Type-1.5 superconductor
Encyclopedia
The term type-1.5 superconductor refers to a multicomponent superconductor with two coherence lengths 
related two magnetic field penetration length as follows 
. As a consequence it has behavior different from that of type-I and type-II superconductors. Namely it has quantum vortex excitations which have long-range attractive, short-range repulsive interaction and low applied magnetic field it allows the macroscopic phase separation into Meissner sate (domains with expelled magnetic field) and clusters of quantum vortices.
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 applicaiton of a magnetic field stronger than what a superconducting condensate can sustain. 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.
where
are two superconducting condensates.
In case if the condensates are coupled only electromagnetically, i.e. by
the model has three length scales: the London penetration length
and two coherence lengths 
.
The vortex excitations in that case have cores in both components which are co-centered because
of electromagnetic coupling.
The necessary but not sufficient condition for occurrence of type-1.5 regime is
. Additional condition of thermodynamic stability is satisfied for a range of parameters.
These vortices have a nonmonotonic interaction: they attract each other at large distances and repel each other at short distances.
It was further shown that there is a range of parameters where these vortices are energetically favorable enough to be excitable by an external field, attractive interaction notwithstanding. This results in the formation of a new superconducting phase in low magnetic fields dubbed "Semi-Meissner" state. The vortices, whose density is controlled by applied magnetic flux density, do not form a regular structure. Instead, they should have a tendency to form vortex "droplets" because of the long-range attractive interaction caused by condensate density suppression in the area around the vortex. Such vortex clusters should coexist with the areas of vortex-less two-component Meissner domains. Inside such vortex cluster the component with larger coherence length is suppressed: so that component has appreciable current only at the boundary of the cluster.
where again
are two superconducting condensates.
In multiband superconductors quite generically
.
When
three length scales of the problem are the London penetration length
and two characteristic length scales associated with normal modes of coupled density fluctuations. In that case the new coherence lengths
are attributed to "mixed" combinations of density fields.
An example of two-component superconductivity is the two-band superconductor magnesium diboride
. There, one can distinguish two superconducting components associated with electrons belong to different bands.
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.
In 2009, experimental results have been reported
indicating that magnesium diboride
may fall into this new class of superconductivity. The term type-1.5 superconductor was coined for this state. Further experimental data backing this conclusion was reported in
. More recent theoretical works show that the type-1.5 may be more general phenomenon because it does not require a material with two truly superconducting bands, but can also happen as a result of even very small interband proximity effect
and is robust in the presence of various inter-band couplings such as interband Josephson coupling.
In Type-I and Type-II superconductors charge flow patterns are dramatically different. Type I has two state-defining properties: Lack of electric resistance and the fact that it does not allow an external magnetic field to pass through it. When a magnetic field is applied to these materials, superconducting electrons produce a strong current on the surface which in turn produces a magnetic field in the opposite direction. Inside this type of superconductor, the external magnetic field and the field created by the surface flow of electrons add up to zero. That is, they cancel each other out.
In Type II superconducting materials where a complicated flow of superconducting electrons can happen deep in the interior. In Type II material, a magnetic field can penetrate, carried inside by vortices which form Abrikosov vortex lattice. It type-1.5 superconductor there are two superconducting components. There the external magnetic field can produce clusters of tightly packed vortex droplets because in such materials vortices should attract each other at large distances and repel at short length scales. Since the attraction originates in vortex core's overlaps in one of the superconducting components, this component will be depleted in the vortex cluster. Thus
a vortex cluster will represent two competing types of superflow. One component will form vortices bunched together while the second component will produce supercurrent flowing on the surface of vortex clusters in a way similar to how electrons flow on the exterior of Type I superconductors. These vortex clusters are separated by "voids," with no vortices, no currents and no magnetic field.
see description on
]
coexist with clusters where vortex droplets form in one superconducting components and macroscopic normal domains in the other.
related two magnetic field penetration length as follows . As a consequence it has behavior different from that of type-I and type-II superconductors. Namely it has quantum vortex excitations which have long-range attractive, short-range repulsive interaction and low applied magnetic field it allows the macroscopic phase separation into Meissner sate (domains with expelled magnetic field) and clusters of quantum vortices.| Type-I superconductor | Type-II superconductor | Type-1.5 superconductor | |
|---|---|---|---|
| Characteristic length scales | The characteristic magnetic field variation length scale is smaller than the characteristic length scale of condensate density variation (coherence length)  |
The characteristic magnetic field variation length scale is larger than the characteristic length scale of the condensate density variation (coherence length)  |
Two characteristic length scales of condensates 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 |
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
Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
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
Quantum vortex
In physics, a quantum vortex is a topological defect exhibited in superfluids and superconductors. Superfluids and superconductors are states of matter without friction. They exist only at very low temperatures. The existence of these quantum vortices was independently predicted by Richard Feynman...
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 applicaiton of a magnetic field stronger than what a superconducting condensate can sustain. 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.
The minimal model of type-1.5 superconductor
For multicomponent superconductors with higher that U(1) symmetry the Ginzburg-Landau model reads:where
are two superconducting condensates.In case if the condensates are coupled only electromagnetically, i.e. by
the model has three length scales: the London penetration length and two coherence lengths .The vortex excitations in that case have cores in both components which are co-centered because
of electromagnetic coupling.
The necessary but not sufficient condition for occurrence of type-1.5 regime is
. Additional condition of thermodynamic stability is satisfied for a range of parameters.These vortices have a nonmonotonic interaction: they attract each other at large distances and repel each other at short distances.
It was further shown that there is a range of parameters where these vortices are energetically favorable enough to be excitable by an external field, attractive interaction notwithstanding. This results in the formation of a new superconducting phase in low magnetic fields dubbed "Semi-Meissner" state. The vortices, whose density is controlled by applied magnetic flux density, do not form a regular structure. Instead, they should have a tendency to form vortex "droplets" because of the long-range attractive interaction caused by condensate density suppression in the area around the vortex. Such vortex clusters should coexist with the areas of vortex-less two-component Meissner domains. Inside such vortex cluster the component with larger coherence length is suppressed: so that component has appreciable current only at the boundary of the cluster.
Extended models
A two-band superconductor is described by the following Ginzburg-Landau modelwhere again
are two superconducting condensates.In multiband superconductors quite generically
.When
three length scales of the problem are the London penetration lengthand two characteristic length scales associated with normal modes of coupled density fluctuations. In that case the new coherence lengths
are attributed to "mixed" combinations of density fields.An example of two-component superconductivity is the two-band superconductor magnesium diboride
Magnesium diboride
Magnesium diboride is a simple ionic binary compound that has proven to be an inexpensive and useful superconducting material.Its superconductivity was announced in the journal Nature in March 2001. Its critical temperature of is the highest amongst conventional superconductors...
. There, one can distinguish two superconducting components associated with electrons belong to different bands.
A different example of two component systems is the projected superconducting states
of liquid metallic hydrogen
Metallic hydrogen
Metallic hydrogen is a state of hydrogen which results when it is sufficiently compressed and undergoes a phase transition; it is an example of degenerate matter. Solid metallic hydrogen is predicted to consist of a crystal lattice of hydrogen nuclei , with a spacing which is significantly smaller...
or deuterium where mixtures of superconducting electrons and superconducting protons or deuterons were theoretically predicted.
In 2009, experimental results have been reported
indicating that magnesium diboride
Magnesium diboride
Magnesium diboride is a simple ionic binary compound that has proven to be an inexpensive and useful superconducting material.Its superconductivity was announced in the journal Nature in March 2001. Its critical temperature of is the highest amongst conventional superconductors...
may fall into this new class of superconductivity. The term type-1.5 superconductor was coined for this state. Further experimental data backing this conclusion was reported in
. More recent theoretical works show that the type-1.5 may be more general phenomenon because it does not require a material with two truly superconducting bands, but can also happen as a result of even very small interband proximity effect
and is robust in the presence of various inter-band couplings such as interband Josephson coupling.
Non-technical explanation
SeeIn Type-I and Type-II superconductors charge flow patterns are dramatically different. Type I has two state-defining properties: Lack of electric resistance and the fact that it does not allow an external magnetic field to pass through it. When a magnetic field is applied to these materials, superconducting electrons produce a strong current on the surface which in turn produces a magnetic field in the opposite direction. Inside this type of superconductor, the external magnetic field and the field created by the surface flow of electrons add up to zero. That is, they cancel each other out.
In Type II superconducting materials where a complicated flow of superconducting electrons can happen deep in the interior. In Type II material, a magnetic field can penetrate, carried inside by vortices which form Abrikosov vortex lattice. It type-1.5 superconductor there are two superconducting components. There the external magnetic field can produce clusters of tightly packed vortex droplets because in such materials vortices should attract each other at large distances and repel at short length scales. Since the attraction originates in vortex core's overlaps in one of the superconducting components, this component will be depleted in the vortex cluster. Thus
a vortex cluster will represent two competing types of superflow. One component will form vortices bunched together while the second component will produce supercurrent flowing on the surface of vortex clusters in a way similar to how electrons flow on the exterior of Type I superconductors. These vortex clusters are separated by "voids," with no vortices, no currents and no magnetic field.
see description on
]
Animations of type-1.5 superconducting behavior
Movies from numerical simulations of the Semi-Meissner state where Meissner domainscoexist with clusters where vortex droplets form in one superconducting components and macroscopic normal domains in the other.
See also
- Type I superconductorType I superconductorSuperconductors cannot be penetrated by magnetic flux lines . This Meissner state breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs...
- Type-II superconductorType-II superconductorA Type-II superconductor is a superconductor characterized by the formation of vortex lattices in magnetic field. It has a continuous second order phase transition from the superconducting to the normal state within an increasing magnetic field....
- Conventional superconductorConventional superconductorConventional superconductors are materials that display superconductivity as described by BCS theory or its extensions.Critical temperatures of some simple metals:ElementTc Al1.20Hg4.15Mo0.92Nb9.26Pb7.19...
- covalent superconductorsCovalent superconductorsCovalent semiconductors are such solids as diamond, silicon, germanium, silicon carbide and silicon-germanium where atoms are linked by covalent bonds. Most of those materials, at least in their bulk form, are well studied and rarely hit the front pages of the top scientific journals in the last...
- List of superconductors
- High-temperature superconductivityHigh-temperature superconductivityHigh-temperature superconductors are materials that have a superconducting transition temperature above . From 1960 to 1980, 30 K was thought to be the highest theoretically possible Tc...
- Room temperature superconductorRoom temperature superconductorA room-temperature superconductor is a material yet to be discovered which would be capable of exhibiting superconducting properties at operating temperatures above 0° C . This is not strictly speaking "room temperature" A room-temperature superconductor is a material yet to be discovered...
- SuperconductivitySuperconductivitySuperconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
- Superconductor classificationSuperconductor classificationSuperconductors can be classified in accordance with several criteria that depend on our interest in their physical properties, on the understanding we have about them, on how expensive is cooling them or on the material they are made of....
- Technological applications of superconductivityTechnological applications of superconductivitySome of the technological applications of superconductivity include:* the production of sensitive magnetometers based on SQUIDs* fast digital circuits ,...
- Timeline of low-temperature technologyTimeline of low-temperature technologyThe following is a timeline of low-temperature technology and cryogenic technology .-16th century BCE – 17th century CE :...
- Unconventional superconductorUnconventional superconductorUnconventional superconductors are materials that display superconductivity which does not conform to either the conventional BCS theory or the Nikolay Bogolyubov's theory or its extensions....