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arXiv:2502.16640 · Physical review. B./Physical review. B

Spin-charge-entangled Kondo effect induced by a side-coupled Majorana zero mode

Haojie Shen, Wei Su, M. N. Chen, Xiaoqun Wang

Published Aug 1, 2025• 2 citations
arXivHTMLPDF

Abstract

We investigate Kondo physics in a quantum dot side coupled to a Majorana zero mode, where the Majorana coupling induces both spin and charge fluctuations that determine low-energy behavior. Using a wave-function-based Schrieffer-Wolff transformation combined with numerical renormalization group calculations, we discover an $S{U}_{L}(2)$ spin-charge-entangled Kondo state, in which conduction electrons screen the spin-charge-entangled degrees of freedom of the Majorana-quantum dot subsystem. We show that the parity degeneracy of this state gives rise to spin-resolved Andreev-normal boundary conditions, resulting in non-Fermi-liquid behavior. Density matrix renormalization group simulations directly resolve a hallmark of these boundary conditions---a subleading even-odd effect in the screening cloud. Our framework bridges strongly correlated and topological phenomena, and naturally extends to ${\mathbb{Z}}_{N}$ parafermions and $SU(N)$ Kondo systems.

DOI
10.1103/kmpz-3ytk

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The prospect of using semiconductor quantum dots as an experimental tool to distinguish Majorana zero modes (MZMs) from other zero-energy excitations such as Kondo resonances has brought up the fundamental question of whether topological superconductivity and the Kondo effect can coexist in these systems. Here, we study the Kondo effect in a quantum dot coupled to a metallic contact and to a pair of MZMs. We consider a situation in which the MZMs are spin polarized in opposite directions. By using numerical renormalization group calculations and scaling analysis of the renormalization group equations, we show that the Kondo effect takes place at low temperatures, regardless of the coupling to the MZMs. Interestingly, we find that the Kondo singlet essentially decouples from the MZMs such that the residual impurity entropy can show local non-Fermi-liquid properties characteristic of the single Majorana excitations. This offers the possibility of tuning between Fermi-liquid and non-Fermi-liquid regimes simply by changing the quantum-dot-MZM couplings.
Entanglement is a defining feature of quantum mechanics, and its relation to quantum criticality is of considerable current interest. Here we show that measurable spin and charge fluctuations provide an entanglement witness of quantum criticality in the two-impurity Kondo model, which has experimental realizations in terms of coupled quantum dots and magnetic impurities added to surfaces. We use density-matrix renormalization group and numerical renormalization group calculations to resolve the non-Fermi-liquid critical point separating two independently Kondo-screened impurities from an inter-impurity singlet and interpret it as a change in the dominant entanglement partner of each local moment: from entanglement of the local moment with an extended set of conduction-electron degrees of freedom to entanglement with the other impurity. This reorganization is accompanied by a singular response of the impurity-bath entanglement and the inter-impurity susceptibility. We show how the same structure is encoded in the quantum Fisher information of collective spin and charge operators at zero and finite temperatures, connecting the entanglement picture to experimentally accessible dynamical response functions. Our results establish impurity systems as controlled settings in which quantum-critical entanglement can be detected through measurable correlations, and provide further insight into the possibility of understanding heavy-fermion physics in terms of entanglement.
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A magnetic moment in a metal or in a quantum dot is, at low temperatures, screened by the conduction electrons through the mechanism of the Kondo effect. This gives rise to spin-spin correlations between the magnetic moment and the conduction electrons, which can have a substantial spatial extension. We study this phenomenon, the so-called Kondo cloud, by means of the density matrix renormalization group method for the case of the single-impurity Anderson model. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, can be extracted from the spin-spin correlations. For several mechanisms---the gate potential and a magnetic field---which destroy the Kondo effect, we investigate the behavior of the screening cloud induced by these perturbations.