Luminous Lyman-alpha Emitters with Very Blue UV-continuum Slopes at Redshift 5.7 <= z <= 6.6

We study six luminous Lyman-alpha emitters (LAEs) with very blue rest-frame UV continua at $5.7\le z\le 6.6$. These LAEs have previous HST and Spitzer IRAC observations. Combining our newly acquired HST images, we find that their UV-continuum slopes $\beta$ are in a range of $-3.4\le \beta \le -2.6$. Unlike previous, tentative detections of $\beta \simeq -3$ in photometrically selected, low-luminosity galaxies, our LAEs are spectroscopically confirmed and luminous ($M_{\mathrm{U}\mathrm{V}}<-20$ mag). We model their broadband spectral energy distributions (SEDs), and find that two $\beta \simeq -2.6\pm 0.2$ galaxies can be well fitted with young and dust-free stellar populations. However, it becomes increasingly difficult to fit bluer galaxies. We explore further interpretations by including non-zero LyC escape fraction $f_{\mathrm{e}\mathrm{s}\mathrm{c}}$, very low metallicities, and/or AGN contributions. Assuming $f_{\mathrm{e}\mathrm{s}\mathrm{c}}\simeq 0.2$, we achieve the bluest slopes $\beta \simeq -2.7$ when nebular emission is considered. This can nearly explain the SEDs of two galaxies with $\beta \simeq -2.8$ and --2.9 (${\sigma }_{\beta }=0.15$). Larger $f_{\mathrm{e}\mathrm{s}\mathrm{c}}$ values and very low metallicities are not favored by the strong nebular line emission (evidenced by the IRAC flux) or the observed (IRAC 1 - IRAC 2) color. Finally, we find that the $\beta \simeq -2.9$ galaxy can potentially be well explained by the combination of a very young population with a high $f_{\rm esc}$($\ge0.5$)andanold,dustypopulation\mathrm{.}Wearenotabletoproducetwo$\beta \simeq -3.4 \pm0.4$ galaxies. Future deep spectroscopic observations are needed to fully understand these galaxies.