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Recently, a new spin-1/2 fermionic quantum field with mass dimension one infour dimensions--Elko field $\lambda$ was introduced as a candidate of darkmatter. In this paper, we investigate the localization of 5D Elko {spinors} onMinkowski branes by presenting the equation of {the} Elko KK modes. For the 5Dfree massless Elko field, the zero mode can be localized on Randall-Sundrumthin brane but can not be localized on the majority of thick branes. There {do}not exist bound massive KK modes on all these branes. If the 5D mass term isintroduced, there will exist bound Elko zero mode in Randall-Sundrum branemodel. And when we introduce the Yukawa type coupling $\eta \phi^2 \mathop\lambda\limits^\neg\lambda$ with $\phi$ the background scalar field, the Elkozero mode can be localized on some special thick branes with a particularcoupling constant $\eta$. Nevertheless, the massive KK modes still can not belocalized on these branes. These results are very different from that of theconventional Dirac spinor {field} and the scalar field.

Localization of 5D Elko Spinors on Minkowski Branes