This is another article in what I'd tag -- if mataroa.blog had tags -- 'Sam read something he liked'. Today we've got the somewhat old review article Quantum defects by design from Lee Bassett, Audrius Alkauskas, Annemarie Exarhos and Kai-Mei Fu¹. This review belongs to the general class of reviews (in fact this is the earliest such in my library) that asks the question: 'how can we find better colour centres?'. In this case, Bassett et al. want to ask if we can design such a defect, by which they mean, start with the application in mind to guide the search. I want to take this opportunity to hone my understanding of what parameters we care about in our defect materials hosts/which materials are 'best' and question whether we need to widen the net of 'hosts' considered.

The Bassett Review

Let's begin by reproducing this nice section in the conclusion:

In a letter to Rudolph Peierls from 1931, Wolfgang Pauli pronounced: “One shouldn’t work on semiconductors; that is a filthy mess. Who knows if they really exist?” Pauli was responding to the difficulty at the time in making sense of various conflicting measurements on semiconductor materials, including strange changes in Hall voltages – and their signs – as a function of temperature, along with apparently random variations between samples. Today we know that the source of that “filthy mess” was in fact defects. Just as it must have been nearly impossible in 1931 to anticipate how early experiments on semiconductors would lead to the age of integrated circuits, it is foolish to assume in the present day that we understand the full scope of future quantum technologies. What seems clear is that Pauli’s filthy mess will continue to drive scientific discovery and technological innovation, as semiconductor devices finally reach the ultimate scale of individual atoms.¹

I would argue that semiconductors continue to be a “filthy mess” and that we cannot guide our search except for with the broadest of brushes. I make this argument largely along the lines that the application space for quantum defects is really quite broad. Alternatively we could argue that there is no clear 'winning application' in which they are most useful, and they act instead as a jack-of-all-trades. The requirements for a single-photon emitter is quite different from that of a dc or even ac magnetic sensor.

However, as Bassett et al. write, there are still some key material parameters we can keep front-of-mind. The presented parameters are: - The band gap: large enough to host optical defects if wanted, lower allows for more Fermi level engineering - The nuclear spin bath: a spin-free bath improves coherence - Spin-orbit coupling: some is required for the spin-photon interface, but too high and you lose spin coherence - The host crystal symmetry: higher symmetry allows for degenerate orbitals and thus higher spin states - The host crystal dimensionality: a lot changes when you go to the 2D limit!

I'll go through a couple more parameters below. But generally, those are some nice guiding principles! In our group we've chosen to focus on the last point (as appears has Bassett²). The work required to explore even two defect systems in a single material is significant, and so the design point in the above paper is somewhat superfluous: you have some reason for exploring a material, and then you just have to go for it! I'm not sure (at least as an experimentalist) there is much allowance for optimisation.

Computational reviews

Adam Gali's group have of course tackled this sort of question from a first-principles approach, in particular calculations as a tool for finding new point defects³. The main takeaway I get from this paper is that we are not yet at the stage where we can combine ab initio defect property calculations (e.g. zero phonon line) with their environment (spin Hamiltonian calculations). One solution posited to this in that paper is to use (hardware) quantum computation - a little further out on the horizon now in 2025 than it appeared in 2020, perhaps.

Complementing that review, Kanai et al.⁴ use Cluster Correlation Expansion (CCE) calculations on many (12,000!) host crystals to explore the general scaling of qubit coherence, based on a small set of material parameters. They do not extend the work to two-dimensional materials, but I would love to see that data! Alternatively, Hebnes et al.⁵ use a machine learning approach to explore the material parameter space. Hebnes et al. find that "the manifestation of quantum effects in semiconductors is related to the crystal structure symmetry and bonding" as opposed to "expectations from the literature focusing on band gap and ionic character as important properties for QT [quantum technology] compatibility." Hebnes et al. do not model the defects themselves, however, and so this approach can be thought of as a sanity-check or pre-filter for materials, or as a method to understand the key material characteristics that "enable quantum effects to manifest".

Other broad reviews

Now for some other general reviews. The one I have found the most useful is Quantum guidelines for solid-state spin defects by Wolfowicz et al.⁶. One guideline I'd like to highlight is the (crystal's) Debye temperature, i.e. the temperature required to activate phonons. Broadly a higher Debye temperature is required for room temperature operation, which is why diamond and SiC are preeminent hosts. There really is too much good stuff in that review to reproduce. In particular I like the structure, dividing into sections on spin, optical and charge properties, and material considerations.

Material platforms for spin-based photonic quantum technologies by Atatüre et al.⁷ is an older review that particularly focuses on the spin-photon or optical component of the above picture. This review has not been particularly useful to me, as yet. Finally, there are two general reviews that are more of an overview of quantum technologies with the available platforms. Neither has been useful to me, but I will list them for completeness. Quantum technologies with optically interfaced solid-state spins from Awschalom et al. (2018)⁸ and Semiconductor qubits in practice from Chatterjee et al. (2021)⁹.

Outstanding questions

• Is there a more succinct way to write down the very key and general properties we care about for broad classes of quantum technologies? Something like Ref.⁶, but more concise.
• Are there some materials that we are not considering in the field, such as diamene, that could contain useful spin defects?
• Are there any ways we can sit back and see where the defect of the future will be? The past examples don't seem to indicate this is possible, unfortunately.
• C.f. Kanai et al.⁴, are there any unexpected scalings of spin coherence when you go to the 2D limit?
• I haven't written at all here on how we characterise quantum point defects - Bassett has a lot of work on that too. You need to understand characterisation well to understand this design question, and vice-versa.

References