TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.13.6.120
TI  - A proposal to extract and enhance four-Majorana interactions in hybrid nanowires
PY  - 2022/12/07
UR  - https://scipost.org/SciPostPhys.13.6.120
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 13
IS  - 6
SP  - 120
A1  - Reza, Tasnum
AU  - Frolov, Sergey M.
AU  - Pekker, David
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.13.6.120,
	title={{A proposal to extract and enhance four-Majorana interactions in hybrid nanowires}},
	author={Tasnum Reza and Sergey M. Frolov and David Pekker},
	journal={SciPost Phys.},
	volume={13},
	pages={120},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.13.6.120},
	url={https://scipost.org/10.21468/SciPostPhys.13.6.120},
}