Exactly solvable Majorana-Anderson impurity models

Abstract

Motivated by recent experimental progress in the realization of hybrid structures with a topologically superconducting nanowire coupled to a quantum dot, viewed through the lens of the emerging field of correlated Majorana fermions, we introduce a class of interacting Majorana-Anderson impurity models which admit an exact solution for a wide range of parameters, including on-site repulsive interactions of arbitrary strength. The model is solved by mapping it via the Z2 slave-spin method to a noninteracting resonant level model for auxiliary Majorana degrees of freedom. The resulting gauge constraint is eliminated by exploiting the transformation properties of the Hamiltonian under a special local particle-hole transformation. For a spin-polarized Kitaev chain coupled to a quantum dot, we obtain exact expressions for the dot spectral functions at both zero and finite temperature. We study how the interaction strength and localization length of the end Majorana zero mode affect physical properties of the dot, such as quasiparticle weight, double occupancy, and odd-frequency pairing correlations, as well as the local electronic density of states in the superconducting chain.Introduction.-The discovery of topological phases of quantum matter has led to a paradigm shift in condensed matter physics. The simplest such topological phase, the one-dimensional (1D) topological superconductor (SC) [1], hosts localized Majorana zero modes (MZMs) at its ends which can form a topological qubit immune to decoherence, with exciting prospects for quantum computation [2,3]. Strong evidence suggests MZMs have been observed in experiments on proximitized semiconductor nanowires [4] and ferromagnetic chains [5], following specific theoretical proposals [5][6][7].On the theoretical front, a new direction has emerged which explores the interplay of pure MZM physics, well understood from single-particle quantum mechanics, and electronic correlations [8]. Recently studied lattice models of interacting MZMs such as the Majorana-Hubbard [9][10][11][12][13][14] and 16] models may be relevant to describe Abrikosov vortex lattices in 2D topological SCs [17], where each vortex hosts an unpaired MZM [18,19]. Motivated by transport experiments on proximitized nanowires, another avenue of research has explored interacting Anderson-type quantum impurity models involving small numbers of MZMs coupled to dissipative baths, some of which are predicted to exhibit exotic Kondo effects [20][21][22]. A geometry of particular interest, that of an end MZM tunnelcoupled to a quantum dot (QD), is now experimentally accessible [23] and argued to directly probe the nonlocality of MZMs [24][25][26][27][28][29][30]. Existing theoretical studies of this problem have largely relied on mean-field approximations [27,28,30] or numerical methods [26,27] to treat correlation effects in the corresponding Anderson model [31]. Such studies also typically model the MZM as a unique on-site Majorana operator, whereas the MZM localization length is generically finite, as known...