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.

20 pages, 7 figures

References in corpus (22)

• Universal Dynamic Conductivity and Quantized Visible Opacity of Suspended Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• 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
• One-dimensional Topological Edge States of Bismuth Bilayers
• Robustness of the Spin-Chern number
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Sign Changes of Intrinsic Spin Hall Effect in Semiconductors and Simple Metals: First-Principles Calculations
• Dichroic f-sum rule and the orbital magnetization of crystals
• Topological aspects of quantum spin Hall effect in graphene: Z${}_2$ topological order and spin Chern number
• Gapped Electronic Structure of Epitaxial Stanene on InSb(111)
• Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
• Universality classes of topological phase transitions with higher-order band crossing
• Measurement of Topological Order based on Metric-Curvature Correspondence
• Universal topological marker
• Unification of topological invariants in Dirac models
• 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