Topological phase transitions via attosecond x-ray absorption spectroscopy

TL;DR

This work demonstrates that attosecond x-ray absorption spectroscopy can directly probe topological phase transitions in a Chern insulator described by a Haldane Hamiltonian with tunable second-order hopping $t_2$ (relative to $t_s=\Delta/(6\sqrt{3})$). By combining EDUS-based out-of-equilibrium simulations with a semiclassical trajectory framework, the authors show that laser-induced x-ray dichroism—differences in absorption for left- vs right-handed IR polarization—produces signatures localized at van Hove singularities that track the Berry structure of the conduction band. A saddle-point approximation provides physical insight, revealing that intra-band Berry connections and dispersion primarily shape the recollision dynamics and thus the dichroic spectrum, with Berry curvature flipping sign across the topological transition. The results offer a practical route to characterize transient topological states and Berry-related properties in 2D materials and Floquet-like systems, with potential implications for ultrafast optoelectronics.

Abstract

We present a numerical experiment that demonstrates the possibility to capture topological phase transitions via an x-ray absorption spectroscopy scheme. We consider a Chern insulator whose topological phase is tuned via a second-order hopping. We perform time-dynamics simulations of the out-of-equilibrium laser-driven electron motion that enables us to model a realistic attosecond spectroscopy scheme. In particular, we use an ultrafast scheme with a circularly polarized IR pump pulse and an attosecond x-ray probe pulse. A laser-induced dichroism-type spectrum shows a clear signature of the topological phase transition. We are able to connect these signatures with the Berry structure of the system. This work extend the applications of attosecond absorption spectroscopy to systems presenting a non-trivial topological phase.

Figures (6)

• Figure 1: Ultrafast x-ray scheme and system under investigation. (a) Two ultrashort laser pulses, separated by a time delay, interact with a boron nitride monolayer. The pump pulse is in the range of mid IR and is circularly polarized, and it is intense in order to drive a strong intra-band current. The probe pulse is in the range of soft x-rays and is linearly polarized, and it excites transitions from the K-edge of boron. (b) Graphical representation of the first ($\gamma$) and second order hopping ($t_2e^{\pm i\phi_0}$) terms between different lattice sites. (c), (d) and (e) represent the energy dispersion of the system. The red and blue arrows represent the IR and x-ray transitions, respectively. The IR pulse couples the conduction and valence bands, while the x-ray pulse couples the core band (1s orbital of boron) with the bands around the Fermi level. The second-order hopping $t_2$ controls the topological phase, which depends on the parameter $t_s=\Delta/6\sqrt{3}$, being $\Delta$ the gap of the system without second-order hopping. (b) and (d) are insulators with a trivial and non-trivial topology, respectively, and their direct bandgap is the same. In (d) the conduction and valence bands join at the K point.
• Figure 2: Laser-induced x-ray absorption dichroism for different topological phases (a) $t_2= \frac{1}{2}t_s$, (b) $t_2= \frac{3}{4}t_s$, (c) $t_2= \frac{5}{4}t_s$, and (d) $t_2= \frac{3}{2}t_s$. The changes are localized around van Hove singularities (K, K', M', and $\Gamma$ points). $\Delta A$ expressed in percentage indicates the difference of absorption intensity normalized with respect to the maximum absorption calculated without the presence of the IR pulse.
• Figure 3: Energy dispersion of the conduction band for (a) $t_2= \frac{1}{2}t_s$, (b) $t_2= \frac{3}{4}t_s$, (c) $t_2= \frac{5}{4}t_s$, and (d) $t_2= \frac{3}{2}t_s$. M' is a saddle point and changes with $t_2$. Note that the energy color scale takes as a 0-eV reference the K point, in which the direct gap is located for each case.
• Figure 4: Laser-induced x-ray absorption dichroism for different pump-probe time delays. (a) Scheme of the IR pumb pulse for right- and left-handed polarized fields. Ultrafast laser-induced x-ray dichroism for (b) a trivial, $t_2= \frac{1}{2}t_s$, and (c) a topological, $t_2= \frac{3}{2}t_s$, phase. The density of states (DOS) is represented on the side.
• Figure 5: Semiclassical approach for the laser-induced x-ray dichroism. (a),(b) Comparison of the laser-induced x-ray dichroism between first-principle and semiclassical calculations for trivial $t_2= \frac{1}{2}t_s$ and topological $t_2= \frac{3}{2}t_s$ phases. (c),(d) The laser-induced x-ray dichroism computed by the semiclassical approach with and without considering the Berry structure for trivial and topological phases. The red (black) line is when energy and Berry phase are included (when energy is only included) in the accumulated dynamical phase, see Eq. (\ref{['eq:phase']}).