  We develop a theory of finite-temperature momentum-resolved tunneling
spectroscopy (MRTS) for disordered, interacting two-dimensional
topological-insulator edges. The MRTS complements conventional electrical
transport measurement in characterizing the properties of the helical Luttinger
liquid edges. Using standard bosonization technique, we study low-energy
spectral function and the MRTS tunneling current, providing a detailed
description controlled by disorder, interaction, and temperature, taking into
account Rashba spin orbit coupling, interedge interaction and distinct edge
velocities. Our theory provides a systematic description of the spectroscopic
signals in the MRTS measurement and we hope will stimulate future experimental
studies on the two-dimensional time-reversal invariant topological insulator.
