Interplay of correlations and Majorana mode from local solution perspective

TL;DR

This work addresses how a correlated quantum dot coupled to a Majorana boundary mode in a topological superconductor exhibits leakage of the zero-energy Majorana mode into the dot, despite strong Coulomb repulsion. Using an exact solution of the low-energy Hamiltonian, the authors derive analytic eigenstates and spectral weights, revealing that the zero-energy mode coexists with finite-energy (trivial) states and that its spectral weight $A_1$ is maximized near $\xi_d=\pm U_d/2$ and grows with dot–Majorana coupling $t_m$. When the Majorana overlap is nonzero, the spectrum becomes richer (eight nondegenerate poles) and exhibits bowtie-like crossings, with four prominent peaks near half-filling; spin-up sectors show no zero-energy Majorana feature. The results extend previous Hubbard-I estimates, provide concrete Green’s-function expressions, and suggest spin-polarized SESAR spectroscopy as a practical probe for Majorana leakage in quantum-dot–Majorana hybrids, with implications for nonequilibrium and driven regimes.

Abstract

We study the quasiparticle spectrum of a hybrid system, comprising a correlated (Anderson-type) quantum dot coupled to a topological superconducting nanowire hosting the Majorana boundarymodes. From the exact solution of the low-energy effective Hamiltonian, we uncover a subtle interplay between Coulomb repulsion and the Majorana mode. Our analytical expressions show that the spectral weight of the leaking Majorana mode is sensitive to both the quantum dot energy level and the repulsive potential. We compare our results with estimations by L.S. Ricco et al. Phys. Rev. B 99, 155159 (2019) obtained for the same hybrid structure using the Hubbard-type decoupling scheme, and analytically quantify the spectral weight of the zero-energy (topological) mode coexisting with the finite-energy (trivial) states of the quantum dot. We also show that empirical verification of these spectral weights could be feasible through spin-polarized Andreev spectroscopy.

Figures (14)

• Figure 1: Schematics of the quantum dot (QD) attached to the topological nanowire, hosting the boundary Majorana modes $\eta_{i}$. Quasiparticles of the QD could be probed by spin-polarized scanning spectroscopy, measuring the conductance of the charge current contributed by electron-to-hole (Andreev) scattering of identical spins (marked by red arrows).
• Figure 2: Dependence of the eigenenergies $E_{i}^{-}$ on the energy level $\varepsilon_{d}$ of the QD. Solid lines refer to the ground-state energy. Results are obtained for $t_m=0.1U_d$ and $\epsilon_m=0.5U_d$. Dashed faded lines represent excited states.
• Figure 3: Five quasiparticle branches of the spin-resolved spectrum $\rho_{d\downarrow}(\omega)$vary with respect to $\xi_{d}=\varepsilon_d+U_d/2$. Dashed lines show the quasiparticle energies, and their spectral weights, $A_{i}$, are displayed according to the r.h.s. bar scale. White faded lines indicate the topological gap separating ordinary states from the induced zero mode.
• Figure 4: Variation of the spectral weights $A_{1-5}$ against the QD energy level obtained for the weak coupling $t_{m}/U_{d}=0.025$ (top panel), intermediate hybridization $t_{m}/U_{d}=0.25$ (middle panel), and in the strong coupling limit $t_{m}/U_{d}=1.5$ (bottom panel).
• Figure 5: Variation of the spectral weights $A_{i}$ with respect to the quantum dot energy level $\xi_{d}=\varepsilon_{d}+U_{d}/2$ obtained for several values of the Coulomb potential $U_d$, as indicated.