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 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.

Probing Chern number by opacity and topological phase transition by a nonlocal Chern marker

“…We also showed that the nonlocal Chern marker becomes increasingly long-ranged as TPTs are approached. Finally, we remark that the notions introduced in the present work have been recently generalized to TR symmetric 2D systems like the Bernevig-Hughes-Zhang model [58]described by spin Chern numbers and markers [59]. We anticipate that these new aspects may be widely applied to investigate the influence of real space inhomogeneities on both bulk topology and the critical behavior near TPTs.…”

Quantum Optics Measurement Scheme for Quantum Geometry and Topological Invariants

“…To this end, several schemes utilizing linear response for the measurement of quantum geometry have been proposed [16][17][18][19][20]. However, while the spectroscopy of topological states of matter using semiclassical descriptions has been studied extensively [19][20][21][22][23][24], the quantum optics side is less explored. In quantum optics, entanglement between light and matter can lead to novel phenomena [25][26][27][28], and it can imprint properties of the matter system into the photon field.…”