A proposal to extract and enhance four-Majorana interactions in hybrid nanowires
Tasnum Reza, Sergey M. Frolov, David Pekker
SciPost Phys. 13, 120 (2022) · published 7 December 2022
- doi: 10.21468/SciPostPhys.13.6.120
We simulate the smallest building block of the Sachdev-Ye-Kitaev (SYK) model, a system of four interacting Majorana modes. We propose a 1D Kitaev chain that has been split into three segments, i.e., two topological segments separated by a non-topological segment in the middle, hosting four Majorana Zero Modes at the ends of the topological segments. We add a non-local interaction term to this Hamiltonian which produces both bilinear (two-body) interactions and a quartic (four-body) interaction between the Majorana modes. We further tune the parameters in the Hamiltonian to reach the regime with a finite quartic interaction strength and close to zero bilinear interaction strength, as required by the SYK model. To achieve this, we map the Hamiltonian from Majorana basis to a complex fermion basis, and extract the interaction strengths using a method of characterization of low-lying energy levels and then finding the differences in energies between odd and even parity levels. We show that the interaction strengths can be tuned using two methods - (i) an approximate method of tuning overlapping Majorana wave functions (without non-local interactions) to a zero energy point followed by addition of a non-local interaction, and (ii) a direct parameter space optimization method using a genetic algorithm. We propose that this model could be further extended to more Majorana modes, and show a 6-Majorana model as an example. Since eigenspectral characterization of one-dimensional nanowire devices can be done via tunneling spectroscopy in quantum transport measurements, this study could be performed in experiment.
Authors / Affiliation: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Tasnum Reza,
- 1 Sergey Frolov,
- 1 David Pekker
- Army Research Office (ARO) (through Organization: United States Army Research Laboratory [ARL])
- National Science Foundation [NSF]
- Office of Naval Research [ONR]