  The discovery of two-dimensional gapless Dirac fermions in graphene and
topological insulators (TI) has sparked extensive ongoing research toward
applications of their unique electronic properties. The gapless surface states
in three-dimensional insulators indicate a distinct topological phase of matter
with a non-trivial Z2 invariant that can be verified by angle-resolved
photoemission spectroscopy or magnetoresistance quantum oscillation. In TI
nanowires, the gapless surface states exhibit Aharonov-Bohm (AB) oscillations
in conductance, with this quantum interference effect accompanying a change in
the number of transverse one-dimensional modes in transport. Thus, while the
density of states (DOS) of such nanowires is expected to show such AB
oscillation, this effect has yet to be observed. Here, we adopt nanomechanical
measurements that reveal AB oscillations in the DOS of a topological insulator.
The TI nanowire under study is an electromechanical resonator embedded in an
electrical circuit, and quantum capacitance effects from DOS oscillation
modulate the circuit capacitance thereby altering the spring constant to
generate mechanical resonant frequency shifts. Detection of the quantum
capacitance effects from surface-state DOS is facilitated by the small
effective capacitances and high quality factors of nanomechanical resonators,
and as such the present technique could be extended to study diverse quantum
materials at nanoscale.
