High-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) can be acquired together with energy-dispersive X-ray spectroscopy (EDX) to give complementary information of the nano-particles being imaged. Recent deep learning approaches show potential for accurate 3D tomographic reconstruction for these applications, but large number of high-quality electron micrographs are usually required for supervised training, which may be difficult to collect due to the damage on the particles from the electron beam. To overcome these limitations and enable tomographic reconstruction even in low-dose sparse-view conditions, here we present an unsupervised deep learning method for HAADF-STEM-EDX tomography. Specifically, to improve EDX image quality from low dose condition, a HAADF-constrained unsupervised denoising approach is proposed. Additionally, to enable extreme sparse-view tomographic reconstruction, unsupervised view enrichment scheme is proposed in the projection domain. Extensive experiments with different types of quantum dots show that the proposed method offers a high quality reconstruction even with only three projection views recorded under low dose conditions.