**2. Milestone of high-temperature superconductivity**

Kamerlingh Onnes was one of researcher who introduced superconductivity in metal solid (1911). Researchers always struggled to make observations towards superconductivity at high temperatures [10, 19] for achieving goals of evaluating normal room temperature superconductors [20, 21]. Besides, superconductivity has been detected in various metallic compounds such as Nb containing compounds, for example (Nb3Ge, NbTi, and Nb3Sn) at much higher- temperatures as compared with elemental-metals, exceeding −253.2 °C (late 1970s). Moreover, in 1986, IBM research lab (Zurich) provided an opportunity to Bednorz and Müller who were working on superconductivity research route for generating a new class of ceramics (maybe cuprates as well as copper oxides). Bednorz discovered a zero resistance copper oxide at 35.1 K = −238 °C [22]. However, collected results were soon supported by numerous thoughts, notably Paul Chu and Shoji Tanaka at Houston and Tokyo universities one after others [23, 24], all the story illustrated in **Figure 1** and **Table 1**. Very shortly after, Anderson worked at Princeton University and presented a new theoretical concept relating to these materials. The theoretical idea was based upon RVBT (resonating valence-bond theory) [43] however still, full exploring relevant to these materials is considered open-ended up-till now.

Above mentioned superconductors may possess identical d-wave pair. The very first suggestion in favor of high-temperature cuprate superconductors d-wave pair symmetry was offered by Scalettar, Scalapino, and Bickers [44], which was associated with theories presented in 1988 by famous researchers known as Hirschfeld, Doniach, Inui, and Ruckenstein [45], they used spin fluctuation theory. Additionally, Rice, Gros, Zhang, and Poilblan [46], and Kotliar, as well as Liu, identified pairing concept representing usual consequence based on RVBT [47]. On the other hand, d-wave shape attributing cuprate superconductors was observed by many experiments. Further, the involvement of d-wave nodes was observed directly during excitation-spectrum by employing Angle-Resolved Photoemission-Spectroscopy. Half-integer flux observation was indicated through tunneling experiments whereas indirect temperature-dependence related to penetration

#### **Figure 1.**

*(a) Maximum known Tc of molecular (TMTSF and BEDTF-TTF), iron-based, metallic, and oxide superconductors. Metallic superconductors' Tc increased from 4.2 K (Hg) to 23.2 K (Nb3Ge) from 1911 and 1974. However, after unexpected discovery of superconductivity in MgB2 in 2001, maximum Tc of 39 K was achieved. In 1986, highest Tc of oxides exceeded the boiling point of liquid nitrogen (77 K), after the discovery of high-Tc superconductivity in (La, Ba)2CuO4. (b) The first molecular superconductor was discovered in 1980 where high Tc of 40 K was discovered in Cs3C60 fullerene. From 2006 to 2013, the maximum known Tc of iron-based superconductors gradually increased from around 4 K for LaOFeP to 58 K for SmO0.74F0.26FeAs. Reproduced from Ref. [25].*


#### **Table 1.**

*Collection of various superconductors and common cooling agents.*

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 superconductivity [51].
