Interplay among Topological Structure, Disorders, and Electron Correlations: Emergent Phases and Anomalous Transport

DoctorThe understanding of topological matters lies at the heart of modern condensed matter physics. As a gapless topological matter, Weyl semimetals attract great attention because its conducting nature provides an opportunity to probe the role of topological structure in transport phenomena. In disordered systems, the interplay between topological structure and disorder casts novel physics problems: the fate of surface states, disorder-driven topological phase transitions, and an effective theory with a topological term in a strong-disorder regime. In this thesis, I investigate the interplay between topological structure and disorder on two aspects: (i) the emergence of Weyl semimetallic phases from topological insulators due to magnetic impurities and (ii) disorder-driven scaling laws in anomalous transport phenomena in Weyl semimetals. In an effective theory, topological insulator bands are represented by the Dirac theory and doped magnetic impurities are represented as local effective magnetic fields coupled to electron spins. Through the renormalization group analysis I find a fixed point at which a variance of local magnetic fields can be enormously enhanced while a band gap diminishes simultaneously due to such local fields. This fixed point is identified as a disordered Weyl metallic phase where insulating islands and Weyl metallic islands coexist inhomogeneously throughout a sample. In the presence of an external magnetic field, Weyl semimetals can be reached more easily. In an effective theory, topological insulator bands are represented by the Dirac theory and doped magnetic impurities, the O(3) vector model with a random mass term. Through the renormalization group analysis I find that a band gap gains negative feedback by spin fluctuations via a Zeeman coupling term. Due to this unusual effect, the band gap can be closed by an external magnetic field, turning a topological insulator into a Weyl semimetal. As a verification for such state, I derive a scaling formula for the negative longitudinal magneto-resistivity. Considering a Weyl metal in the presence of disorder, I investigate disorder-driven renormalization of a topological term referred an inhomogeneous theta-term responsible for the negative longitudinal magneto-resistivity. A difficulty in this study is that a naive Kubo formula calculation fails to incorporate the role of the chiral anomaly. The difficulty is circumvented by incorporating the renormalization effect of the $\theta$-term with the Boltzmann theory. As a result, I derive a scaling theory of the negative longitudinal magneto-resistivity. A breakdown of the B/T scaling behavior may be regarded as a fingerprint of the interplay between disorder scattering and topological structure in Weyl semimetal phases. Another main topic of this thesis is the interplay between electronic correlations and disorder. Strong correlations result in an electronic nematic phase where a point group symmetry of a crystal system is spontaneously broken. At the nematic quantum critical point in the absence of disorder, a non-Fermi liquid fixed point was obtained with a control parameter. However, the role of disorder should be figured out to understand anomalous transport phenomena in the metallic quantum critical point. In the presence of disorder, I construct an effective theory where intra and inter scattering channels on two momentum patches of Fermi surface are included in addition to critical order parameter fluctuations. By generalizing the co-dimension of the Fermi surface I can access to a perturbative regime for both fermion-boson interaction and disorder scattering. However, the intra scattering channel is strongly enhanced due to the extended momentum patches, inhibiting me from accessing to a weak disoder fixed point in the one loop order. This is interpreted as the interplay between electronic correlation effects and disorder scattering. Higher loop analysis is left for a future work. Lastly, I investigate the interplay between an inversion-symmetry breaking and disorder. When an inversion symmetry is broken in crystal systems, a spin-orbit coupling term originating from an effective electric field gives rise to two Fermi surfaces having different spin chiralities. In an experiment on BiTeI, the mobility of electrons in the inner Fermi surface shows a divergent behavior, increasing to order of 10^4 times that of the outer Fermi surface. This disparity is well explained within the self-consistent Born approximation on disorder scattering where the vanishing of the density of states in the inner Fermi surface is responsible for this phenomenon