The electronic topology of ${\mathrm{Bi}}_4{\mathrm{Te}}_3$, composed of alternating ${\mathrm{Bi}}_2$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ layers, is investigated by density functional theory and angle-resolved photoemission spectroscopy. We find, remarkably, that there are three adjacent strong topological gaps with associated protected surface states within a 2-eV range of the Fermi level. The existence of three consecutive Dirac cones in $k$ space gives promise for alternative phenomena and applications, e.g., production of single photons with different energies (in the infrared and visible ranges) for multichannel transport of quantum information as well as multiple degrees of freedom in electron pumping for lasers. Additionally, a surface-state Fermi surface with strong hexagonal warping is observed.

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• Electronic structure
• Topological materials
• Angle-resolved photoemission spectroscopy
• Density functional theory