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49-409: Bismuth strontium calcium copper oxide ( BSCCO , pronounced bisko ), is a type of cuprate superconductor having the generalized chemical formula Bi 2 Sr 2 Ca n −1 Cu n O 2 n +4+ x , with n  = 2 being the most commonly studied compound (though n  = 1 and n  = 3 have also received significant attention). Discovered as a general class in 1988, BSCCO

98-666: A 4-vector . Charge carriers which are free to move constitute a free current density, which are given by expressions such as those in this section. Electric current is a coarse, average quantity that tells what is happening in an entire wire. At position r at time t , the distribution of charge flowing is described by the current density: j ( r , t ) = ρ ( r , t ) v d ( r , t ) {\displaystyle \mathbf {j} (\mathbf {r} ,t)=\rho (\mathbf {r} ,t)\;\mathbf {v} _{\text{d}}(\mathbf {r} ,t)} where A common approximation to

147-453: A superlattice of superconducting CuO 2 layers separated by spacer layers, where the misfit strain between different layers and dopants in the spacers induce a complex heterogeneity that in the superstripes scenario is intrinsic for high-temperature superconductivity. Superconductivity in the cuprates is considered unconventional and is not explained by BCS theory . Possible pairing mechanisms for cuprate superconductivity continue to be

196-406: A correlation between a cuprate's critical temperature and the size of the charge transfer gap in that cuprate, providing support for the superexchange hypothesis. A 2022 study found that the varying density of actual Cooper pairs in a bismuth strontium calcium copper oxide superconductor matched with numerical predictions based on superexchange. But so far there is no consensus on the mechanism, and

245-504: A current of 200 A at 77 K, giving a critical current density in the Bi-2223 filaments of 5 kA/mm. This rises markedly with decreasing temperature so that many applications are implemented at 30–35 K, even though T c is 108 K. Electrical power transmission : Electromagnets and their current leads : BSCCO as a new class of superconductor was discovered around 1988 by Hiroshi Maeda and colleagues at

294-419: A family of high-temperature superconducting materials made of layers of copper oxides (CuO 2 ) alternating with layers of other metal oxides, which act as charge reservoirs. At ambient pressure, cuprate superconductors are the highest temperature superconductors known. However, the mechanism by which superconductivity occurs is still not understood . The first cuprate superconductor was found in 1986 in

343-604: A maximum of about 123 K due to optimization of the two outer planes. Following an extended decline, T c then rises again towards 140 K due to optimization of the inner plane. A key challenge therefore is to determine how to optimize all copper-oxygen layers simultaneously. BSCCO is a Type-II superconductor . The upper critical field H c2 in Bi-2212 polycrystalline samples at 4.2 K has been measured as 200 ± 25 T (cf 168 ± 26 T for YBCO polycrystalline samples). In practice, HTS are limited by

392-445: A year after their discovery. From 1986, many cuprate superconductors were identified, and can be put into three groups on a phase diagram critical temperature vs. oxygen hole content and copper hole content: Cuprates are layered materials, consisting of superconducting planes of copper oxide , separated by layers containing ions such as lanthanum , barium , strontium , which act as a charge reservoir, doping electrons or holes into

441-438: Is a current density corresponding to the net movement of electric dipole moments per unit volume, i.e. the polarization P : j P = ∂ P ∂ t {\displaystyle \mathbf {j} _{\mathrm {P} }={\frac {\partial \mathbf {P} }{\partial t}}} Similarly with magnetic materials , circulations of the magnetic dipole moments per unit volume, i.e.

490-612: Is a small surface centered at a given point M and orthogonal to the motion of the charges at M . If I A (SI unit: A ) is the electric current flowing through A , then electric current density j at M is given by the limit : j = lim A → 0 I A A = ∂ I ∂ A | A = 0 , {\displaystyle j=\lim _{A\to 0}{\frac {I_{A}}{A}}=\left.{\frac {\partial I}{\partial A}}\right|_{A=0},} with surface A remaining centered at M and orthogonal to

539-482: Is an important term in Ampere's circuital law , one of Maxwell's equations, since absence of this term would not predict electromagnetic waves to propagate, or the time evolution of electric fields in general. Since charge is conserved, current density must satisfy a continuity equation . Here is a derivation from first principles. The net flow out of some volume V (which can have an arbitrary shape but fixed for

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588-431: Is now a complex function . In many materials, for example, in crystalline materials, the conductivity is a tensor , and the current is not necessarily in the same direction as the applied field. Aside from the material properties themselves, the application of magnetic fields can alter conductive behaviour. Currents arise in materials when there is a non-uniform distribution of charge. In dielectric materials, there

637-527: Is referred to as optimal doping. Samples with lower doping (and hence lower T c ) are generally referred to as underdoped, while those with excess doping (also lower T c ) are overdoped. By changing the oxygen content, T c can thus be altered at will. By many measures, overdoped HTS are strong superconductors, even if their T c is less than optimal, but underdoped HTS become extremely weak. The application of external pressure generally raises T c in underdoped samples to values that well exceed

686-549: Is simply the sum of the free and bound currents: j = j f + j b {\displaystyle \mathbf {j} =\mathbf {j} _{\mathrm {f} }+\mathbf {j} _{\mathrm {b} }} There is also a displacement current corresponding to the time-varying electric displacement field D : j D = ∂ D ∂ t {\displaystyle \mathbf {j} _{\mathrm {D} }={\frac {\partial \mathbf {D} }{\partial t}}} which

735-403: Is the dot product of the unit vectors. That is, the component of current density passing through the surface (i.e. normal to it) is j cos θ , while the component of current density passing tangential to the area is j sin θ , but there is no current density actually passing through the area in the tangential direction. The only component of current density passing normal to the area

784-540: Is the cosine component. Current density is important to the design of electrical and electronic systems. Circuit performance depends strongly upon the designed current level, and the current density then is determined by the dimensions of the conducting elements. For example, as integrated circuits are reduced in size, despite the lower current demanded by smaller devices , there is a trend toward higher current densities to achieve higher device numbers in ever smaller chip areas. See Moore's law . At high frequencies,

833-404: Is the integral of the flux of j across S between t 1 and t 2 . The area required to calculate the flux is real or imaginary, flat or curved, either as a cross-sectional area or a surface. For example, for charge carriers passing through an electrical conductor , the area is the cross-section of the conductor, at the section considered. The vector area is a combination of

882-503: Is used to probe the physics underlying the nature of solids, including not only metals, but also semiconductors and insulators. An elaborate theoretical formalism has developed to explain many fundamental observations. The current density is an important parameter in Ampère's circuital law (one of Maxwell's equations ), which relates current density to magnetic field . In special relativity theory, charge and current are combined into

931-419: Is very difficult to synthesize. BSCCO was the first HTS material to be used for making practical superconducting wires. All HTS have an extremely short coherence length , of the order of 1.6 nm. This means that the grains in a polycrystalline wire must be in extremely good contact – they must be atomically smooth. Further, because the superconductivity resides substantially only in the copper-oxygen planes,

980-413: The insulating material failing, or the desired electrical properties changing. At high current densities the material forming the interconnections actually moves, a phenomenon called electromigration . In superconductors excessive current density may generate a strong enough magnetic field to cause spontaneous loss of the superconductive property. The analysis and observation of current density also

1029-445: The irreversibility field H *, above which magnetic vortices melt or decouple. Even though BSCCO has a higher upper critical field than YBCO it has a much lower H * (typically smaller by a factor of 100) thus limiting its use for making high-field magnets. It is for this reason that conductors of YBCO are preferred to BSCCO, though they are much more difficult to fabricate. Cuprate superconductor Cuprate superconductors are

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1078-633: The magnetization M , lead to magnetization currents : j M = ∇ × M {\displaystyle \mathbf {j} _{\mathrm {M} }=\nabla \times \mathbf {M} } Together, these terms add up to form the bound current density in the material (resultant current due to movements of electric and magnetic dipole moments per unit volume): j b = j P + j M {\displaystyle \mathbf {j} _{\mathrm {b} }=\mathbf {j} _{\mathrm {P} }+\mathbf {j} _{\mathrm {M} }} The total current

1127-540: The non-stoichiometric cuprate lanthanum barium copper oxide by IBM researchers Georg Bednorz and Karl Alex Müller . The critical temperature for this material was 35K, well above the previous record of 23 K. The discovery led to a sharp increase in research on the cuprates, resulting in thousands of publications between 1986 and 2001. Bednorz and Müller were awarded the Nobel Prize in Physics in 1987, only

1176-469: The CuO 2 sheets, resulting in a large anisotropy in normal conducting and superconducting properties, with a much higher conductivity parallel to the CuO 2 plane than in the perpendicular direction. Critical superconducting temperatures depend on the chemical compositions, cations substitutions and oxygen content. Chemical formulae of superconducting materials generally contain fractional numbers to describe

1225-722: The National Research Institute for Metals in Japan, though at the time they were unable to determine its precise composition and structure. Almost immediately several groups, and most notably Subramanian et al. at Dupont and Cava et al. at AT&T Bell Labs, identified Bi-2212. The n = 3 member proved quite elusive and was not identified until a month or so later by Tallon et al. in a government research lab in New Zealand. There have been only minor improvements to these materials since. A key early development

1274-863: The SI units of newtons per coulomb (N⋅C ) or, equivalently, volts per metre (V⋅m ). A more fundamental approach to calculation of current density is based upon: j ( r , t ) = ∫ − ∞ t [ ∫ V σ ( r − r ′ , t − t ′ ) E ( r ′ , t ′ ) d 3 r ′ ] d t ′ {\displaystyle \mathbf {j} (\mathbf {r} ,t)=\int _{-\infty }^{t}\left[\int _{V}\sigma (\mathbf {r} -\mathbf {r} ',t-t')\;\mathbf {E} (\mathbf {r} ',t')\;{\text{d}}^{3}\mathbf {r} '\,\right]{\text{d}}t'} indicating

1323-744: The USA and Sumitomo in Japan, though AMSC has now abandoned BSCCO wire in favour of 2G wire based on YBCO . Typically, precursor powders are packed into a silver tube, which is then extruded down in diameter. These are then repacked as multiple tubes in a silver tube and again extruded down in diameter, then drawn down further in size and rolled into a flat tape. The last step ensures grain alignment. The tapes are then reacted at high temperature to form dense, crystallographically aligned Bi-2223 multifilamentary conducting tape suitable for winding cables or coils for transformers, magnets, motors and generators. Typical tapes of 4 mm width and 0.2 mm thickness support

1372-423: The antiferromagnetic Brillouin zone where spin waves exist and that the superconducting energy gap is larger at these points. The weak isotope effects observed for most cuprates contrast with conventional superconductors that are well described by BCS theory. In 1987, Philip Anderson proposed that superexchange could act as a high-temperature superconductor pairing mechanism. In 2016, Chinese physicists found

1421-504: The charge contained in the volume formed by dA and v d t {\displaystyle v\,dt} will flow through dA . This charge is equal to d q = ρ v d t d A , {\displaystyle dq=\rho \,v\,dt\,dA,} where ρ is the charge density at M . The electric current is d I = d q / d t = ρ v d A {\displaystyle dI=dq/dt=\rho vdA} , it follows that

1470-429: The conducting region in a wire becomes confined near its surface which increases the current density in this region. This is known as the skin effect . High current densities have undesirable consequences. Most electrical conductors have a finite, positive resistance , making them dissipate power in the form of heat. The current density must be kept sufficiently low to prevent the conductor from melting or burning up,

1519-447: The copper-oxide planes. Thus the structure is described as a superlattice of superconducting CuO 2 layers separated by spacer layers, resulting in a structure often closely related to the perovskite structure. Superconductivity takes place within the copper-oxide (CuO 2 ) sheets, with only weak coupling between adjacent CuO 2 planes, making the properties close to that of a two-dimensional material. Electrical currents flow within

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1568-437: The current density assumes the current simply is proportional to the electric field, as expressed by: j = σ E {\displaystyle \mathbf {j} =\sigma \mathbf {E} } where E is the electric field and σ is the electrical conductivity . Conductivity σ is the reciprocal ( inverse ) of electrical resistivity and has the SI units of siemens per metre (S⋅m ), and E has

1617-444: The current density vector is the vector normal d A {\displaystyle dA} (i.e. parallel to v ) and of magnitude d I / d A = ρ v {\displaystyle dI/dA=\rho v} j = ρ v . {\displaystyle \mathbf {j} =\rho \mathbf {v} .} The surface integral of j over a surface S , followed by an integral over

1666-557: The definition given above: d A = d A n ^ . {\displaystyle d\mathbf {A} =dA\mathbf {\hat {n}} .} If the current density j passes through the area at an angle θ to the area normal n ^ , {\displaystyle \mathbf {\hat {n}} ,} then j ⋅ n ^ = j cos ⁡ θ {\displaystyle \mathbf {j} \cdot \mathbf {\hat {n}} =j\cos \theta } where ⋅

1715-789: The doping required for superconductivity. There are several families of cuprate superconductors which can be categorized by the elements they contain and the number of adjacent copper-oxide layers in each superconducting block. For example, YBCO and BSCCO can alternatively be referred to as Y123 and Bi2201/Bi2212/Bi2223 depending on the number of layers in each superconducting block ( n ). The superconducting transition temperature has been found to peak at an optimal doping value ( p =0.16) and an optimal number of layers in each superconducting block, typically n =3. The undoped "parent" or "mother" compounds are Mott insulators with long-range antiferromagnetic order at sufficiently low temperatures. Single band models are generally considered to be enough to describe

1764-424: The electronic properties. Cuprate superconductors usually feature copper oxides in both the oxidation states 3+ and 2+. For example, YBa 2 Cu 3 O 7 is described as Y (Ba ) 2 (Cu )(Cu ) 2 (O ) 7 . The copper 2+ and 3+ ions tend to arrange themselves in a checkerboard pattern, a phenomenon known as charge ordering . All superconducting cuprates are layered materials having a complex structure described as

1813-587: The entire past history up to the present time. The above conductivity and its associated current density reflect the fundamental mechanisms underlying charge transport in the medium, both in time and over distance. A Fourier transform in space and time then results in: j ( k , ω ) = σ ( k , ω ) E ( k , ω ) {\displaystyle \mathbf {j} (\mathbf {k} ,\omega )=\sigma (\mathbf {k} ,\omega )\;\mathbf {E} (\mathbf {k} ,\omega )} where σ ( k , ω )

1862-534: The general formula Tl 2 Ba 2 Ca n −1 Cu n O 2 n +4+ x , and a mercury family HBCCO of formula Hg Ba 2 Ca n −1 Cu n O 2 n +2+ x . There are a number of other variants of these superconducting families. In general, their critical temperature at which they become superconducting rises for the first few members and then falls. Thus Bi-2201 has T c ≈ 33 K, Bi-2212 has T c ≈ 96 K, Bi-2223 has T c ≈ 108 K, and Bi-2234 has T c ≈ 104 K. This last member

1911-699: The grains must be crystallographically aligned. BSCCO is therefore a good candidate because its grains can be aligned either by melt processing or by mechanical deformation. The double bismuth-oxide layer is only weakly bonded by van der Waals forces. So like graphite or mica , deformation causes slip on these BiO planes, and grains tend to deform into aligned plates. Further, because BSCCO has n = 1, 2 and 3 members, these naturally tend to accommodate low angle grain boundaries, so that indeed they remain atomically smooth. Thus, first-generation HTS wires (referred to as 1G) have been manufactured for many years now by companies such as American Superconductor Corporation (AMSC) in

1960-424: The lag in response by the time dependence of σ , and the non-local nature of response to the field by the spatial dependence of σ , both calculated in principle from an underlying microscopic analysis, for example, in the case of small enough fields, the linear response function for the conductive behaviour in the material. See, for example, Giuliani & Vignale (2005) or Rammer (2007). The integral extends over

2009-403: The magnitude of the area through which the charge carriers pass, A , and a unit vector normal to the area, n ^ . {\displaystyle \mathbf {\hat {n}} .} The relation is A = A n ^ . {\displaystyle \mathbf {A} =A\mathbf {\hat {n}} .} The differential vector area similarly follows from

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2058-406: The maximum at ambient pressure. This is not fully understood, though a secondary effect is that pressure increases the doping. Bi-2223 is complicated in that it has three distinct copper-oxygen planes. The two outer copper-oxygen layers are typically close to optimal doping, while the remaining inner layer is markedly underdoped. Thus the application of pressure in Bi-2223 results in T c rising to

2107-418: The motion of the charges during the limit process. The current density vector j is the vector whose magnitude is the electric current density, and whose direction is the same as the motion of the positive charges at M . At a given time t , if v is the velocity of the charges at M , and dA is an infinitesimal surface centred at M and orthogonal to v , then during an amount of time dt , only

2156-504: The search for an explanation continues. BSCCO superconductors already have large-scale applications. For example, tens of kilometers of BSCCO-2223 at 77 K superconducting wires are being used in the current leads of the Large Hadron Collider at CERN (but the main field coils are using metallic lower temperature superconductors, mainly based on niobium–tin ). Current density Assume that A (SI unit: m )

2205-413: The sequence of the numbers of the metallic ions. Thus Bi-2201 is the n = 1 compound ( Bi 2 Sr 2 Cu O 6+ x ), Bi-2212 is the n = 2 compound ( Bi 2 Sr 2 Ca Cu 2 O 8+ x ), and Bi-2223 is the n = 3 compound ( Bi 2 Sr 2 Ca 2 Cu 3 O 10+ x ). The BSCCO family is analogous to a thallium family of high-temperature superconductors referred to as TBCCO and having

2254-524: The subject of considerable debate and further research. Similarities between the low-temperature antiferromagnetic state in undoped materials and the low-temperature superconducting state that emerges upon doping, primarily the d x −y orbital state of the Cu ions, suggest that electron-phonon coupling is less relevant in cuprates. Recent work on the Fermi surface has shown that nesting occurs at four points in

2303-464: The time duration t 1 to t 2 , gives the total amount of charge flowing through the surface in that time ( t 2 − t 1 ): q = ∫ t 1 t 2 ∬ S j ⋅ n ^ d A d t . {\displaystyle q=\int _{t_{1}}^{t_{2}}\iint _{S}\mathbf {j} \cdot \mathbf {\hat {n}} \,dA\,dt.} More concisely, this

2352-449: Was the first high-temperature superconductor which did not contain a rare-earth element . It is a cuprate superconductor , an important category of high-temperature superconductors sharing a two-dimensional layered ( perovskite ) structure (see figure at right) with superconductivity taking place in a copper-oxide plane. BSCCO and YBCO are the most studied cuprate superconductors. Specific types of BSCCO are usually referred to using

2401-474: Was to replace about 15% of the Bi by Pb, which greatly accelerated the formation and quality of Bi-2223. BSCCO needs to be hole-doped by an excess of oxygen atoms ( x in the formula) in order to superconduct. As in all high-temperature superconductors (HTS) T c is sensitive to the exact doping level: the maximal T c for Bi-2212 (as for most HTS) is achieved with an excess of about 0.16 holes per Cu atom. This

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