Classification of Fragile Topology Enabled by Matrix Homotopy

Ki Young Lee; Stephan Wong; Sachin Vaidya; Terry A. Loring; Alexander Cerjan

doi:10.1103/PhysRevLett.61.2015

Paper details

Research paper

TheoreticalComputational

Classification of Fragile Topology Enabled by Matrix Homotopy

Ki Young Lee, Stephan Wong, Sachin Vaidya, Terry A. Loring et al.

arXiv·2025·arXiv:2503.03948

Samples

Each sample groups how it was prepared, characterized, and measured. Click a card to expand.

Finite C₂T-symmetric four-band twisted bilayer graphene model used to evaluate the position-space fragile-topology marker under varying hopping phase and disorder.

1 characterization4 properties2 figures

SimulatedCStudied Material

Two-dimensional photonic crystal embedded in an air background used as a continuum example of fragile topology classification.

1 characterization1 figure

Simulatedphotonic crystalStudied MaterialN/ASubstrate / Dielectric

Materials

graphene

Studied Material

Also known as

twisted bilayer graphene layer constituent

studied material

twisted bilayer graphene

Studied Material

Also known as

Why these are connected

Related documents with shared materials, methods, properties, or citations.

Classification of Fragile Topology Enabled by Matrix Homotopy | Matter42 Literature

Properties

Type	Label	Value	Material	Sample	Source
Topological Transition Point	NNN hopping phase ϕ at first bulk-gap closing	π/3rad	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—
Topological Transition Point	NNN hopping phase ϕ at second bulk-gap closing	2π/3rad	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—
Topological Marker State	fragile topology marker ζ_E	-1	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—
Topological Marker State	fragile topology marker ζ_E	1	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—

Properties

Type	Label	Value	Material	Sample	Source
Topological Transition Point	NNN hopping phase ϕ at first bulk-gap closing	π/3rad	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—
Topological Transition Point	NNN hopping phase ϕ at second bulk-gap closing	2π/3rad	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—
Topological Marker State	fragile topology marker ζ_E	-1	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—
Topological Marker State	fragile topology marker ζ_E	1	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—

Properties

Type	Label	Value	Material	Sample	Source
Topological Transition Point	NNN hopping phase ϕ at first bulk-gap closing	π/3rad	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—
Topological Transition Point	NNN hopping phase ϕ at second bulk-gap closing	2π/3rad	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—
Topological Marker State	fragile topology marker ζ_E	-1	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—
Topological Marker State	fragile topology marker ζ_E	1	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—

Properties

Type	Label	Value	Material	Sample	Source
Topological Transition Point	NNN hopping phase ϕ at first bulk-gap closing	π/3rad	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—
Topological Transition Point	NNN hopping phase ϕ at second bulk-gap closing	2π/3rad	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—
Topological Marker State	fragile topology marker ζ_E	-1	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—
Topological Marker State	fragile topology marker ζ_E	1	C	Finite C₂T-symmetric four-band twisted bilayer graphene mode	—

Classification of Fragile Topology Enabled by Matrix Homotopy

Samples

Finite C₂T-symmetric four-band twisted bilayer graphene model used to evaluate the position-space fragile-topology marker under varying hopping phase and disorder.

Two-dimensional photonic crystal embedded in an air background used as a continuum example of fragile topology classification.

Materials

Why these are connected

Classification of Fragile Topology Enabled by Matrix Homotopy

Samples

Finite C₂T-symmetric four-band twisted bilayer graphene model used to evaluate the position-space fragile-topology marker under varying hopping phase and disorder.

Two-dimensional photonic crystal embedded in an air background used as a continuum example of fragile topology classification.

Materials

Why these are connected

Classification of Fragile Topology Enabled by Matrix Homotopy

Samples

Finite C₂T-symmetric four-band twisted bilayer graphene model used to evaluate the position-space fragile-topology marker under varying hopping phase and disorder.

Two-dimensional photonic crystal embedded in an air background used as a continuum example of fragile topology classification.

Materials

Why these are connected

Classification of Fragile Topology Enabled by Matrix Homotopy

Samples

Finite C₂T-symmetric four-band twisted bilayer graphene model used to evaluate the position-space fragile-topology marker under varying hopping phase and disorder.

Two-dimensional photonic crystal embedded in an air background used as a continuum example of fragile topology classification.

Materials

Why these are connected

Classification of Fragile Topology Enabled by Matrix Homotopy

Samples

Finite C₂T-symmetric four-band twisted bilayer graphene model used to evaluate the position-space fragile-topology marker under varying hopping phase and disorder.

Two-dimensional photonic crystal embedded in an air background used as a continuum example of fragile topology classification.

Materials

Why these are connected

Classification of Fragile Topology Enabled by Matrix Homotopy

Samples

Finite C₂T-symmetric four-band twisted bilayer graphene model used to evaluate the position-space fragile-topology marker under varying hopping phase and disorder.

Two-dimensional photonic crystal embedded in an air background used as a continuum example of fragile topology classification.

Materials

Why these are connected

Classification of Fragile Topology Enabled by Matrix Homotopy

Samples

Finite C₂T-symmetric four-band twisted bilayer graphene model used to evaluate the position-space fragile-topology marker under varying hopping phase and disorder.

Two-dimensional photonic crystal embedded in an air background used as a continuum example of fragile topology classification.

Materials

Why these are connected

Classification of Fragile Topology Enabled by Matrix Homotopy

Samples

Finite C₂T-symmetric four-band twisted bilayer graphene model used to evaluate the position-space fragile-topology marker under varying hopping phase and disorder.

Two-dimensional photonic crystal embedded in an air background used as a continuum example of fragile topology classification.

Materials

Why these are connected

Characterization

Properties

Simulations

Characterization

Properties

Simulations

Characterization

Properties

Simulations

Characterization

Properties

Simulations