Theoretical study of charge density waves in transition metal materials

In this thesis we theoretically study new aspects of charge density waves in transition metal materials recently revealed by scanning tunneling microscopy measurements. The two important problems that we have investigated are the effects of orbital degeneracy on the formation of the charge-density waves in cobalt nanowires, and the effects of dilute but strongly pinning impurities on the charge-density wave in niobium diselenide. We first present an overview on charge-density waves, and then introduce a general theoretical model describing charge-density waves. We also explain several known results about disorder effects on charge-density waves. We briefly touch on the principle of scanning tunneling microscopy and its advantages compared to other experimental tools. Second, we discuss the physics of one-dimensional cobalt nanowires along with experimental results. We propose a theoretical model that is relevant to cobalt nanowires, and then analyze the model by two theoretical tools: mean-field theory and bosonization. Our results show that the multi-orbitals allow a spin-triplet interaction among electrons leading to different phase diagrams from the ones considered previously for similar models. Numerical results obtained by first-principles calculations are also briefly explained. Third, we consider the effects of dilute strong impurities on the charge-density wave in niobium diselenide, a transition metal dichalcogenide. We first explain the material and properties of its charge-density wave phase. Then, detailed analysis of a scanning tunneling microscopy measurement is presented. Next, we analytically and numerically study a phenomenological model relevant to the experiment. We show that the dilute strong impurities have little effects at large length scales compared to the average inter-impurity distance, leading to a topologically ordered phase with a (quasi-)long-range autocorrelation; this result is quite different from conventional pictures predicting short-range order with the proliferation of topological defects.