Optical absorption measurement of spin Berry curvature and spin Chern marker

Abstract

In two-dimensional time-reversal symmetric topological insulators described by Dirac models, the ${\mathbb{Z}}_2$ topological invariant can be described by the spin Chern number. We present a linear response theory for the spin Berry curvature that integrates to the spin Chern number, and introduce its spectral function that can be measured at finite temperature by momentum- and spin-resolved circular dichroism, which may be achieved by pump-probe type of experiments using spin- and time-resolved ARPES. As a result, the sign of the Pfaffian of the ${\mathbb{Z}}_2$ invariant can be directly measured. The spin Chern number expressed in real space yields a spin Chern marker, whose spatial variation may be measured by circular dichroism and spin-resolved photoemission with a spatial resolution. A spin Chern correlator and a nonlocal spin Chern marker are further proposed to characterize the quantum criticality near topological phase transitions, which are shown to take the form of overlaps between spin-selected Wannier states.

arXiv comment20 pages, 7 figures

References in corpus (50)

• Universal Dynamic Conductivity and Quantized Visible Opacity of Suspended Graphene
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Maximally-localized generalized Wannier functions for composite energy bands
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Maximally localized Wannier functions: Theory and applications
• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Bismuthene on a SiC Substrate: A Candidate for a New High-Temperature Quantum Spin Hall Paradigm
• Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells
• Realization of Quantum Spin Hall State in Monolayer 1T'-WTe2
• Observation of the Quantum Spin Hall Effect up to 100 Kelvin in a Monolayer Crystal
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Edge conduction in monolayer WTe2
• Ab initio calculation of the anomalous Hall conductivity by Wannier interpolation
• Near-field heat transfer in a scanning thermal microscope
• One-dimensional Topological Edge States of Bismuth Bilayers
• Robustness of the Spin-Chern number
• Angle Dependent Van Hove Singularities in Slightly Twisted Graphene Bilayer
• Mapping topological order in coordinate space
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Observation of topological states residing at step edges of WTe2
• Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
• Sign Changes of Intrinsic Spin Hall Effect in Semiconductors and Simple Metals: First-Principles Calculations
• Imaging Quantum Spin Hall Edges in Monolayer WTe2
• Disordered Topological Insulators: A Non-Commutative Geometry Perspective
• Direct Visualization of 2D Topological Insulator in Single-layer 1T'-WTe2
• Dichroic f-sum rule and the orbital magnetization of crystals
• Extracting the quantum metric tensor through periodic driving
• Topological aspects of quantum spin Hall effect in graphene: Z${}_2$ topological order and spin Chern number
• Theory of spin Bott index for quantum spin Hall states in non-periodic systems
• Gapped Electronic Structure of Epitaxial Stanene on InSb(111)
• Non-Commutative Tools for Topological Insulators
• Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
• Orbital Magnetization as a Local Property
• Detecting fractional Chern insulators through circular dichroism
• Universality classes of topological phase transitions with higher-order band crossing
• Measurement of Topological Order based on Metric-Curvature Correspondence
• Locality of the anomalous Hall conductivity
• Universal topological marker
• Unification of topological invariants in Dirac models
• Absence of equilibrium edge currents in theoretical models of topological insulators
• Slow quenches in two-dimensional time-reversal symmetric Z2 topological insulators
• Two-Dimensional Large Gap Topological Insulators with Large Rashba Spin-Orbit Coupling in Group-IV films
• Global and Local Topological Quantized Responses from Geometry, Light and Time

Cited by in corpus (9)

• Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker
• Probing Chern number by opacity and topological phase transition by a nonlocal Chern marker
• Quantum optics measurement scheme for quantum geometry and topological invariants
• Theory of local ${\mathbb{Z}}_2$ topological markers for finite and periodic two-dimensional systems
• Controlling the orbital Hall effect in gapped bilayer graphene in the terahertz regime
• Detecting the spread of valence band Wannier functions by optical sum rules
• Quantum geometrical properties of topological materials
• Topological Phases in Fractals: Local Spin Chern Marker in the Sierpinski carpet Kane-Mele-Rashba Model
• Topological characterization of modified Kane-Mele-Rashba models via local spin Chern marker