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In this book, the author theoretically studies two aspects of topological states. First, novel states arising from hybridizing surface states of topological insulators are theoretically introduced. As a remarkable example, the author shows the existence of gapless interface states at the interface between two different topological insulators, which belong to the same topological phase. While such interface states are usually gapped due to hybridization, the author proves that the interface states are in fact gapless when the two topological insulators have opposite chiralities. This is the first time that gapless topological novel interface states protected by mirror symmetry have been proposed. Second, the author studies the Weyl semimetal phase in thin topological insulators subjected to a magnetic field. This Weyl semimetal phase possesses edge states showing abnormal dispersion, which is not observed without mirror symmetry. The author explains that the edge states gain a finite velocity by a particular form of inversion symmetry breaking, which makes it possible to observe the phenomenon by means of electric conductivity.

Physics. --- Phase Transitions and Multiphase Systems. --- Strongly Correlated Systems, Superconductivity. --- Surfaces and Interfaces, Thin Films. --- Solid State Physics. --- Surface and Interface Science, Thin Films. --- Surfaces (Physics). --- Physique --- Surfaces (Physique) --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Interfaces (Physical sciences) --- Symmetry (Physics) --- Topological dynamics. --- Dynamics, Topological --- Invariance principles (Physics) --- Symmetry (Chemistry) --- Solid state physics. --- Superconductivity. --- Superconductors. --- Phase transitions (Statistical physics). --- Interfaces (Physical sciences). --- Thin films. --- Materials --- Surfaces. --- Conservation laws (Physics) --- Surface chemistry --- Surfaces (Physics) --- Differentiable dynamical systems --- Surfaces (Technology) --- Materials—Surfaces. --- Solids --- Films, Thin --- Solid film --- Solid state electronics --- Coatings --- Thick films --- Superconducting materials --- Superconductive devices --- Cryoelectronics --- Electronics --- Electric conductivity --- Critical currents --- Superfluidity --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium --- Statistical physics --- Surface phenomena --- Friction --- Tribology --- Surfaces

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