Disorder-enhanced topological protection and universal quantum criticality in a spin-3/2 topological superconductor

summary

Video file (mp4)

The gist

The gist: Disorder stabilizes higher-spin topological superconductors by inducing a surface conformal field theory that quantizes thermal transport, suggesting a close analogy between bulk

In short

The study investigates Majorana surface states in spin-3/2 topological superconductors, generalizing 3He-B. While clean surfaces show instability towards a thermal quantum Hall effect upon interaction, quenched disorder stabilizes the system into a critical Conformal Field Theory (CFT). This disorder enhances topological protection and leads to quantized thermal transport at low temperatures, suggesting an analogy with the integer quantum Hall effect.

Key concepts

Majorana Surface States
These are zero-energy bound states found on the surface of a topological superconductor. In this study, they arise from p-wave pairing of spin-3/2 fermions and exhibit coexisting linear and cubic dispersing bands, which are crucial for understanding the system's properties.
Thermal Quantum Hall Effect (TQHE)
This is a state induced by interactions on the surface when certain parameters are met. The paper shows that interactions can drive the surface into this gapped state, which is a competition against the disorder-stabilized topological phase.
Conformal Field Theory (CFT)
A CFT describes the universal behavior of critical systems at low energies, especially those influenced by disorder. Quenched disorder drives the non-interacting surface into an SO(n)4 CFT phase, which governs universal features like the density of states and multifractal fluctuations.
Quantized Thermal Conductivity ($\kappa_{xx}/T$)
This ratio measures how heat flows through the surface at very low temperatures. The paper finds that disorder quantizes this ratio as $T \rightarrow 0$, providing a universal signature that links bulk topological superconductors to the integer quantum Hall effect.

Terminology used across episodes

This episode discusses

The paper

Disorder-enhanced topological protection and universal quantum criticality in a spin-3/2 topological superconductor · Read on arXiv

Sayed Ali Akbar Ghorashi, Seth Davis, Matthew S. Foster

Texas Center for Superconductivity · Department of Physics and Astronomy · Rice Center for Quantum Materials

DOI: 10.1103/PhysRevB.95.144503

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: Today's paper: "Disorder-enhanced topological protection and universal quantum criticality in a spin-3/2 topological superconductor".

Mira: The gist: Disorder stabilizes higher-spin topological superconductors by inducing a surface conformal field theory that quantizes thermal transport,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: To recap, we saw that this paper studies the Majorana surface states of higher-spin topological superconductors that could be realized in things like ultracold atomic systems or doped semimetals with spin-orbit coupling > page one <ref:1701.02787#pg1,ultracold atomic systems or doped semimetals with spin-orbit coupling>. The authors use a model generalizing 3He-B with p-wave pairing of spin-three/two fermions, which has these coexisting linear and cubic dispersing surface bands > page one <ref:1701.02787#pg1,with p-wave pairing of spin-3/2 fermions>.

Mira: They show that these bands are unstable to interactions, which leads to a spontaneous surface thermal quantum Hall effect or TQHE if you have attractive interactions > page two <ref:1701.02787#pg1,a spontaneous surface thermal quantum Hall effect>.

Lev: The crucial point they make is the contrast with quenched disorder, because nonmagnetic disorder induces a surface conformal field theory that is stable against weak interactions > page one <ref:1701.02787#pg1,disorder induces a surface conformal field theory>.

Kai: That CFT is governed by the bulk topological winding number, and it predicts things like power-law scaling of the density of states and a universal multifractal spectrum for fluctuations > page one <ref:1701.02787#pg1>.

Mira: And they mention that this CFT is exactly what you expect in spin-one/two bulk TSCs with relativistic surface fluids when you look at disordered noninteracting surface states > page one <ref:1701.02787#pg1>.

Lev: The paper also predicts the low-energy global density of states will diverge like epsilon to the minus one over five, which they link to a SO(n)four CFT > page one <ref:1701.02787#pg1>.

Kai: And for us in terms of real hardware, Lev, what does that divergence mean when we actually try to build something? It seems like we need a specific tuning for this thing > page three <ref:1701.02787#pg1>.

Mira: Exactly, the paper states that the coupling strength is pinned to a special value equal to the winding number four times a universal constant > page one <ref:1701.02787#pg1>.

Lev: That pinning implies that the topology itself fine-tunes that coupling strength right to its fixed point value > page one <ref:1701.02787#pg1>.

Kai: So if we build this, Lev, what would be the practical implication of needing that precise tuning? Would we have to spend all our time trying to hit this exact parameter?

Lev: It suggests that the topological protection is really tied to maintaining that specific coupling strength for it to work > page one <ref:1701.02787#pg1>.

Kai: And if we don't hit it, does the system just revert back to being unstable, or does disorder still offer some protection?

Mira: Disorder keeps things stable because it drives the noninteracting surface into that SO(n)four CFT phase, which is what the authors say is stable against weak interactions > page one <ref:1701.02787#pg1,is stable against weak interactions>.

Lev: But you have to remember that this CFT itself can be unstable to the thermal metal phase, so it only works if you are tuned precisely to that SO(n)four fixed point > page one <ref:1701.02787#pg1>.

Conclusion: Kai: So wrapping up, the title itself points to what they found: disorder enhancing topological protection through universal quantum criticality in a spin-three/two TSC > page one <ref:1701.02787#pg1,universal quantum criticality in a spin-3/2>.

Mira: The authors are talking about how this happens because the surface Majorana bands have that special linear and cubic dispersion which makes them vulnerable to interactions > page two <ref:1701.02787#pg1>.

Lev: And the whole point is that quenched disorder acts as a strong perturbation, driving the noninteracting surface into a phase described by that SO(n)four CFT > page one <ref:1701.02787#pg1>.

Kai: So what does this mean for us in terms of what we actually build, Lev? It means we need to be very careful about how we tune the system to get that specific coupling strength right > page one <ref:1701.02787#pg1>.

Mira: And if you get it right, then the low-temperature limit predicts a quantized ratio of thermal conductivity over temperature proportional to the bulk winding number > page three <ref:1701.02787#pg1>.

Lev: So in simple terms, this paper suggests that bulk TSCs look like they are very closely analogous to the integer quantum Hall effect in two dimensions > page three <ref:1701.02787#pg1>.

Kai: It seems like they’re using these higher-spin systems to probe some kind of deep connection between topology and transport > page one <ref:1701.02787#pg1>.

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