Quantifying wave-function overlaps in inhomogeneous Majorana nanowires
EntityUAM. Departamento de Física de la Materia Condensada
PublisherAmerican Physical Society
10.1103/PhysRevB.98.235406Physical Review B 98.23 (2018): 235406
ISSN2469-9969 (online); 2469-9950 (print)
Funded byWe acknowledge financial support from the Spanish Ministry of Economy and Competitiveness through Grants No. FIS2015-65706-P, No. FIS2015-64654-P, and No. FIS2016-80434-P (AEI/FEDER, EU), the Ramón y Cajal programme, Grants No. RYC-2011-09345 and No. RYC-2013-14645, and the “María de Maeztu” Programme for Units of Excellence in Research and Development (MDM-2014-0377)
ProjectGobierno de España. FIS2015-65706-P; Gobierno de España. FIS2015-64654-P; Gobierno de España. FIS2016-80434-P; Gobierno de España. MDM-2014-0377
SubjectsMajorana bound states; Quantum nonlocality; Topological quantum computing; Nanowires; Física
Rights© 2018 American Physical Society.
A key property of Majorana zero modes is their protection against local perturbations. In the standard picture, this protection is guaranteed by a high degree of spatial nonlocality of the Majoranas, namely a suppressed wave-function overlap, in the topological phase. However, a careful characterization of resilience to local noise goes beyond mere spatial separation and must also take into account the projection of wave-function spin. By considering the susceptibility of a given zero mode to different local perturbations, we find the relevant forms of spin-resolved wave-function overlaps that measure its resilience. We quantify these overlaps and study their dependence with nanowire parameters in several classes of experimentally relevant configurations. These include nanowires with inhomogeneous depletion and induced pairing, barriers, and quantum dots. Smooth inhomogeneities have been shown to produce near-zero modes, so-called pseudo-Majoranas, below the critical Zeeman field in the bulk. Surprisingly, their resilience is found to be comparable or better than that of topological Majoranas in realistic systems. We further study how accurately their overlaps can be estimated using a purely local measurement on one end of the nanowire, accessible through conventional transport experiments. In uniform nanowires, this local estimator is remarkably accurate. In inhomogeneous cases, it is less accurate but can still provide reasonable estimates for potential inhomogeneities of the order of the superconducting gap. We further analyze the zero-mode wave-function structure, spin texture, and spectral features associated with each type of inhomogeneity. All our results highlight the strong connection between internal wave-function degrees of freedom, nonlocality, and protection in smoothly inhomogeneous nanowires
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