Daily Summary for 2026-10-21

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

Kai: It's the twenty-first of October, twenty twenty-six, and this is the day's research.

Mira: One new paper came out today.

Kai: I'm Kai.

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

Kai: We'll take the day in one pass, then pull out the paper we're staying with.

Mira: Start us off with Disorder Suppression in Topological Semiconductor-Superconductor Junctions.

The summary: Kai: Welcome. Today is the twenty-first of October, twenty twenty six.

Mira: We are diving into disorder in a bulk superconductor messing with a topological state because that is the real physics now.

Lev: The core idea is disorder scatters quasiparticles which can destroy the topological nature of pairing.

Kai: We started by using random-matrix theory to figure out scattering from the superconductor onto a junction.

Mira: This involves composing scattering matrices for the semiconductor interface, diffusive region, and bulk superconductor to find an effective scattering rate.

Lev: That calculation involves composing those matrices for finding the effective rate.

Kai: So we are finding how much scattering happens across that entire structure.

Mira: The material describes how disorder scatters quasiparticles eventually destroying topological nature of pairing.

Lev: That process is what we need to understand the impact on the state.

Lucky paper: 2207.05109: Kai: So, we are looking at Disorder Suppression in Topological Semiconductor-Superconductor Junctions today.

Mira: The paper uses a random-matrix theory approach to understand how disorder scattering affects the density and tunnel coupling dependence of that scattering from the proximitizing superconductor.

Lev: It models a planar Josephson junction with a short semiconducting region, where strong coupling lets you cross into a topological phase by tuning the phase difference between the superconductors to pi.

Kai: That specific model for the right interface of that junction is shown in Fig. 1b in that paper.

Mira: The calculation involves composing scattering matrices for the semiconductor interface, diffusive region, and superconductor to solve for the normal reflection probability ree2, which gives you the effective scattering rate according to Eq. one.

Lev: The zero-energy conductance resulting from Andreev reflection is bounded by GNS greater than 4e2h over Nsm minus 4Tr h rLr dagger L.

Kai: That expression for the conductance sets a minimum bound for the mean free path lambda, suggesting that disorder effects are suppressed if lambda is greater than a value related to the Fermi wave-length mismatch.

Mira: This result connects to classical estimates where electrons are treated as random walkers due to collisions with impurities in that paper.

Lev: The total probability of a scattered electron reflecting into the semiconductor is P e over e equal to two over pi kFsm over kFsc rxi0 lambda.

Kai: The authors show that these results for both the planar Josephson junction and the thin superconducting shell are qualitatively consistent with a semi-classical estimate of Andreev scattering.

Mira: They also looked at how a small magnetic field changes things, introducing a momentum shift deltaek equal to qe delta r times B over the electron part of the trajectory r over t.

Lev: The average magnitude of that momentum shift gives an estimate for the mean-free path from this magnetic-field induced scattering, which is lambda mag equal to deltaek squared over two.

Kai: This field can have a significant effect on topological superconductivity if the ratio ξ0 over lambda mag is comparable to one.

Mira: The numerical evaluation of diagonal Andreev reflection using Kwant shows that the diagonal part of the Andreev reflection dominates in time-reversal invariant cases with large momentum mismatch.

Lev: The numerical results for the no-field case shown in Fig. three agree quite well with the random matrix result in Eqs. fourteen and thirteen of that paper.

Kai: Applying a magnetic field, like those green dots in Fig. three is enough to suppress diagonal Andreev reflection substantially.

Mira: The conclusion is that using scattering theory and random-matrix calculations, the effects of disorder scattering in the bulk superconductor are suppressed as the ratio of the Fermi wave-length in the semiconductor to that in the superconductor.

Lev: They demonstrate that near perfect Andreev reflection at a semiconductor-superconductor interface is a good indicator that such a condition has been met without a magnetic field.

Kai: That means controlling disorder scattering at an interface can lead to near perfect Andreev reflection even when there's no magnetic field present.

Mira: The authors also thank Anton Akhmerov for discussions about Fermi momentum mismatch suppressing disorder scattering and David Goldhaber Gordon for motivating the work on controlling that interface.

Lev: Stuart Thomas is also thanked for support through a JQI fellowship, and JS acknowledges NSF DMR one million five hundred fifty-five thousand one hundred thirty-five for support.

Kai: And this work is also supported by the Laboratory for Physical Sciences through its continuous support of the Condensed Matter Theory Center at the University of Maryland.