Elko spinor localized on branes as a candidate for dark matter

Recently, a new spin-1/2 fermionic quantum field with mass dimension one– Elko was introduced as a candidate of dark matter. In this paper, we investigate the lcalization and mass spectra of Elko field on Minkowski thick branes by presenting the potentials of the corresponding Schodinger equations of the Elko Kaluza-Klein (KK) modes. We categorize these potentials into three cases and find that there do not exist bound Elko KK states with mn ≥ 0 (mn are the masses of KK modes) on the branes for volcano potentials. There will exist some massive bound modes and a set of continuous massive delocalized KK modes for Poschl-Teller-like ones. For infinitely deep potentials, the spectra are discrete and all KK modes are massive. In all cases, there do not exist 4D massless Elko spinor (zero mode) on the branes and the Elko ground state (if it exists) on these branes is massive. The conclusion is a support for the conjecture that 4D Elko may be considered as a candidate for dark matter.