Zero-energy Majorana modes in spin ladders and a possible realization of the Kitaev model

Abstract

We show that in double-chain Mott insulators (ladders), disordered alternating ionic potentials may locally destroy coherence of magnetic excitations and lead to the appearance of spontaneously dimerized islands inside the Haldane spin-liquid phase. We argue that a boundary between the dimerized and Haldane phases of a spin-1/2 ladder supports a localized zero-energy Majorana fermion mode. Based on these findings we suggest a realization of a generalized Kitaev model where Majorana fermions can propagate in more than one dimension.

Majorana fermions in a topological superconducting wire out of equilibrium: Exact microscopic transport analysis of ap-wave open chain coupled to normal leads

“…One of the pressing theoretical problems in this context is to sort out the experimental signatures of MFs. Several proposals for their realization in (effective) onedimensional (1D) topological (p-wave) superconductors have been put forward recently [2]. A natural way to probe superconducting (SC) nanowires is via transport measurements and STM spectroscopy.…”

“…While different proposals for realizing MBSs in 1D differ in details [2], all essential features of realistic systems are expected to be minimally described by the so called Kitaev chain (linked to the early theoretical proposals for topological quantum computation) [10]. We thus study non-equilibrium electrical transport in Kitaev's tight-binding model of a single-channel 1D quantum wire with triplet (p-wave) SC pairing between electrons with the same spin orientation (equal-spin pairing).…”

“…In view of theoretically capturing the physics of realistic experiments, we are interested in studying non-equilibrium transport through the 1D quantum wire in an openquantum-system geometry, i.e., the wire is connected to external baths which incorporate both decoherence and dissipation. This is a minimal setup that can capture the essential features of recent proposals for realizing p-wave SC wires [2]. We develop a novel extension of the quantum Langevin Equations and Green's Function (LEGF) approach [12] to SC wires with BCS-type pairing.…”

Spinful fermionic ladders at incommensurate filling: Phase diagram, local perturbations, and ionic potentials

“…This is closely related to the existence of a gap in antiferromagnetic spin chains with an integer spin and its absence for chains with a half-integer spin [86]. This implies that the ground state of the system may be a Haldane spin-liquid [42], a topological phase of matter showing Majorana-fermion edge states [87]. On top of this, in half-filled ladders with a ground state of a spin-gapped Mott insulator, already weak doping causes dominance of superconducting fluctuations -the fact going in a remarkable parallel with the two-dimensional cuprate high-temperature superconductors [62].…”

Emerging Majorana Modes in Junctions of One-Dimensional Spin Systems

“…Located at the edges of 1D devices, they are responsible for the emergence of stretched nonlocal electron states 13,19 allowing for distance independent tunnelling, 20 crossed Andreev reflection, 21 teleportationlike coherent transfer of a fermion 22 and fractional Josephson effects. 23,24 Their effects emerge in a variety of platforms: quantum wires immersed in a p-wave superconductor, 13,19,20 cold atomic systems, 25 topological insulator-superconductor magnetic structures, 22,26,27 semiconductor heterostructures, [28][29][30][31] superconducting wires, 32 Josephson arrays 33 and spin systems 34 In addition, they may be relevant excitations also in conventional s-wave superconductors. 35 It is worth to stress here that, when a superconductor is coupled to a conducting wire in a SN-junction, the Majorana mode hybridizes with the conducting electrons at the normal side of the junction.…”