# Why are Topological Superconductors hard to make?

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?

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I just thought of mentioning that at least one topological superconductor (TSC) is already known to exist in the lab, which is, He-3B. It belongs to DIII Class TSC in the conventional notation. –  user20304 Jan 28 '13 at 3:05

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.

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Thank you very much! –  ChenChao Nov 9 '12 at 8:41

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.

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Hi Oaoa, and welcome to Physics Stack Exchange! When you post something as an answer, it should be limited to answering the question, so I've removed the part of your post that didn't do that. –  David Z Dec 9 '12 at 1:49
I am actually curious about what was removed. –  ChenChao Dec 9 '12 at 9:26
Can we detect long range entanglement in general? –  ChenChao Dec 9 '12 at 9:28
Hi David, Thanks for teaching me. I nevertheless thought I was answering the question. One of the reason the topological superconductor are harder to make is that we have no clear picture on what they are. I even believe we do not have a single undoubted theoretical proof they exist. That's what I've tried to say. Maybe it was unclear, sorry for that. Bets regards David. –  FraSchelle Dec 9 '12 at 9:29