Detailed Explanation
Type-I superconductors completely expel external magnetic fields if the strength of the applied field is sufficiently low; This state is called the Meissner state. However at elevated magnetic field, when the magnetic field energy becomes comparable with the superconducting condensation energy, the superconductivity is destroyed by the formation of macroscopically large inclusions of non-superconducting phase.
Type-II superconductors, besides the Meissner state, possess another state: a sufficiently strong applied magnetic field can produce quantum vortices which can carry magnetic flux through the interior of the superconductor. These quantum vortices repel each other and thus tend to form uniform vortex lattices or liquids. Formally, vortex solutions exist also in models of type-I superconductivity, but the interaction between vortices is purely attractive, so a system of many vortices is unstable against a collapse onto a state of a single giant macroscopic vortex. More importantly, the vortices in type-I superconductor are energetically unfavorable. To produce them would require the application of a magnetic field stronger than what a superconducting condensate can sustain. Thus a type-I superconductor goes to non-superconducting states rather than forming vortices. In the usual Ginzburg–Landau theory, only the quantum vortices with purely repulsive interaction are energetically cheap enough to be induced by applied magnetic field.
It was recently observed that the type-I/type-II dichotomy could be broken in a two-component superconductor.
Examples of two-component superconductivity are multi-band superconductors magnesium diboride and oxypnictides oxypnictide. There, one can distinguish two superconducting components associated with electrons belong to different bands band structure. A different example of two component systems is the projected superconducting states of liquid metallic hydrogen or deuterium where mixtures of superconducting electrons and superconducting protons or deuterons were theoretically predicted.
| Type-I superconductor | Type-II superconductor | Type-1.5 superconductor | |
|---|---|---|---|
| Characteristic length scales | The characteristic magnetic field variation length scale (London penetration depth) is smaller than the characteristic length scale of condensate density variation (superconducting coherence length) | The characteristic magnetic field variation length scale (London penetration depth) is larger than the characteristic length scale of the condensate density variation (superconducting coherence length) | Two characteristic length scales of condensate density variation, . Characteristic magnetic field variation length scale is smaller than one of the characteristic length scales of density variation and larger than another characteristic length scale of density variation |
| Intervortex interaction | Attractive | Repulsive | Attractive at long range and repulsive at short range |
| Phases in magnetic field of a clean bulk superconductor | (1) Meissner state at low fields; (2) Macroscopically large normal domains at larger fields. First-order phase transition between the states (1) and (2) | (1) Meissner state at low fields, (2) vortex lattices/liquids at larger fields. | (1) Meissner state at low fields (2) "Semi-Meissner state": vortex clusters coexisting with Meissner domains at intermediate fields (3) Vortex lattices/liquids at larger fields. |
| Phase transitions | First-order phase transition between the states (1) and (2) | Second-order phase transition between the states (1) and (2) and second-order phase transition between from the state (2) to normal state | First-order phase transition between the states (1) and (2) and second-order phase transition between from the state (2) to normal state. |
| Energy of Superconducting/normal boundary | Positive | Negative | Negative energy of superconductor/normal interface inside a vortex cluster, positive energy at the boundary of vortex cluster |
| Weakest magnetic field required to form a vortex | Larger than thermodynamical critical magnetic field | Smaller than thermodynamical critical magnetic field | In some cases larger than critical magnetic field for single vortex but smaller than critical magnetic field for a vortex cluster |
| Energy E(N) of N-quanta axially symmetric vortex solutions | E(N)/N < E(N–1)/(N–1) for all N, i.e. N-quanta vortex does not decay in 1-quanta vortices | E(N)/N > E(N–1)/(N–1) for all N, i.e. N-quanta vortex decays in 1-quanta vortices | There is a characteristic number of flux quanta Nc such that E(N)/N < E(N–1)/(N–1) for N |
Read more about this topic: Type-1.5 Superconductor
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