In two-dimensional time-reversal symmetric topological insulators described by Dirac models, the 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 invariant can be directly measured. A spin Chern number spectral function is further introduced from the optical spin current response, and is shown to be measurable from the spin-resolved opacity of two-dimensional materials under circularly polarized light, pointing to an optical measurement of the invariant and a frequency sum rule. The spin Chern number expressed in real space is known to yield a spin Chern marker, and we propose that it may be measurable from spin-resolved local heating rate caused by circularly polarized light. A nonlocal spin Chern marker is further proposed to characterize the quantum criticality near topological phase transitions, and is shown to be equivalent to an overlap between spin-selected Wannier states.
Correlated electron systems

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Optical absorption measurement of spin Berry curvature and spin Chern marker
Wei Chen 2023 J. Phys.: Condens. Matter 35 155601
In two-dimensional time-reversal symmetric topological insulators described by Dirac models, the ℤ2 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 ℤ2 invariant can be directly measured. A spin Chern number spectral function is further introduced from the optical spin current response, and is shown to be measurable from the spin-resolved opacity of two-dimensional materials under circularly polarized light, pointing to an optical measurement of the ℤ2 invariant and a frequency sum rule. The spin Chern number expressed in real space is known to yield a spin Chern marker, and we propose that it may be measurable from spin-resolved local heating rate caused by circularly polarized light. A nonlocal spin Chern marker is further proposed to characterize the quantum criticality near topological phase transitions, and is shown to be equivalent to an overlap between spin-selected Wannier states
Section scope
- Topological insulators
- Superconductors and superconductivity
- Heavy fermion physics
- Metal-insulator transitions
- Quantum phase transitions and quantum criticality
- Quantum dynamics of correlated matter
- Correlated atoms in optical lattices
- Non-Fermi liquid phenomena
- Electron-phonon coupling
Section editor

Krishnendu Sengupta Indian Association for the Cultivation of Science, India
Krishnendu is a Professor of Physics at the Theoretical Physics Department, Indian Association for the Cultivation of Science, Kolkata.
His research interests include physics of ultracold atoms, quantum transport in Dirac materials, and non-equilibrium quantum dynamics of strongly
correlated systems.