Higher order topological matter and fractional chiral states

Abstract

We develop a chiral anomalous fermion hamiltonian proposal to study the higher order topological (HOT) phase with chiral symmetry $\mathcal{C}$ fractionalized like ${\mathcal{C}}_x{\mathcal{C}}_y{\mathcal{C}}_z$. First, we solve the $\mathcal{C}$-chiral symmetry constraint for eight band models and describe those induced by the partial ${\mathcal{C}}_i$'s. Then, we determine the explicit expression of fractional states characterising HOT matter and comment on the relationships amongst them and with the standard Altland-Zirnbauer gapless modes. We also give characteristic properties of the gapless fractional states and compute their contribution to the topological index of the chiral model. The findings of this work are shown to be crucial for investigating and handling high order topological phase.

arXiv comment18 PAGES, 3 Figures

References in corpus (42)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantized Electric Multipole Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Symmetry protected topological orders and the group cohomology of their symmetry group
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Structural and Electronic Properties of Oxidized Graphene
• Electronic transport and quantum Hall effect in bipolar graphene p-n-p junction
• Fermion Path Integrals And Topological Phases
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Higher Order Topological Phases: A General Principle of Construction
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Lattice models with exactly solvable topological hinge and corner states
• Many-Body Order Parameters for Multipoles in Solids
• Higher-order Floquet topological phases with corner and bulk bound states
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Creutz Fermions on an Orthogonal Lattice
• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Three-dimensional superconductors with hybrid higher order topology
• Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology
• Electronic Properties and Hidden Symmetries of Graphene
• Aoki Phases in the Lattice Gross-Neveu Model with Flavored Mass terms
• Search for Fermion Actions on Hyperdiamond Lattices
• Lattice Fermions Based on Higher-Dimensional Hyperdiamond Lattices
• Four Dimensional Graphene
• Topological stability of Majorana zero-modes in superconductor-topological insulator systems
• On Dirac Zero Modes in Hyperdiamond Model
• Scaling of polarization amplitude in quantum many-body systems in one dimension
• Topological invariant for two-dimensional open systems
• A Dirac fermion model associated with second order topological insulator
• Topological Aspects of Fermions on Hyperdiamond
• Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S>1$): Quantized Berry phase and valence-bond solids
• Anomalous Quantum Hall Effect of 4D Graphene in Background Fields
• Supersymmetry in 6d Dirac Action
• Gapped gravitinos, isospin $\frac{1}{2}$ particles and $\mathcal{N}=2$ partial breaking

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