  Creating, manipulating, and detecting coherent electrons is at the heart of
future quantum microscopy and spectroscopy technologies. Leveraging and
specifically altering the quantum features of an electron beam source at low
temperatures can enhance its emission properties. Here, we describe electron
field emission from a monocrystalline, superconducting niobium nanotip at a
temperature of 5.9 K. The emitted electron energy spectrum reveals an
ultra-narrow distribution down to 16 meV due to tunable resonant tunneling
field emission via localized band states at a nano-protrusion's apex and a
cut-off at the sharp low-temperature Fermi-edge. This is an order of magnitude
lower than for conventional field emission electron sources. The self-focusing
geometry of the tip leads to emission in an angle of 3.7 deg, a reduced
brightness of 3.8 x 10exp8 A/(m2 sr V), and a stability of hours at 4.1 nA beam
current and 69 meV energy width. This source will decrease the impact of lens
aberration and enable new modes in low-energy electron microscopy, electron
energy loss spectroscopy, and high-resolution vibrational spectroscopy.

Applied Physics;Quantum Physics