Current cross-correlations as probes for poor man’s Majorana states

Experimental signatures of Majorana zero modes (MZMs) in hybrid semiconductor-superconductor structures are often mimicked by trivial zero-energy states, making it difficult to confirm true topological non-locality using standard differential conductance spectroscopy. This paper investigates whether current-current correlations—specifically cross-correlations—can provide a more reliable diagnostic framework for identifying true poor man's Majorana (PMM) modes in a minimal Kitaev chain (MKC) setup.

The authors model a minimal Kitaev chain consisting of three quantum dots, where the central dot is proximitized by a superconductor and the outer dots are coupled to normal metallic leads. By tuning the Zeeman field and gate potentials, the system can be brought to a 'sweet spot' where PMM modes emerge. The researchers employ a scattering matrix formalism and the Keldysh non-equilibrium Green’s function (NEGF) method to calculate local and nonlocal transport properties. They specifically compare the behavior of 'true' PMMs (which connect to a topological regime in the infinite-chain limit) against 'false' PMMs (trivial states) when the outer quantum dot is detuned from the sweet spot.

The study demonstrates that while conductance spectroscopy often fails to distinguish between true and false PMMs, current cross-correlations offer a clear signature. The authors show that the relative magnitudes of elastic cotunneling (ECT) and crossed Andreev reflection (CAR) processes are sensitive to the underlying Majorana wavefunction. For true PMMs, the cross-correlation signatures remain remarkably stable under detuning of the outer dot. In contrast, false PMMs show significant sensitivity and hybridization, leading to distinct changes in the cross-correlation signal. This stability serves as a diagnostic feature, allowing researchers to verify the non-locality of the entangled states even in short, finite-sized chains.