Radiation-induced dynamical formation of Floquet-Bloch bands in Dirac Hamiltonians

TL;DR

This paper extends Floquet theory to analyze how short, intense laser pulses induce transient Floquet-Bloch bands in Dirac materials, revealing polarization-dependent sideband formation in systems like graphene and topological insulators.

Contribution

It introduces a generalized Floquet-$t-t'$ formalism to study non-strictly periodic driving fields and analyzes the dynamical formation of Floquet-Bloch bands in Dirac Hamiltonians with realistic pulse envelopes.

Findings

Circular polarization induces sidebands in linear Dirac systems.

Both linear and circular pulses excite sidebands in warped Dirac systems.

The formalism links transient spectral features to pulse shape and polarization.

Abstract

Recent experiments, combing ultrafast strong-field irradiation of surfaces with time- and angle-resolved photoemission spectroscopy, allow for monitoring the time-dependent charge carrier dynamics and the build-up of transient sidebands due to the radiation pulses. While these structures are reminiscent of Floquet-Bloch bands, standard Floquet theory is not applicable since it requires a strictly time-periodic driving field. To study the emergence and formation of such sidebands, i.e. to provide a link between common Floquet physics and dynamical mechanisms underlying short driving pulses, we consider a generalization of Floquet theory, the so-called $t-t^{\prime}$ formalism. This approach naturally extents Floquet theory to driving field amplitudes with a superimposed envelope shape. Motivated by experiments we study 2D Dirac Hamiltonians subject to linearly and circularly polarised light waves with a Gaussian field envelope of a few cycles. For these Floquet-Bloch Hamiltonians we study the evolution of their Floquet-Bloch spectra, accompanied by a systematic analysis of the time-dependent (sideband) transitions. We show that sideband occupation requires circularly polarized light for linear Dirac systems such as graphene, while for Dirac models with trigonal warping, describing surface states of topological insulators such as Bi$_2$ Se$_3$, both linearly and circularly polarised pulses induce sideband excitations.