Superconductivity in topological materials has drawn significant interest from the scientific community as these materials provide a hint of the existence of Majorana fermions conceived from the quantized thermal conductivity, a zero-biased conduction peak and the anomalous Josephson effect. In this review, we make a systematic study of recent advances in the field of topological superconductivity. The article comprises of both bulk systems as well as heterostructures. A brief description of Majorana fermions and their relationship with topological superconductors and heterostructures is also carried out. This review also consists of details of key experimental techniques to characterize candidates for topological superconductivity. Moreover, we summarize the potential material candidate that may demonstrate topological superconductivity. We also consider some intrinsic odd-parity superconductors, non-centrosymmetric, centrosymmetric superconductors, doped topological insulators, doped topological crystalline insulators and some other materials that are expected to show superconductivity along with topological non-trivial states in bulk form. The effects of pressure, emergence of superconductivity in topological materials and muon spin rotation studies are also summarized in this article.

The report of the synthesis of modified lead apatite (LK-99), with evidence of superconductivity at more than boiling water temperature, has steered the scientific community. There have been several failures to reproduce superconductivity in LK-99, despite partial successes. Here, we have continued our efforts to synthesize phase-pure LK-99 with improved precursors. The synthesis process being followed is the same as suggested by Sukbae Lee et al. The phase purity of each precursor is evidenced by powder X-ray diffraction (PXRD) and is well-fitted by Rietveld refinement. The PXRD confirms the synthesis of phase-pure polycrystalline LK-99 with a lead apatite structure. The sample is highly resistive, showing insulator-like behavior in resistivity measurement in the temperature range from 215 to 325 K, which confirms the absence of superconductivity in synthesized LK-99 at room temperature. The magnetization measurements of LK-99 on the SQUID magnetometer resemble the behavior of a resistive diamagnetic material at 280 K. Moreover, we have also performed first principle calculations to investigate the electronic band structure of LK-99 in the vicinity of the Fermi level. Our study verifies that the copper (Cu)-doped lead apatite (LK-99) exhibits band crossing at the Fermi level, indicating the generation of strong correlation in the presently studied system. Our experimental results do not approve the appearance of superconductivity in LK-99, i.e., Pb₉CuP₆O₂₅.

The quest for room temperature superconductors has been teasing scientists and physicists, since its inception in 1911 itself. Several assertions have already been made about room temperature superconductivity, but have never been verified or reproduced across the labs. The cuprates were the earliest high transition temperature (T _c) superconductors, and it seems that copper has done the magic once again. In July 2023, a Korean group synthesized a lead apatite based compound LK-99, showing a T _c of above 400 K (Lee et al 2023 arXiv: 2307.12008; 2023 arXiv: 2307.12037; Lee et al 2023 J. Korean Cryst. Growth Cryst. 33 61). The signatures of superconductivity in the compound are very promising, in terms of resistivity (ρ = 0) and diamagnetism at T _c. Although, the heat capacity (C _p) did not show the obvious transition at T _c. Inspired by the interesting claims of the above room temperature superconductivity in LK-99, in this article, we report the synthesis of polycrystalline samples of LK-99, by following the same heat treatment as reported in Lee et al (2023 arXiv: 2307.12008; 2023 arXiv: 2307.12037) using a two-step precursor method. The phase is confirmed through x-ray diffraction measurements, performed after each heat treatment. The room temperature diamagnetism is not evidenced by the levitation of a permanent magnet over the sample or vice versa. The isothermal magnetization measurement at 280 K shows that as synthesized sample of LK-99 is paramagnetic. Further measurements for the confirmation of bulk superconductivity in variously synthesized samples are underway. Our results on the present LK-99 sample, synthesized at 925 °C, as of now do not confirm the appearance of bulk superconductivity at room temperature. Further studies with different heat treatments are underway.

We report detailed structural, electrical, magnetic, and specific heat studies on ${\text{La}}_{0.7}{\text{Ca}}_{0.3}{\text{Mn}}_{1-\text{x}}{\text{Cr}}_{\text{x}}{\text{O}}_3$ manganites. Rietveld analysis of fitted and observed x-ray diffraction patterns exhibited the single-phase nature of all the studied materials, which crystallize in $Pbnm$ space group. Successive substitution of Cr at Mn-site in ${\text{La}}_{0.7}{\text{Ca}}_{0.3}{\text{Mn}}_{1-\text{x}}{\text{Cr}}_{\text{x}}{\text{O}}_3$ manganites increases the electrical resistivity and decreases the characteristic insulator-metal transition temperature $\left({\text{T}}_{\text{IM}}\right)$ of the parent compound along with a humplike feature for higher Cr-content $\left(\text{x}>0.06\right)$ samples. The hump structure basically signifies the onset of antiferromagnetic (AFM) interactions as inferred by both the magnetic and infrared (IR) spectroscopy studies. The systematic suppression of FM state results in a spin glass (SG)-like behavior. IR studies revealed that the vibration mode at $413{\text{cm}}^{-1}$ being associated with internal bending of ${\text{MnO}}_6$ octahedra, becomes softer, indicating an increase in distortion and hence the possible SG behavior. The critical exponents ($\alpha$ , $\beta$ , and $\gamma$ ) are calculated from the heat capacity $\left({\text{C}}_{\text{P}}\right)$ data near the ${\text{T}}_{\text{IM}}/{\text{T}}_{\text{FM}}$ . The same exhibited variations of their values with doping. In particular, the value of $\beta$ increases from $0.37\left(\text{x}=0.0\right)$ to $0.43\left(\text{x}=0.04\right)$ , clearly indicating the coexistence of both long and short range magnetic orders, i.e., tendency toward SG state for Cr-doped samples. On the basis of present results, it is suggested that Cr dilutes double-exchange based FM and rather promotes the AFM based superexchange interactions via ${\text{Cr}}^{3+}/{\text{Mn}}^{4+}$ ions. Substitution of Cr systematically destroys both the metallic state and long range FM order.

Here we report the optimized magnetotransport properties of polycrystalline ${\text{La}}_{0.70}{\text{Ca}}_{0.3-\text{x}}{\text{Sr}}_{\text{x}}{\text{MnO}}_3$ and their composites with Ag. The optimization was carried out by varying the Sr and Ag contents simultaneously to achieve large temperature coefficient of resistance (TCR) as well as low field magnetoresistance (MR) at room temperature. Sharpest paramagnetic (PM)-ferromagnetic (FM) and insulator-metal (IM) transition is observed in the vicinity of the room temperature $\left({\text{T}}_{\text{C}}\approx 300\text{K}\approx {\text{T}}_{\text{IM}}\right)$ for the composition ${\text{La}}_{0.70}{\text{Ca}}_{0.20}{\mathrm{Sr}}_{0.10}{\text{MnO}}_3:{\text{Ag}}_{0.20}$ . Partial substitution of larger ${\text{Sr}}^{2+}$ ions at the ${\text{Ca}}^{2+}$ ions sites controls the magnitude of the FM and IM transition temperatures, while the Ag induces the desired sharpness in these transitions. For the optimized composition, maximum TCR and MR are tuned to room temperature (300 K) with the former being as high as 9% and the later being $\sim 20\mathrm{\%}$ and $\sim 30\mathrm{\%}$ at 5 and 10 kOe magnetic fields respectively. Such sharp single peak $\left(\text{TCR}\sim 9\mathrm{\%}\right)$ at room temperature can be used for the bolometric and infrared detector applications. The achievement of large TCR and low field MR at $\text{T}\sim 300\text{K}$ in polycrystalline samples is encouraging and we believe that further improvements can be achieved in thin films which by virtue of their low conduction noise are more suitable for device applications.

The high field magnetization and magnetotransport measurements are carried out to determine the critical superconducting parameters of ${\text{MgB}}_{2-x}{\text{C}}_x$ system. The synthesized samples are pure phase and the lattice parameter evaluation is carried out using the Rietveld refinement. The $R-T\left(H\right)$ measurements are done up to a field of 140 kOe. The upper critical field values, $H_{c2}$ , are obtained from these data based on the criterion of 90% of normal resistivity, i.e., $H_{c2}=H$ at which $\rho =90\%{\rho }_N$ , where ${\rho }_N$ is the normal resistivity, i.e., resistivity of about 40K in our case. The Werthamer–Helfand–Hohenberg prediction of $H_{c2}\left(0\right)$ underestimates the critical field value even below the field up to which measurement is carried out. After this model, the Ginzburg–Landau theory is applied to the $R-T\left(H\right)$ data which not only calculate the $H_{c2}\left(0\right)$ value but also determine the dependence of $H_{c2}$ on temperature in the low temperature high field region. The estimated $H_{c2}\left(0\right)=157.2\text{kOe}$ for pure ${\text{MgB}}_2$ is profoundly enhanced to 297.5 kOe for the $x=0.15$ sample in ${\text{MgB}}_{2-x}{\text{C}}_x$ series. Magnetization measurements are done up to 120 kOe at different temperatures and the other parameters such as irreversibility field $H_{\text{irr}}$ and critical current density $J_c\left(H\right)$ are also calculated. The nano carbon doping results in substantial enhancement of critical parameters such as $H_{c2}$ , $H_{\text{irr}}$ , and $J_c\left(H\right)$ in comparison to the pure ${\text{MgB}}_2$ sample.