Kumar Ghosh
5 min
Chiral superconductivity is predicted to host chiral Majorana modes along its edges, with the number of these modes defined by a signed integer, the Bogoliubov-de Gennes (BdG) Chern number. Despite decades of searching, this integer has never been measured in candidate materials because traditional magnetic signatures are not topologically protected. This paper proposes using the low-temperature thermal Hall conductance as a direct probe of this topological invariant in rhombohedral graphene. The author employs an occupied-vortex rule, which relates the Chern number to the sum of gap-vortex windings enclosed by the occupied regions of momentum space, effectively bypassing the need to reconstruct the intricate normal-state Fermi surface.
The study demonstrates that the thermal Hall conductance plateau, defined by the relation , provides a direct readout of the Chern number. By decomposing the intravalley Hamiltonian into symmetric and antisymmetric parts, the author shows that trigonal warping and finite Cooper pair momentum are topologically inert, meaning they do not alter the Chern number as long as the direct gap remains open. Numerical calculations across 525 parameter points confirm that the invariant is preserved throughout the realistic regime of the material. Furthermore, the study identifies a clear criterion for when the quantization is lost due to the formation of a Bogoliubov Fermi surface, which can be experimentally verified by measuring the longitudinal thermal conductance.
This work transforms the search for chiral superconductivity from an indirect diagnostic problem into a precise measurement of a topological integer. By linking the thermal Hall plateau to the imaged isospin domains in rhombohedral graphene, the approach allows researchers to verify the chirality of the superconducting state directly. Additionally, the proposed bulk-boundary test—measuring the heat transport across a written domain wall—offers a definitive way to confirm the presence of Majorana channels. This method utilizes existing millikelvin thermometry technology, making it immediately applicable to current experimental platforms.
A chiral superconductor carries chiral Majorana modes along its edges, and a single integer, the Bogoliubov--de Gennes Chern number, counts them. Thirty years of candidate materials have not yielded a measurement of that integer, because the magnetic signatures usually invoked are not topologically protected. Rhombohedral graphene makes the question both urgent and answerable: magnetic imaging resolves rewritable time-reversal-breaking domains inside the superconducting phase, while quantum oscillations reveal a normal state too intricate to reconstruct pocket by pocket. We show that the low-temperature thermal Hall conductance returns the integer directly, with no such reconstruction. For band-projected pairing it equals the pairing-vortex winding enclosed by the occupied regions of momentum space. Splitting the intravalley Hamiltonian into symmetric and antisymmetric parts isolates the trigonal warping and finite Cooper pair momentum of the real material: the antisymmetric part is topologically inert, direct Chern calculations across $525$ parameter points show the invariant preserved, and one inequality marks where a Bogoliubov Fermi surface removes quantization. The plateau $κ_{xy}/T=(π^2k_B^2/6h)\,C_{\rm BdG}$ then reads out the integer, its sign reverses with the imaged domain, a written domain wall should carry $2|C_{\rm BdG}|$ Majorana channels, and the thermometry required already resolves single thermal quanta in encapsulated graphene at millikelvin temperatures.
Alex: So the gap closing is both a physical transition and a diagnostic failure mode. What does that mean for running this in practice?
Sam: It means the experimental demands are significant. You need high-precision thermal transport at sub-Kelvin temperatures, and the primary challenge isn't just probe sensitivity—it's isolating the bulk contribution from edge modes and impurity scattering. Ordinary potential disorder can generate an anomalous thermal Hall effect that mimics the quantized signal. That's a real confound.
Alex: So how do you distinguish the topological signal from a disorder-induced artifact?
Sam: The authors propose a discriminant based on temperature scaling. The quantized edge contribution is robust as temperature approaches zero—it sits on a plateau at an integer multiple of the fundamental thermal conductance quantum. Disorder-induced responses typically show qualitatively different scaling behavior in that limit. The plateau quality itself is the diagnostic: if you're seeing a clean integer plateau, bulk quasiparticles are absent and the gap is open. If the plateau is soft or temperature-dependent, something else is going on.
Alex: That's a falsifiability criterion built into the measurement protocol itself.
Sam: Exactly. And that's arguably the broader contribution here. The paper doesn't just propose a new measurement—it provides a framework for testing the topological nature of these superconductors in a way that's discriminating enough to be useful. By separating the Chern number from Bogoliubov Fermi surface effects, and by giving experimentalists a scaling-based way to distinguish signal from artifact, it moves the field from speculative modeling toward a falsifiable protocol for mapping the phase diagram.
Alex: It's a shift from indirect inference to a direct topological measurement, with a built-in sanity check. That's a substantive advance. Thanks for walking through the mechanism—this has been a genuinely clarifying look at where the chiral superconductor problem actually stands. Thanks for listening to ResearchPod.