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Topological insulators (TI) have already been made in lab. Topological superconductors (TSC), being close cousins of TI, seem harder to make. Why is that?
It seems that materials in connection with majorana zero modes all have bad fate in lab. Are there any deep reasons behind?
It's not the making as opposed to verifying of topological superconductors that is difficult experimentally. One of the most useful techniques in identifying topological properties of a material is Angle-Resolved Photoemission Spectroscopy (ARPES). ARPES can independently image the bulk and surface modes of a 3-D solid with very good energy and momentum resolution. As a result, it can detect the Dirac-like edge states, which are a signature of its topological nature. As a matter of fact, the first 3-D topological insulator that was identified, i.e. Bi$_x$Sb$_{1-x}$, was using ARPES in 2008. Interestingly, other 3-D topological insulators such as Bi$_2$Se$_3$ and Bi$_2$Te$_3$ have been around since the 1960s as thermoelectric materials. Even their band structures were studied using the pseudopotential technique. They were identified as topological insulators only very recently. The reason has to do partly with the fact that ARPES itself has experienced a renaissance very recently; that's primarily due to the study of high-temperature superconductivity in cuprates. In a way, you can say that the critical factor in the study of topological superconductors has been that of limitations in characterization technology.
One of the proposed topological superconductors is Cu$_x$Bi$_2$Se$_3$. You can check out this paper:
Liang Fu and Erez Berg. Odd-Parity Topological Superconductors: Theory and Application to Cu$_x$Bi$_2$Se$_3$. Phys. Rev. Lett. 105 no. 9, 097001 (2010). doi:10.1103/PhysRevLett.105.097001.
It has a superconducting transition temperature of 3.8 K and an superconducting energy gap of < 1meV. Current state-of-the-art ARPES systems cannot easily access these parameter regimes. Other than characterization difficulties, Cu$_x$Bi$_2$Se$_3$ is extremely hard to work with. The Cu atoms are dopants; i.e. Cu$_x$Bi$_2$Se$_3$ is not stoichiometrically stable. The diffusion of Cu atoms during the measurement process obfuscates the interpretation of data. ARPES already is notorious for difficult data analysis in normal stoichiometrically stable materials.
So, long story short, people are still improving instrument capabilities to identify topological superconductors. I hope that was helpful.
As for the second question (are the Majorana difficult to realize in lab ?) the answer is obviously yes, and for the same reason that we have no idea what to look for ! (NB: of course there are some predictions about the experimental signature of the Majorana, but no smoking gun experiment.
