  Topological insulators exhibit gapless edge or surface states that are
topologically protected by time-reversal symmetry. However, several promising
candidates for topologically insulating materials (such as Bi$_2$Se$_3$ and
HgTe) contain spinful nuclei or other types of magnetic impurities that break
time-reversal symmetry. We investigate the consequences of such impurities
coupled to electronic edge states in a topological insulator quantum ring
threaded by a magnetic flux. We use spin conservation and additional symmetry
arguments to derive a universal formula for the spectrum of propagating edge
modes in terms of the amplitude of transmission through the impurity. Our
results apply for impurities of arbitrary spin. We show that there exists an
energy regime in which the spectrum becomes nearly independent of the flux and
significant spectral gaps form. We further analyze the electron-impurity
entanglement entropy, finding that maximal entanglement occurs near the gaps in
the spectrum. Our predictions can be investigated with quantum ring transport
interference experiments or through spin-resolved STM measurements, providing a
new approach to understand the role of impurities in topological insulator edge
transport.
