Localization of 5D Elko spinors on Minkowski branes

Recently, a new spin-$1/2$ fermionic quantum field with mass dimension one in four dimensions--Elko field λ was introduced as a candidate of dark matter. In this paper, we investigate the localization of 5D Elko spinors on Minkowski branes by presenting the equation of the Elko KK modes. For the 5D free massless Elko field, the zero mode can be localized on Randall-Sundrum thin branes but cannot 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 is introduced, there will exist a bound Elko zero mode in the Randall-Sundrum brane model. And when we introduce the Yukawa type coupling ηφ²λλ with φ the background scalar field, the Elko zero mode can be localized on some special thick branes with a particular coupling constant η. Nevertheless, the massive KK modes still cannot be localized on these branes. These results are very different from that of the conventional Dirac spinor field and the scalar field.