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I have investigated atomic-scale condensed matter, with a view towards future technology, covering two areas: point defects in a well studied and used system, Si; and a less studied semiconductor, MoS2, where I have focussed on the fundamental properties and have observed charge density waves (CDWs). Scanning tunnelling microscopy (STM) has been used over the past two decades to investigate semiconductor point defects. Here, an investigation of dangling bonds (DBs) on H-terminated Si(001) is presented. The STM tip is used to desorb H atoms to create DBs [1]. Pairs, or dimers, of DBs interact as their excited states overlap, signalled by a bright protrusion appearing between them [2]. Tip-induced band bending calculations show the dimer’s excited state comes into tunnelling range at high biases and low currents. The energy alignment with the tip Fermi level is also affected by additional DBs in the vicinity. 2D structures of DBs, including trimers and tetramers, exhibited 2D excited states. By modelling each DB with a 2D potential well holding two bound states, we could simulate the DB structure’s bound states. Using a tunnelling matrix element approximation, the bound states were combined to successfully re-create imaged quantum states. STM has been used to study correlated ground states of layered materials, including transition-metal dichalcogenides (TMDs). Here, it is used to discover and characterise the CDW of K-intercalated MoS2. This TMD is semiconducting but it is doped by the intercalating species, giving it metallic character and inducing superconductivity [3, 4]. The CDW was observed at temperatures of 78 K and below, appearing in patches localised to subsurface defects. The CDW coverage increased as the bias magnitude was decreased, however the wavevector or periodicity remained invariant; a feature of CDWs. Other evidence presented includes a gap in the density of states and the occupied and unoccupied state modulations being out of phase.