Examining the surface phase diagram of IrTe$_2$ with photoemission

In the transition metal dichalcogenide IrTe$_2$, low-temperature charge-ordered phase transitions involving Ir dimers lead to the occurrence of stripe phases of different periodicities, and nearly degenerate energies. Bulk-sensitive measurements have shown that, upon cooling, IrTe$_2$ undergoes two such first-order transitions to $(5\times1\times5)$ and $(8\times1\times8)$ reconstructed phases at $T_{c_1}\sim 280$~K and $T_{c_2}\sim 180$~K, respectively. Here, using surface sensitive probes of the electronic structure of IrTe$_2$, we reveal the first-order phase transition at $T_{c_3}=165$~K to the $(6\times1)$ stripes phase, previously proposed to be the surface ground state. This is achieved by combining x-ray photoemission spectroscopy and angle-resolved photoemission spectroscopy, which give access to the evolution of stripe domains and a particular surface state, the energy of which is dependent on the Ir dimer length. By performing measurements over a full thermal cycle, we also report the complete hysteresis of all these phases.