**3. State-of-the-art superconductivity**

As for physical properties, attributing to high-temperature superconductors are concerned, these are purely based upon behavior of conventional and metallic superconductors. In this literature, properties owing to superconducting state are widely described in the sense of detailed properties of simple and metallic

**61**

**Figure 2.**

*Reproduced from Ref. [25].*

*High Temperature Superconductors*

*DOI: http://dx.doi.org/10.5772/intechopen.96419*

interior of superconductor [20, 29].

superconductors. It was observed that below critical temperature (Tc), electrical resistance decreases to zero for SCs. However, Tc (critical temperature) is an important parameter for superconductors that are still in question mark. More apparently for pure metals, it was evaluated that zero-resistance-state may have reached in the range of a few mK as shown in **Figure 2a**. Moreover, for complex cuprate high critical temperature superconducting materials, transition state corresponding to superconducting state, observed is not sharp as compared with metallic SCs having low values of Tc. Transition-width possessing single-phase-cuprate SCs are critically identified as 1 K. Results indicate that critical temperature slightly belongs to the criteria that were used to specify (Tc). Various criteria support as suggested in **Figure 2b**. Whereas at observed transition temperature, resistance-drop has typically been searched corresponding to numerous orders of magnitude [25, 52].

Besides, it may be in the form of principle and not still possible to prove experimentally; that ideal resistance corresponding to superconducting state may become zero. t Subsequently, it was proved that the most effective technique determining the peak value of the resistance, is evaluated in detecting decay-state owing to magnetic fields, produced by those currents that were induced during an SC loop. Peak resistivity values occurred ranging from 2 × 10−18 [25, 53] to 7 × 10−23 Ωcm [54] were reported for YBa2Cu3O7 that is identified as high (Tc) superconductor, and whereas 3.6 × 10−23 Ωcm value was found to be low (Tc) superconductors of type-I [25]. The aforementioned resistivity limits are considered to be several orders of magnitude indicating minute resistivity valuating 10 × 10−10 Ωcm (at 4.2 K), which was achievable at annealing state about pure metals. Therefore, it was strongly justified to make assure of zero-resistance, however, below (Tc) in all experimental work. While next extraordinary property belonging to superconducting state was diagnosed as perfect diamagnetism. More interestingly magnetic-behavior of superconductors may be understood through two variety of situations as shown in **Figure 3**. Firstly, the superconductor is made zero field-cooled below Tc. Secondly, superconductor is again cooled, however below Tc by applying magnetic field in this case. Both approaches are followed without incorporating magnetic flux in the

On the other hand, screening-currents induced through surface-layer of superconductor will produce magnetic flux but in opposite direction to the applied field. In this case, magnetic flux density becomes zero throughout the superconductor. Whereas outside the superconducting-sphere, magnetic field increases caused by

*(a) Plot of resistance as a function of temperature for mercury generated by Heike Kammerlingh Onnes. (b) Resistance-temperature plot for a multicore wire of Bi2Sr2CaCu2O8/Ag labeled with Tc referring to different definitions of transition temperature. The width of the transition* ∆*Tc = Tc(90%)-Tc(10%) is* ≈ *1.2 k* 

#### *High Temperature Superconductors DOI: http://dx.doi.org/10.5772/intechopen.96419*

*Transition Metal Compounds - Synthesis, Properties, and Application*

203 −70 High-pressure phase of hydrogen

92 −181 YBa2Cu3O7 (YBCO)

*Collection of various superconductors and common cooling agents.*

**in K in °C**

*T***c boiling point Material (HTS) Comments**

sulfide at 100 GPa

[32, 33] <sup>41</sup> <sup>−</sup><sup>232</sup> CeOFeAs

287 14 H2S + CH4 at 267 GPa First room temperature

250 −23 LaH10 at 170 GPa Metallic superconductor with one of the

138 −135 Hg12Tl3Ba30Ca30Cu45O127 High-temperature superconductors with

45 −228 SmFeAsO0.85F0.15 Low-temperature superconductors with

39 −234 MgB2 Metallic superconductor with relatively

30 −243 La2 − xBaxCuO4 First high-temperature superconductor

18 −255 Nb3Sn Metallic low-temperature

relevance [38–40] 9.2 <sup>−</sup>264.0 NbTi 4.15 −269.00 Hg Metallic low-temperature superconductors [41, 42] 1.09 <sup>−</sup>272.06 Ga

critical temperatures [25, 29–31] <sup>110</sup> <sup>−</sup><sup>163</sup> Bi2Sr2Ca2Cu3O10 (BSCCO)

superconductor [26]

highest known critical temperature [27]

Mechanism unclear, observable isotope effect [28]

Copper oxide with relatively high

relatively high critical temperatures

high critical temperature at atmospheric pressure [34, 35]

with copper oxide, discovered by Bednorz and Müller [36, 37]

superconductors with technical

depth, and that of specific heat as well as thermal conductivity. Some superconductors possessing high transition- temperature but at ambient pressure, were declared as cuprate of elements such as mercury and calcium at around temperature (133 K) [48, 49]. Among superconductors some are, showing higher transition- temperatures like lanthanum super-hydride at around 250 K, whereas these may often occur at high-pressures [27, 50]. Resultantly, source of high-temperature- superconductivity of conductors is out of range. However, it seems to be conventional superconductivity in the form of an electron–phonon mechanism as well as by antiferromagnetic correlation mechanism. Again instead of conventional, pure s-wave pairing symmetry which is identified as exotic pairing symmetry is considered to be involved. Subsequently (2014), evidence relevant to fractional particles was presented in favor of the occurrence of quasi-2d magnetic-materials. EPFL scientists discovered these materials [51] which supported "Anderson's theory" based on HT

As for physical properties, attributing to high-temperature superconductors are concerned, these are purely based upon behavior of conventional and metallic superconductors. In this literature, properties owing to superconducting state are widely described in the sense of detailed properties of simple and metallic

**60**

**Table 1.**

superconductivity [51].

**3. State-of-the-art superconductivity**

superconductors. It was observed that below critical temperature (Tc), electrical resistance decreases to zero for SCs. However, Tc (critical temperature) is an important parameter for superconductors that are still in question mark. More apparently for pure metals, it was evaluated that zero-resistance-state may have reached in the range of a few mK as shown in **Figure 2a**. Moreover, for complex cuprate high critical temperature superconducting materials, transition state corresponding to superconducting state, observed is not sharp as compared with metallic SCs having low values of Tc. Transition-width possessing single-phase-cuprate SCs are critically identified as 1 K. Results indicate that critical temperature slightly belongs to the criteria that were used to specify (Tc). Various criteria support as suggested in **Figure 2b**. Whereas at observed transition temperature, resistance-drop has typically been searched corresponding to numerous orders of magnitude [25, 52].

Besides, it may be in the form of principle and not still possible to prove experimentally; that ideal resistance corresponding to superconducting state may become zero. t Subsequently, it was proved that the most effective technique determining the peak value of the resistance, is evaluated in detecting decay-state owing to magnetic fields, produced by those currents that were induced during an SC loop. Peak resistivity values occurred ranging from 2 × 10−18 [25, 53] to 7 × 10−23 Ωcm [54] were reported for YBa2Cu3O7 that is identified as high (Tc) superconductor, and whereas 3.6 × 10−23 Ωcm value was found to be low (Tc) superconductors of type-I [25]. The aforementioned resistivity limits are considered to be several orders of magnitude indicating minute resistivity valuating 10 × 10−10 Ωcm (at 4.2 K), which was achievable at annealing state about pure metals. Therefore, it was strongly justified to make assure of zero-resistance, however, below (Tc) in all experimental work. While next extraordinary property belonging to superconducting state was diagnosed as perfect diamagnetism. More interestingly magnetic-behavior of superconductors may be understood through two variety of situations as shown in **Figure 3**. Firstly, the superconductor is made zero field-cooled below Tc. Secondly, superconductor is again cooled, however below Tc by applying magnetic field in this case. Both approaches are followed without incorporating magnetic flux in the interior of superconductor [20, 29].

On the other hand, screening-currents induced through surface-layer of superconductor will produce magnetic flux but in opposite direction to the applied field. In this case, magnetic flux density becomes zero throughout the superconductor. Whereas outside the superconducting-sphere, magnetic field increases caused by

#### **Figure 2.**

*(a) Plot of resistance as a function of temperature for mercury generated by Heike Kammerlingh Onnes. (b) Resistance-temperature plot for a multicore wire of Bi2Sr2CaCu2O8/Ag labeled with Tc referring to different definitions of transition temperature. The width of the transition* ∆*Tc = Tc(90%)-Tc(10%) is* ≈ *1.2 k Reproduced from Ref. [25].*

superposition of flux generated due to applied field as well as of screening currents. However, in both states, superconductor is observed to be un-magnetized whenever a magnetic field accidentally vanishes. Resultantly when superconductor is cooled without applying magnetic field, its behavior may be identified only in the form of screening effect but still caused by perfect-conductivity. While contrary to screening effect magnetic flux expulsion arising out from the Meissner effect has not still been explained (perfect conductivity) [55, 56]. Additionally, varied behaviors attributed to field-cooled perfect- conductor have also been illustrated in **Figure 3a**-**c**. Relative magnetic-permeability found by different repeated experiments was evaluated close to unity comparatively owing to non-ferromagnetic metals. Resultantly, magnetic flux that was observed within the metal is.

analogous to an external magnetic field. Since dB/dt is zero in this case, and therefore no screening currents arise eventually. Consequently, no magnetic flux is extracted within perfect conductor's interior region at low kelvin temperatures. When magnetic field i.e., dB/dt becomes non-zero, then magnetization has occurred relevant to perfect conductor. The superconductivity may be diminished by applying large amount of magnetic field. The B-field at which superconductivity of the material is lost is termed as Bc (critical field) under consideration [57, 58]. Temperature-dependent critical-magnetic-field is mathematically described by the well-known Eq. (1).

$$B\_{\epsilon} \left( T \right) = B\_{\epsilon} \mathbf{O} \left[ \mathbf{1} - \left( \frac{T}{T\_{\epsilon}} \right)^{2} \right] \tag{1}$$

**63**

**Figure 5.**

*High Temperature Superconductors*

field as well as temperature [25].

≈*10* − ≈ *80 mT. Reproduced from Ref. [25].*

**4. Cuprates**

**Figure 4.**

*DOI: http://dx.doi.org/10.5772/intechopen.96419*

confirms arising properties that are observed during superconducting state, and also proved independent order of the final conditions reached to applied-magnetic-

*Critical field as a function of temperature plots for selected metallic superconductors. The Bc0 values vary from* 

Layered material cuprates consisting of copper-oxide superconducting-layers (**Figure 5**), which are separated by spacer-layers is an interesting field of research also. The crystal structure of cuprates is closely related to the structure of twodimensional materials. The superconductivity of these materials is evaluated by electrons randomly moving within intercalated layers of copper oxide (CuO2) that are weakly coupled in nature. However, other layers containing metal and non-metal ions (lanthanum, strontium, and barium atoms) perform an active role to stabilize the structure through doping process of electrons/holes upon copper oxide layers.

*Schematic geometry of a cuprate HTS superconductor. Reproduced from Ref. [59].*

Where Tc and Bc0 are critical temperatures as well as critical field at T = 0, respectively. Bc is considered as temperature-dependent function as depicted in **Figure 4** corresponding to different metallic SCs. The Bc(T) graphs differentiate the normal and superconducting state of Scs. Furthermore, the Meissner effect

#### **Figure 3.**

*(a) The magnetic flux is excluded from the interior of a superconductor, (b) in the presence and absence of field-cooling, (c) In contrast, a field-cooled perfect conductor shows presence of interior magnetic flux. Reproduced from Ref. [25].*

#### **Figure 4.**

*Transition Metal Compounds - Synthesis, Properties, and Application*

magnetic flux that was observed within the metal is.

well-known Eq. (1).

superposition of flux generated due to applied field as well as of screening currents. However, in both states, superconductor is observed to be un-magnetized whenever a magnetic field accidentally vanishes. Resultantly when superconductor is cooled without applying magnetic field, its behavior may be identified only in the form of screening effect but still caused by perfect-conductivity. While contrary to screening effect magnetic flux expulsion arising out from the Meissner effect has not still been explained (perfect conductivity) [55, 56]. Additionally, varied behaviors attributed to field-cooled perfect- conductor have also been illustrated in **Figure 3a**-**c**. Relative magnetic-permeability found by different repeated experiments was evaluated close to unity comparatively owing to non-ferromagnetic metals. Resultantly,

analogous to an external magnetic field. Since dB/dt is zero in this case, and therefore no screening currents arise eventually. Consequently, no magnetic flux is extracted within perfect conductor's interior region at low kelvin temperatures. When magnetic field i.e., dB/dt becomes non-zero, then magnetization has occurred relevant to perfect conductor. The superconductivity may be diminished by applying large amount of magnetic field. The B-field at which superconductivity of the material is lost is termed as Bc (critical field) under consideration [57, 58]. Temperature-dependent critical-magnetic-field is mathematically described by the

2

(1)

*c*

*T* = −

( )

*c c*0 1

*<sup>T</sup> BT B*

Where Tc and Bc0 are critical temperatures as well as critical field at T = 0, respectively. Bc is considered as temperature-dependent function as depicted in **Figure 4** corresponding to different metallic SCs. The Bc(T) graphs differentiate the normal and superconducting state of Scs. Furthermore, the Meissner effect

*(a) The magnetic flux is excluded from the interior of a superconductor, (b) in the presence and absence of field-cooling, (c) In contrast, a field-cooled perfect conductor shows presence of interior magnetic flux.* 

**62**

**Figure 3.**

*Reproduced from Ref. [25].*

*Critical field as a function of temperature plots for selected metallic superconductors. The Bc0 values vary from*  ≈*10* − ≈ *80 mT. Reproduced from Ref. [25].*

confirms arising properties that are observed during superconducting state, and also proved independent order of the final conditions reached to applied-magneticfield as well as temperature [25].

### **4. Cuprates**

Layered material cuprates consisting of copper-oxide superconducting-layers (**Figure 5**), which are separated by spacer-layers is an interesting field of research also. The crystal structure of cuprates is closely related to the structure of twodimensional materials. The superconductivity of these materials is evaluated by electrons randomly moving within intercalated layers of copper oxide (CuO2) that are weakly coupled in nature. However, other layers containing metal and non-metal ions (lanthanum, strontium, and barium atoms) perform an active role to stabilize the structure through doping process of electrons/holes upon copper oxide layers.

On the other hand, the undoped materials such as mott insulators are identified as of long-range order of magnitudes of antiferromagnetic atoms at relatively low temperatures. However, single-band-models describe electronic properties other than unique behavior [47, 60–62]. The hole-doped HTS presenting a region of antiferromagnetic behavior ordering at low *p* and superconductivity at a higher doping ratio [63].

Furthermore, cuprates superconductors possess unique perovskite structures. Copper oxide planes indicate checkerboard lattices in square shape oxide (O2− ions) as well as cupric (Cu2+ ions) residing at centers of squares. Unit cells are rotated through 45° angles from these squares. Chemical formulae corresponding to each superconductor possess fractional numbers to represent required doping necessary for sufficient superconductivity. Cuprate superconductors have been classified into several families with respect to containing elements as well as the number of layers of copper-oxide attributed to every superconducting block. As an example, YBCO may be referred to as Y123 and BSCCO as Bi2201/Bi2212/Bi2223 alternatively which depends on contribution of each layer to every superconducting block (n). Optimum Tc was evaluated against optimum doping of *p* = 0.16 whereas optimal layers were n = 3 corresponding to each superconducting block [62, 64, 65].

Superconductivity related to cuprates is still a continuously researchable subject and considerable debate obviously for further research. Considerable aspects common to superconducting materials are to be diagnosed. Common characteristics of antiferromagnetic materials indicate low-temperature state containing undoped material whereas superconducting state has emerged upon doped material. Primarily Cu2+ ions (*d*<sup>x</sup> 2 -y 2 orbital-state) diagnosed that electron–electron interactions were significantly dominant as compared with electron–phonon interactions in case of cuprate superconducting materials, thereby indicating unconventional superconductivity. Recently, Fermi surface work suggested occurrence of nesting caused by four points appearing in Brillouin zone of antiferromagnetic materials, and at those points, spin waves may lie due to which superconducting energy-gap may appear larger enough at those points. Minute isotope-effect was also observed for numerous cuprates relatively conventional-superconductor described deeply by BCS theory [25, 62, 66]. The cuprate process is based on the spectral distance and/or sharp peak appearance or absence. The above suggests the presence of well-defined quasi-particle excitations, e.g. as in the overdoped region of the more conventional metallic state (**Figure 6**).

#### **Figure 6.**

*Region of antiferromagnetic (AF) ordering at low p and superconductivity (SC) at higher doping observed in the universal phase diagram for hole-doped HTS superconductors. Reproduced from Ref. [63].*

**65**

**Figure 7.**

*High Temperature Superconductors*

cuprate superconductors are:

[68–70].

*DOI: http://dx.doi.org/10.5772/intechopen.96419*

Electronic structure, indicating not isotropic nature of superconducting cuprates is illustrated in **Figure 1** that is highly anisotropic such as of YBCO/BSCCO. Hence, HTS fermi-surface is observed near to multi-planes of CuO2 (doped) in the form of multi-layer structured cuprates which may appear over 2D momentum space corresponding to CuO2 lattice space. Moreover, It might be extracted from measurements of band structure as well as from ARPES (angle-resolved photoemission spectroscopy) analysis. **Figure 7** presents BSCCO Fermi surface, which is evaluated through ARPES. Consequently, results were obtained corresponding to in-plane anisotropic nature correspond to electronic properties relevant to HTS. Contrast properties of hole-doped cuprates as compared with electron-doped

• Pseudogap phase existence upto optimal doping is observed.

strongly indicate material physics, which is logically 2d.

during spin excitations of cuprates.

• Different behaviors attributing to Uemura plot transition-temperature towards superfluid-density. London penetration depth inverse square effect appears proportional to be an as critical temperature that is for cuprate superconductors during doping process; however, proportionality constant is different for hole-doped as well as electron-doped cuprate superconductors. Linear trends

• Neutron diffraction (inelastic) is used to evaluate universal hourglass quality

• "Nernst effect" is evident with superconductivity as well as pseudogap phases

*The phase diagram of cuprate based on either the presence or absence of sharp peak and/or spectral gap. The latter represents the presence of well-defined quasi-particulate excitations. Reproduced from Ref. [67].*

#### *High Temperature Superconductors DOI: http://dx.doi.org/10.5772/intechopen.96419*

*Transition Metal Compounds - Synthesis, Properties, and Application*

On the other hand, the undoped materials such as mott insulators are identified as of long-range order of magnitudes of antiferromagnetic atoms at relatively low temperatures. However, single-band-models describe electronic properties other than unique behavior [47, 60–62]. The hole-doped HTS presenting a region of antiferromagnetic behavior ordering at low *p* and superconductivity at a higher doping ratio [63].

Furthermore, cuprates superconductors possess unique perovskite structures. Copper oxide planes indicate checkerboard lattices in square shape oxide (O2− ions) as well as cupric (Cu2+ ions) residing at centers of squares. Unit cells are rotated through 45° angles from these squares. Chemical formulae corresponding to each superconductor possess fractional numbers to represent required doping necessary for sufficient superconductivity. Cuprate superconductors have been classified into several families with respect to containing elements as well as the number of layers of copper-oxide attributed to every superconducting block. As an example, YBCO may be referred to as Y123 and BSCCO as Bi2201/Bi2212/Bi2223 alternatively which depends on contribution of each layer to every superconducting block (n). Optimum Tc was evaluated against optimum doping of *p* = 0.16 whereas optimal layers were n = 3 corresponding to each superconducting block [62, 64, 65].

Superconductivity related to cuprates is still a continuously researchable subject and considerable debate obviously for further research. Considerable aspects common to superconducting materials are to be diagnosed. Common characteristics of antiferromagnetic materials indicate low-temperature state containing undoped

tions were significantly dominant as compared with electron–phonon interactions in case of cuprate superconducting materials, thereby indicating unconventional superconductivity. Recently, Fermi surface work suggested occurrence of nesting caused by four points appearing in Brillouin zone of antiferromagnetic materials, and at those points, spin waves may lie due to which superconducting energy-gap may appear larger enough at those points. Minute isotope-effect was also observed for numerous cuprates relatively conventional-superconductor described deeply by BCS theory [25, 62, 66]. The cuprate process is based on the spectral distance and/or sharp peak appearance or absence. The above suggests the presence of well-defined quasi-particle excitations, e.g. as in the overdoped region of the more

*Region of antiferromagnetic (AF) ordering at low p and superconductivity (SC) at higher doping observed in* 

*the universal phase diagram for hole-doped HTS superconductors. Reproduced from Ref. [63].*

orbital-state) diagnosed that electron–electron interac-

material whereas superconducting state has emerged upon doped material.

Primarily Cu2+ ions (*d*<sup>x</sup>

2 -y 2

conventional metallic state (**Figure 6**).

**64**

**Figure 6.**

Electronic structure, indicating not isotropic nature of superconducting cuprates is illustrated in **Figure 1** that is highly anisotropic such as of YBCO/BSCCO. Hence, HTS fermi-surface is observed near to multi-planes of CuO2 (doped) in the form of multi-layer structured cuprates which may appear over 2D momentum space corresponding to CuO2 lattice space. Moreover, It might be extracted from measurements of band structure as well as from ARPES (angle-resolved photoemission spectroscopy) analysis. **Figure 7** presents BSCCO Fermi surface, which is evaluated through ARPES. Consequently, results were obtained corresponding to in-plane anisotropic nature correspond to electronic properties relevant to HTS.

Contrast properties of hole-doped cuprates as compared with electron-doped cuprate superconductors are:


#### **Figure 7.**

*The phase diagram of cuprate based on either the presence or absence of sharp peak and/or spectral gap. The latter represents the presence of well-defined quasi-particulate excitations. Reproduced from Ref. [67].*
