Transport and anomaly phenomena in a Weyl metallic phase & Universal phenomena in a charge/spin density wave quantum critical metal

DoctorThis thesis is composed of two parts. In part 1, we have dealt with transport and anomaly phenomena in a Weyl metallic phase. In part 2, universal phenomena in a charge/spin density wave quantum critical metal have been discussed. Therefore we give two separated abstracts for an each part. Part 1. Transport and anomaly phenomena in a Weyl metallic phase. After a discovery of the topological insulator, a topological matter with a non-trivial band topology has been a main theme in the condensed matter physics. Although many researches on the topological phases of the matter starts with the topological insulating phase, a "topological" metallic phase became the another main issue after a proposal of the Weyl semi metal phase. This non-trivial topological metallic phase is distinguished from the conventional metallic phase due to non-trivial properties driven by the non-tribal band topology. The most famous distinguished feature is the Adler-Bell-Jackiw(ABJ) anomaly related transport phenomena. In the part 1 of the thesis, we discuss the new transport phenomena and anomaly cancellation phenomena in the Weyl metal phase. In the Ch.1, we introduce the definition of the Weyl metallic phase and its non-trivial transport phenomena driven by Berry flux effects. Also concepts of anomaly and anomaly cancellation phenomena in a topological matter are discussed as an introduction for Ch. 3. In the Ch. 2, new transport phenomena in the Weyl metal phase driven by Berry electric field is discussed. In the momentum space, Weyl points can be thought as a monopole or an anti-monopole of the Berry flux. The monopole-anti monopole structure has played an important role in the exotic transport phenomena such as Adler-Bell-Jackiw transport phenomena and anomalous Hall effects. However only a static monopole-anti monopole structure was studied in the previous researches. Here we study the effects of the moving monopole-anti monopole by a time-varying external magnetic field on the transport phenomena. We find that moving monopole-anti monopole pair induces a Berry electric field and it results the new transport phenomena. In the Ch. 3, an anomaly cancellation in the the Weyl metal phases has been discussed. Due to the its non-trivial topological band structure of the Weyl metal phase, a non-trivial surface structure called ‘Fermi arc’ is observed. Theoretically, this non-trivial surface states are connected to the anomaly phenomena in the bulk effective theory of the Weyl metallic phase. We study the anomaly phenomena in two different Weyl metal phases; a Time reversal broken Weyl metallic phase and an Inversion symmetry broken Weyl metallic phase. First, we review about the anomaly cancellation in the time reversal symmetry broken Weyl metal phase. Based on this work, we investigate the anomaly cancellation in the inversion symmetry broken Weyl metal phase. Since a minimal number of Weyl points is four in inversion symmetry broken case while a minimal number of two in time reversal symmetry broken case, there are subtle points in the anomaly cancellation in the inversion symmetry broken case. We discuss about these points and it physical meaning. Part 2. Universal phenomena in a charge/spin density wave quantum critical metal. Many unsolved problems in condensed matter physics are related to strong interactions which forbids perturbative approach. One of the problems is an identifying the low energy properties of non-Fermi liquid states(Here we will only focus on the two dimensional non-Fermi liquid states). As you can guess from the name "non-Fermi liquid states", these states are metallic states which do not obey the "Landau Fermi liquid theorem". In the part 2 of the thesis, we have discussed about two different non-Fermi liquid systems; the first one is a charge density wave quantum critical metal and the second one is a spin-density wave quantum critical metal system using a renormalization group analysis. In the Ch. 4, we give introduction about Landau Fermi liquid theory and non-Fermi liquid states. Related to the non-Fermi liquid states, a history of the theoretical approaches to the non-Fermi liquid states and recent developments in analytic methods are also introduced. In the Ch. 5, a research on the low energy properties of the two dimensional VSe2 system is be discussed. Motivated by the experimental facts, we have studied about perfect Fermi-surface nesting driven by electron-electron correlation in monolayer vanadium diselenide VSe2. Based on the symmetry, we construct the low energy effective theory of a fermion and a charge density order parameter near the quantum critical point. Applying the renormalization group technique to this model, we figure out the low energy properties of the system and explain the reason for the perfect Fermi surface nesting effects observed in the experiments. In the Ch 6, we discuss about effects of disorders on the low energy properties of a spin density wave quantum critical metallic system. The spin density wave quantum critical metallic system has been a main research interest since it is related to the many quantum critical systems such as an electron-doped Cuprate, an iron based superconductor, a heavy fermion material showing non-Fermi liquid states behavior. However theoretical understanding of this system has been a very difficult problem since the conventional perturbative approaches are not applicable to this system. Fortunately, there have been many theoretical developments for this system in an analytical and numerical way recently. However a disorder is not considered in the most of the theoretical researches. As a result, it is difficult to compare the theoretical results with the experimental facts. We study the effects of the disorder on the system by using field theoretical techniques. We construct the theoretical model and apply the renormalization group analysis to the model using co-dimension regularization. Up to 1-loop calculations, we find that there is no stable fixed point unfortunately. As a next plan, we are going to calculate the two-loop diagrams and find that whether there is fixed point or not