.1}Characteristic potential of the field effect}{221}
{16.3.2}Phase transition in thin layers under bias}{223}
{16.3.3}Reduced transition temperature of thick layers}{225}
{16.3.4}Field-induced surface superconductivity}{226}
{17}Outlook and perspectives}{229}
{A}Estimate of material parameters}{231}
{A.1}Coefficient $\partial \gamma /\partial n$}{231}
{A.1.1}Models of free electrons}{232}
{A.1.2}Increase of $\gamma $ due to interaction with lattice vibrations}{233}
{A.2}Coefficient $\partial \varepsilon _{\rm con}/\partial n$}{233}
{A.2.1}The BCS estimate}{234}
{A.2.2}McMillan formula}{235}
{A.3}Material parameters of Niobium}{236}
{B}Numerical solution}{241}
{B.1}Dimensionless notation}{241}
{B.2}Fourier representation}{243}
{B.3}Simple iteration scheme}{244}
{B.4}Accelerated iteration scheme}{244}
{B.5}Description of the Ginzburg-Landau program}{245}
{C}Internal versus applied magnetic field}{251}
{C.1}Virial theorem}{251}
{C.2}Magnetic properties of the GL theory}{253}
{C.3}Magnetic properties of the extended GL theory}{254}
{References}{257}
{Index}{263}
Rev. Type:
-
Identifiers:
eDoc: 320904
Degree:
-
