Monolayer transition metal dichalcogenides in the distorted octahedral 1T$^prime$ phase exhibit a large bulk bandgap and gapless boundary states, which is an asset in the ongoing quest for topological electronics. In single-layer tungsten diselenide (WSe$_2$), the boundary states have been observed at well ordered interfaces between 1T$^prime$ and semiconducting (1H) phases. This paper proposes an effective 4-band theory for the boundary states in single-layer WSe$_2$,describing a Kramers pair of in-gap states as well as the behaviour at the spectrum termination points on the conduction and valence bands of the 1T$^prime$ phase. The spectrum termination points determine the temperature and chemical potential dependences of the ballistic conductance and thermopower at the phase boundary. Notably, the thermopower shows an ambipolar behaviour, changing the sign in the bandgap of the 1T$^prime$ - WSe$_2$ and reflecting its particle-hole asymmetry. The theory establishes a link between the bulk band structure and ballistic boundary transport in single-layer WSe$_2$ and is applicable to a range of related topological materials.
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