THESIS
2017

xvi, 92 pages : illustrations (chiefly color) ; 30 cm

**Abstract**
The topological states of matter recognized as new phases of matter has become a central research
field in condensed matter physics in the past two decades due to its exotic properties like
nontrivial band topology, topologically protected edge and surface states, and topological phase
transitions without symmetry breaking. In this thesis, we give a brief introduction to the topological
Chern insulator and Weyl semimetal in Chapter 1, study the disorder-induced topological
phase transitions in topological Chern insulators and Weyl semimetals in Chapters 2 and 3, and
topological magnetic states in ferromagnetic materials in Chapters 4 and 5.

The disordered-induced topological phase transition was firstly found in topological Anderson
insulator (TAI) suggests that when time-revers...[

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The topological states of matter recognized as new phases of matter has become a central research
field in condensed matter physics in the past two decades due to its exotic properties like
nontrivial band topology, topologically protected edge and surface states, and topological phase
transitions without symmetry breaking. In this thesis, we give a brief introduction to the topological
Chern insulator and Weyl semimetal in Chapter 1, study the disorder-induced topological
phase transitions in topological Chern insulators and Weyl semimetals in Chapters 2 and 3, and
topological magnetic states in ferromagnetic materials in Chapters 4 and 5.

The disordered-induced topological phase transition was firstly found in topological Anderson
insulator (TAI) suggests that when time-reversal symmetry (TRS) is maintained, the pertinent topological
phase transition, marked by re-entrant 2e

^{2}/h quantized conductance contributed by helical
edge states, is driven by disorder. In Chapter 2, we show that when TRS is broken, the physics
of TAI becomes even richer. The pattern of longitudinal conductance and nonequilibrium local current distribution displays novel TAI phases characterized by nonzero Chern numbers, indicating
the occurrence of multiple chiral edge modes. Tuning either disorder or Fermi energy (in both
topologically trivial and nontrivial phases), drives transitions between these distinct TAI phases,
characterized by jumps of the quantized conductance from 0 to e

^{2}/h and from e

^{2}/h to 2e

^{2}/h. An
effective medium theory based on the Born approximation yields an accurate description of different
TAI phases in parameter space.

In Chapter 3, the Quantum phase transitions of three-dimensional (3D)Weyl semimetals (WSMs)
subject to uncorrelated on-site disorder are investigated through quantum conductance calculations
and finite-size scaling of localization length. Contrary to a previous belief that a direct transition
from a WSM to a diffusive metal (DM) occurs, an intermediate phase of Chern insulator (CI) between
the two distinct metallic phases should exist due to internode scattering that is comparable
to intranode scattering and persists at Weyl nodes for nonzero disorder. The critical exponent of
localization length is v ≃ 1.3 for both the WSM-CI and CI-DM transitions, in the same universality
class of the 3D Gaussian unitary ensemble of Anderson localization transition. The CI phase
was confirmed by quantized nonzero Hall conductance in the bulk insulating phase established by
localization length calculations. The disorder-induced various plateau-plateau transitions in both
WSM and CI phases were observed and explained by the self-consistent Born approximation.

The initial studies of topological states were exclusively for electronic systems. It is now known
that topological states can also exist for other particles. Indeed, topologically protected edge states
have already been found for phonons and photons. In spite of active searching for topological states
in many fields, the studies in magnetism are relatively rare although topological states are apparently
important and useful in magnonics. In Chapter 4, we show that the pyrochlore ferromagnets
with the Dzyaloshinskii-Moriya interaction are intrinsic magnonic Weyl semimetals. Similar to
the electronic Weyl semimetals, the magnon bands in a magnonic Weyl semimetal are nontrivially
crossing in pairs at special points (called Weyl nodes) in momentum space. The equal energy contour
around the Weyl node energy is made up by the magnon arcs on sample surfaces due to the
topologically protected surface states between each pair of Weyl nodes. Additional Weyl nodes
and magnon arcs can be generated in lower energy magnon bands when an anisotropic exchange
interaction is introduced. In Chapter 5, the chiral anomaly of Weyl magnons (WMs), featured by
nontrivial band crossings at paired Weyl nodes (WNs) of opposite chirality, is investigated. It is shown that WMs can be realized in stacked honeycomb ferromagnets. Using the Aharonov-Casher
effect that is about the interaction between magnetic moments and electric fields, the magnon motion
in honeycomb layers can be quantized into magnonic Landau levels (MLLs). The zeroth MLL
is chiral so that unidirectional WMs propagate in the perpendicular (to the layer) direction for a
given WN under a magnetic field gradient from one WN to the other and change their chiralities,
resulting in the magnonic chiral anomaly (MCA). A net magnon current carrying spin and
heat through the zeroth MLL depends linearly on the magnetic field gradient and the electric field
gradient in the ballistic transport.

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