Advanced Solid State Physics

Figure 156: Brillouin Zone of diamond, silicon, germanium and tin ...

16 Superconductivity Literature Rickayzen,Theory of Superconductivity, Interscience Publishers, 1965. Buckel, Kleiner,Supraleit ...

Figure 157: Resistance as a function of temperature for a mercury sample as investigated by K.Onnes. The history of the theoreti ...

Londonequations and theGinzburg - Landauequations, are the topic of the third subsection. In the fourth subsection we will give ...

Table 3: Transition temperaturesTcfor some selected materials. Material Tc/K Ti 0. 4 Hg 4. 2 C 60 19. 2 Rb 2 CsC 60 19. 2 YBa 2 ...

Figure 158: The critical magnetic fieldHc(T)as a function of temperatureT. ForT =Tcwe have Hc(Tc) = 0. Hc(T)separates the normal ...

Figure 159: Illustration of the dependence of the magnetization on the applied magnetic field for type I and type II superconduc ...

Figure 160: In the superconducting state the entropy is decreased with respect to the normal state. Figure 161: Schematic illust ...

Figure 162: Schematic illustration of the energy gap in a superconductor. Table 4: Some selected values of the exponentαrelated ...

16.3 Phenomenological Description 16.3.1 Thermodynamic Considerations Since the transition between the superconducting and the n ...

16.3.2 TheLondonEquations It is the aim of the following considerations to derive theMeissner - Ochsenfeld effect from a particu ...

Figure 163: Illustration of the above example of a semi-infinite superconductor in a homogeneous magnetic field in vacuum. Equiv ...

of second order phase transitions,GinzburgandLandausuggested that the free energyFSin the superconducting state can be written i ...

In the last step (integration by parts) we used thatfis some test function, i.e. it decays sufficiently fast for|r|→∞. From the ...

Comparison with the Eq. (279) yields λL= √ mβ μ 0 q^2 α . (301) We now introduce the dimensionless parameterκ: κ= λL ξ ≡ m ~q √ ...

16.4 Microscopic Theories 16.4.1 BCS Theory of Superconductivity We briefly discuss the fundamental concepts of the BCS theory o ...

Figure 164: The superconducting band gap versus temperature. Comparison between theoretical (BCS) and experimental data for Ta. ...

16.4.3 CooperPairs We regard a two electron system in a cube of volume 1 and periodic boundary conditions. We write the wave fun ...

Hence, (E−ε)g(E) =V ∫ 2 εm 2 εF dE′g(E′)N(E′) =C, (321) withCa constant. We readily obtain g(E) = C E−ε (322) and V ∫ 2 εm 2 εF ...

Taking the curl of both sides of this equation yields theLondonequation: ∇×j= q^2 n m ∇×A, (330) since∇×∇g= 0independent of the ...