Gapless Criterion for Crystals from Effective Axion Field

Axion crystals

The low-energy effective theories for gapped insulators are classified by three parameters: permittivity $ε$, permeability $μ$, and theta angle $θ$. Crystals with periodic $ε$ are known as photonic crystals. We here study the band structure of photons in a new type of crystals with periodic $θ$ (modulo $2π$) in space, which we call the axion crystals. We find that the axion crystals have a number of new properties that the usual photonic crystals do not possess, such as the helicity-dependent mass gap and nonrelativistic gapless dispersion relation at small momentum. We briefly discuss possibl…

Axion electrodynamics and nonrelativistic photons in nuclear and quark matter

We argue that the effective theory for electromagnetic fields in spatially varying meson condensations in dense nuclear and quark matter is given by the axion electrodynamics. We show that one of the helicity states of photons there has the nonrelativistic gapless dispersion relation $ω\sim k^2$ at small momentum, while the other is gapped. This "nonrelativistic photon" may also be realized at the interface between topological and trivial insulators in condensed matter systems.

外尔半金属中的轴子与超流性

Axions and Superfluidity in Weyl Semimetals

本文提出了外尔半金属中动力学轴子的有效场论，证明在低温下轴子作为超流态的手征密度波或相子模式存在，并验证了't Hooft反常匹配，为实验测试超流、非费米液体行为与轴子提供了理论基础。

Green's Function Method for Line Defects and Gapless Modes in Topological Insulators : Beyond Semiclassical Approach

Defects which appear in heterostructure junctions involving topological insulators are sources of gapless modes governing the low energy properties of the systems, as recently elucidated by Teo and Kane [Physical Review B82, 115120 (2010)]. A standard approach for the calculation of topological invariants associated with defects is to deal with the spatial inhomogeneity raised by defects within a semiclassical approximation. In this paper, we propose a full quantum formulation for the topological invariants characterizing line defects in three-dimensional insulators with no symmetry by using t…

Nonlinear level attraction of cavity axion polariton in antiferromagnetic topological insulator

Strong coupling between cavity photons and various excitations in condensed matters boosts the field of light-matter interaction and generates several exciting sub-fields, such as cavity optomechanics and cavity magnon polariton. Axion quasiparticles, emerging in topological insulators, were predicted to strongly couple with the light and generate the so-called axion polariton. Here, we demonstrate that there arises a gapless level attraction in cavity axion polariton of antiferromagnetic topological insulators, which originates from a nonlinear interaction between axion and the odd-order reso…

Topological mass generation in gapless systems

Mass generation of gauge fields can be universally described by topological couplings in gapped systems, such as the Abelian Higgs model in $(3+1)$ dimensions and the Maxwell-Chern-Simons theory in $(2+1)$ dimensions. These systems also exhibit the spontaneous breaking of higher-form $\mathbb{Z}_k$ symmetries and topological orders for level $k \geq 2$. In this paper, we consider topological mass generation in gapless systems. As a paradigmatic example, we study the axion electrodynamics with level $k$ in $(3+1)$ dimensions in background fields that hosts both gapped and gapless modes. We argu…

Facet dependent surface energy gap on magnetic topological insulators

Magnetic topological insulators (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$ ($n=0,1,2,3$) are promising to realize exotic topological states such as the quantum anomalous Hall effect (QAHE) and axion insulator (AI), where the Bi$_2$Te$_3$ layer introduces versatility to engineer electronic and magnetic properties. However, whether surface states on the Bi$_2$Te$_3$ terminated facet are gapless or gapped is debated, and its consequences in thin-film properties are rarely discussed. In this work, we find that the Bi$_2$Te$_3$ terminated facets are gapless for $n \ge 1$ compounds by calculations. Despite …

三维绝缘体中的自旋分辨拓扑与部分轴子角

Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators

本文通过嵌套自旋分辨Wilson环和层构造，揭示三维螺旋高阶拓扑晶体绝缘体可实现三维量子自旋霍尔绝缘体、自旋-Weyl半金属和T-DAXI态，并在β-MoTe₂和α-BiBr中验证了这些相。

Part II: Witten effect and $\mathbb{Z}$-classification of axion angle $θ=n π$

The non-trivial third homotopy class of three-dimensional topological insulators leads to quantized, magneto-electric coefficient or axion angle $θ= n π$, with $n \in \mathbb{Z}$. In Part I, we developed tools for computing $n$ from a staggered symmetry-indicator $κ_{AF,j}$ and Wilson loops of non-Abelian, Berry connection in momentum-space, which clearly distinguished between magneto-electrically trivial ($n=0$), and non-trivial ($n=2s$) topological crystalline insulators. In this work, we perform $\mathbb{Z}$-classification of real-space, topological response or $θ$ by carrying out thought e…

Higher-order topological phase without crystalline symmetry

A wide variety of higher-order symmetry protected topological phase(HOSPT) with gapless corners or hinges had been proposed as a descendant of topological crystalline insulator protected by spatial symmetry. In this work, we address a new class of higher-order topological state which does not require crystalline symmetries but instead relies on subsystem symmetry for protection. We propose several strong interacting models with gapless hinge or corner based on a `decorated hinge-wall condensate' picture. The hinge-wall, which appears as the defect configuration of $Z_2$ paramagnet is decorated…

无耗散拓扑电子学的规则

Rules for dissipationless topotronics

本研究针对拓扑系统电输运中存在能量耗散的问题，提出无耗散设计的模式数匹配判据，指出高陈数Chern绝缘体的必要性，并设计出满足判据的无耗散拓扑分流与集流器件，为拓扑电子学发展奠定基础。

Weyl semimetals with short-range interactions

We construct a low-energy effective field theory of electrons interacting via short-range interactions in a Weyl semimetal and investigate possible broken-symmetry ground states through an unbiased one-loop renormalization group (RG) analysis. Using the symmetries of the noninteracting Weyl semimetal to constrain the form of the interaction term leads to four independent coupling constants. We investigate the stability of RG flows towards strong coupling and find a single stable trajectory. In order to determine the most likely broken-symmetry ground state, we calculate susceptibilities in the…