A Unified View of Topological Phase Transition in Band Theory

Abstract

<jats:p>We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Reevaluating the band evolution from an “atomic crystal” (a normal insulator (NI)) to a solid crystal, such as a semiconductor, we demonstrate that there exists ubiquitously an intermediate phase of topological insulator (TI), whose critical transition point displays a linear scaling between electron hopping potential and average bond length, underlined by deformation-potential theory. The validity of the scaling relation is verified in various two-dimensional (2D) lattices regardless of lattice symmetry, periodicity, and form of electron hoppings, based on a generic tight-binding model. Significantly, this linear scaling is shown to set an upper bound for the degree of structural disorder to destroy the topological order in a crystalline solid, as exemplified by formation of vacancies and thermal disorder. Our work formulates a simple framework for understanding the physical nature of TPTs with significant implications in practical applications of topological materials.</jats:p>

Switchable Topological Phase Transition and Novel Nonlinear Optical Properties in ReC2H Monolayer

“…Murakami. 1 The TPT can be driven by external stimulus like electric field 2 , magnetization 3 , strain and pressure 4,5 . Essentially, these methods control the mass parameter 'm' 1 to tune the band inversion accompanied by the Dirac semimetal or WSM in system with or without inversion symmetry.…”

Topological Anderson Insulator in Cation-Disordered Cu2ZnSnS4

“…Topological insulators, including the multinary compounds mentioned above, are generally known to host a bulk band gap coupled to gapless surface states, robust to weak levels of disorder. Several recent studies have highlighted how TI behavior can exist in aperiodic systems such as quasicrystals 21 , and can persist in systems with bulk defects such as grain boundaries and vacancies below a certain threshold 22,23 , nevertheless, sufficiently strong disorder is expected to close the bulk gap and destroy all topological features 10,23 . In light of this, a surprising prediction was made by Li et al 24 , who claimed that adding disorder to otherwise trivial systems can lead to the emergence of topological behavior.…”

Topological states in quasicrystals

“…Historically, the integer quantum Hall effect (IQHE) discovered in the 1980s [4] is an early example of topological states where the quantized Hall conductance was later explained by the Thouless-Kohmoto-Nightingale-den Nijs (TKNN) integer of occupied energy bands (a topological invariant also known as the Chern number) [5]. Recently, the discovery of topological insulators and superconductors and their classification for the ten Altland-Zirnbauer symmetry classes based on internal discrete symmetries (time-reversal, particle-hole, and chiral symmetry) [6][7][8][9] have stimulated various theoretical and experimental studies of real topological materials [10][11][12][13][14][15][16]. The subsequent development of topological classification has been extended to materials in which the crystal structure is essential for the protection of topological phases.…”