Conversely, if A>5, the surface er Bergy associated with the boundary is negative and lowers the total system energy. It is therefore thermodynamically favorable for a normal-superconducting interface to form inside these type II materials. Consequently, this class of superconductors does not exhibit the simple Meissner effect as do type I materials. Instead, there are now two critical fields: for applied fields below the lower critical field, Hal a type II superconductor is in the Meissner state, and for applied fields greater than the upper critical field, H2, superconductivity is destroyed. The three critical field are related to each other by H.-HeHe2 In the range H <H< H2, a type II superconductor is said to be in the vortex state because now the applied field can enter the bulk superconductor. Because flux exists in the material, however, the superconductivity is destroyed locally, creating normal regions. Recall that for type II materials the boundary between the normal and superconducting regions lowers the overall energy of the system. Therefore, the flux in the superconductor creates as many normal-superconducting interfaces as possible without violating quantum criteria. The net result is that flux enters a type II superconductor in quantized bundles of magnitude p, known as vortices or fluxons(the former name derives from the fact that current flows around each quantized bundle in the same manner as a fluid vortex circulates around a drain). The central portion of a vortex, known as the core, is a normal region with an approximate radius of E. If a defect-free superconductor is placed in a magnetic field, he individual vortices, whose cores essentially follow the local average field lines, form an ordered triangular array, or flux lattice. As the applied field is raised beyond H,( where the first vortex enters the superconductor), the distance between adjacent vortex cores decreases to maintain the appropriate flux density in the material. Finally, the upper critical field is reached when the normal cores overlap and the material is no longer superconducting. Indeed, a precise calculation of Ha using the phenomenological theory developed by vitaly H 2 which verifies our simple picture. The values of typical type II material parameters are listed in Tables 53.3 and Type II superconductors are of great technical importance because typical H, values are at least an order of magnitude greater than the typical H values of type I materials. It is therefore possible to use type II materials to make high-field magnet wire. Unfortunately, when current is applied to the wire, there is a Lorentz-like force on the vortices, causing them to move. Because the moving vortices carry flux, their motion creates a static voltage drop along the superconducting wire by Faradays law. As a result, the wire no longer has a zero dc TABLE 53.3 Material Parameters for Conventional Type II Superconductors* Material T(k) AG(o)(nm) Ea(o)(nm) (mev) Hge(t) PbIn 0.2 Pb-B 0.5 NE 1.5 13.0 16.0 PbMo ss 15.0 2.4 15.0 06 2 4523333 23.0 16.0 20.0 Nb Sn 18.0 3.4 23.0 Nb_ Ge " The values are only representative because the parameters for alloys and depend on how the material is fabricated. The penetration depth Ag(O)is oefficient of the Ginzburg-Landau temperature dependence as AG)=2g(o)(I kewise for the coherence length where SG(T)=EG(o)(1-77T)-. The uppe Source: R.J. Donnelly, " Cryogenics, in Physics Vade mecum, H L. Anderson, Ed, New York: American Institute of Physics, 1981. With permission. c2000 by CRC Press LLC© 2000 by CRC Press LLC Conversely, if l > j, the surface energy associated with the boundary is negative and lowers the total system energy. It is therefore thermodynamically favorable for a normal–superconducting interface to form inside these type II materials. Consequently, this class of superconductors does not exhibit the simple Meissner effect as do type I materials. Instead, there are now two critical fields: for applied fields below the lower critical field, Hc1, a type II superconductor is in the Meissner state, and for applied fields greater than the upper critical field, Hc2, superconductivity is destroyed. The three critical field are related to each other by Hc ª . In the range Hc 1 < H < Hc2, a type II superconductor is said to be in the vortex state because now the applied field can enter the bulk superconductor. Because flux exists in the material, however, the superconductivity is destroyed locally, creating normal regions. Recall that for type II materials the boundary between the normal and superconducting regions lowers the overall energy of the system. Therefore, the flux in the superconductor creates as many normal–superconducting interfaces as possible without violating quantum criteria. The net result is that flux enters a type II superconductor in quantized bundles of magnitude Fo known as vortices or fluxons (the former name derives from the fact that current flows around each quantized bundle in the same manner as a fluid vortex circulates around a drain). The central portion of a vortex, known as the core, is a normal region with an approximate radius of j. If a defect-free superconductor is placed in a magnetic field, the individual vortices, whose cores essentially follow the local average field lines, form an ordered triangular array, or flux lattice. As the applied field is raised beyond Hc 1 (where the first vortex enters the superconductor), the distance between adjacent vortex cores decreases to maintain the appropriate flux density in the material. Finally, the upper critical field is reached when the normal cores overlap and the material is no longer superconducting. Indeed, a precise calculation of Hc2 using the phenomenological theory developed by Vitaly Ginzburg and Lev Landau yields (53.20) which verifies our simple picture. The values of typical type II material parameters are listed in Tables 53.3 and 53.4. Type II superconductors are of great technical importance because typical Hc2 values are at least an order of magnitude greater than the typical Hc values of type I materials. It is therefore possible to use type II materials to make high-field magnet wire. Unfortunately, when current is applied to the wire, there is a Lorentz-like force on the vortices, causing them to move. Because the moving vortices carry flux, their motion creates a static voltage drop along the superconducting wire by Faraday’s law. As a result, the wire no longer has a zero dc TABLE 53.3 Material Parameters for Conventional Type II Superconductors* Material Tc (K) lGL(0) (nm) jGL(0) (nm) Do (meV) m0Hc2,o (T) Pb-In 7.0 150 30 1.2 0.2 Pb-Bi 8.3 200 20 1.7 0.5 Nb-Ti 9.5 300 4 1.5 13.0 Nb-N 16.0 200 5 2.4 15.0 PbMo6 S8 15.0 200 2 2.4 60.0 V3Ga 15.0 90 2–3 2.3 23.0 V3Si 16.0 60 3 2.3 20.0 Nb3Sn 18.0 65 3 3.4 23.0 Nb3Ge 23.0 90 3 3.7 38.0 *The values are only representative because the parameters for alloys and compounds depend on how the material is fabricated. The penetration depth lGL(0) is given as the coefficient of the Ginzburg–Landau temperature dependence as lGL(T) = lGL(0)(1 – T/Tc)–1/2; likewise for the coherence length where jGL(T) = jGL(0)(1 – T/Tc)–1/2. The upper critical field Hc2,o is given at zero temperature as well as the energy gap Do . Source: R.J. Donnelly, “Cryogenics,” in Physics Vade Mecum, H.L. Anderson, Ed., New York: American Institute of Physics, 1981. With permission. Hc1Hc2 Hc o o 2 2 2 = m F p x