Non-equilibrium topological phenomena can be induced in quantum many-body systems using time-periodic fields (for example, by laser or microwave illumination). This Review begins with the key principles underlying Floquet band engineering, wherein such fields are used to change the topological properties of a system’s single-particle spectrum. In contrast to equilibrium systems, non-trivial band structure topology in a driven many-body system does not guarantee that robust topological behaviour will be observed. In particular, periodically driven many-body systems tend to absorb energy from their driving fields and thereby tend to heat up. We survey various strategies for overcoming this challenge of heating and for obtaining new topological phenomena in this non-equilibrium setting. We describe how drive-induced topological edge states can be probed in the regime of mesoscopic transport, and three routes for observing topological phenomena beyond the mesoscopic regime: long-lived transient dynamics and prethermalization, disorder-induced many-body localization, and engineered couplings to external baths. We discuss the types of phenomena that can be explored in each of the regimes covered, and their experimental realizations in solid-state, cold atomic, and photonic systems. Time-periodic fields provide a versatile platform for inducing non-equilibrium topological phenomena in quantum systems. We discuss how such fields can be used for topological band structure engineering, and the conditions for observing robust topological behaviour in a many-body setting.

Band structure engineering and non-equilibrium dynamics in Floquet topological insulators

Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems with exotic properties In particular, it has been employed to study topological phenomena in a variety of different platforms In driven systems, the topological properties of the quasienergy bands can often be determined by standard topological invariants, such as Chern numbers, which are commonly used in static systems However, due to the periodic nature of the quasienergy spectrum, this topological description is incomplete and new invariants are required to fully capture the topological properties of these driven settings Most prominently, there are two-dimensional anomalous Floquet systems that exhibit robust chiral edge modes, despite all Chern numbers being equal to zero Here we realize such a system with bosonic atoms in a periodically driven honeycomb lattice and infer the complete set of topological invariants from energy gap measurements and local Hall deflections Standard topological invariants commonly used in static systems are not enough to fully capture the topological properties of Floquet systems In a periodically driven quantum gas, chiral edge modes emerge despite all Chern numbers being equal to zero

Realization of an anomalous Floquet topological system with ultracold atoms

Strong light–matter coupling in quantum cavities provides a pathway to break fundamental materials symmetries, like time-reversal symmetry in chiral cavities. This Comment discusses the potential to realize non-equilibrium states of matter that have so far been only accessible in ultrafast and ultrastrong laser-driven materials.

/pdf/engineering-quantum-materials-with-chiral-optical-cavities-264ir6faju.pdf

Engineering quantum materials with chiral optical cavities

Ultrafast laser pulses can be used to drive materials into nonequilibrium states that have unusual properties and are promising for technological applications. Different classes of phenomena are observed during and after the optical illumination. This Colloquium discusses the recent developments in this field, and the prospects for using these techniques to create materials with novel functionalities in a controlled way.

/pdf/colloquium-nonthermal-pathways-to-ultrafast-control-in-soapk6o8gk.pdf

Colloquium: Nonthermal pathways to ultrafast control in quantum materials

The dynamics of a vortex in a thin-film ferromagnet resembles the motion of a charged massless particle in a uniform magnetic field. Similar dynamics is expected for other magnetic textures with a nonzero Skyrmion number. However, recent numerical simulations reveal that Skyrmion magnetic bubbles show significant deviations from this model. We show that a Skyrmion bubble possesses inertia and derive its mass from the standard theory of a thin-film ferromagnet. In addition to center-of-mass motion, other low energy modes are waves on the edge of the bubble traveling with different speeds in opposite directions.

http://absimage.aps.org/image/MAR13/MWS_MAR13-2012-007691.pdf

Inertia and chiral edge modes of a skyrmion magnetic bubble

Many non-equilibrium phenomena have been discovered or predicted in optically driven quantum solids1. Examples include light-induced superconductivity2,3 and Floquet-engineered topological phases4–8. These are short-lived effects that should lead to measurable changes in electrical transport, which can be characterized using an ultrafast device architecture based on photoconductive switches9. Here, we report the observation of a light-induced anomalous Hall effect in monolayer graphene driven by a femtosecond pulse of circularly polarized light. The dependence of the effect on a gate potential used to tune the Fermi level reveals multiple features that reflect a Floquet-engineered topological band structure4,5, similar to the band structure originally proposed by Haldane10. This includes an approximately 60 meV wide conductance plateau centred at the Dirac point, where a gap of equal magnitude is predicted to open. We find that when the Fermi level lies within this plateau the estimated anomalous Hall conductance saturates around 1.8 ± 0.4 e2/h. A transient topological response in graphene is driven by a short pulse of light. When the Fermi energy is in the predicted band gap the Hall conductance is around two conductance quanta. An ultrafast detection technique enables the measurement.

/pdf/light-induced-anomalous-hall-effect-in-graphene-4m1acwe9gt.pdf

Light-induced anomalous Hall effect in graphene.

Many striking non-equilibrium phenomena have been discovered or predicted in optically-driven quantum solids, ranging from light-induced superconductivity to Floquet-engineered topological phases. These effects are expected to lead to dramatic changes in electrical transport, but can only be comprehensively characterized or functionalized with a direct interface to electrical devices that operate at ultrafast speeds. Here, we make use of laser-triggered photoconductive switches to measure the ultrafast transport properties of monolayer graphene, driven by a mid-infrared femtosecond pulse of circularly polarized light. The goal of this experiment is to probe the transport signatures of a predicted light-induced topological band structure in graphene, similar to the one originally proposed by Haldane. We report the observation of an anomalous Hall effect in the absence of an applied magnetic field. We also extract quantitative properties of the non-equilibrium state. The dependence of the effect on a gate potential used to tune the Fermi level reveals multiple features that reflect the effective band structure expected from Floquet theory. This includes a ~60 meV wide conductance plateau centered at the Dirac point, where a gap of approximately equal magnitude is expected to open. We also find that when the Fermi level lies within this plateau, the estimated anomalous Hall conductance saturates around ~1.8$\pm$0.4 e$^2$/h.

/pdf/light-induced-anomalous-hall-effect-in-graphene-19qask2vro.pdf

Light-induced anomalous Hall effect in graphene

The dynamics of emergent magnetic quasiparticles, such as vortices, domain walls, and bubbles are studied by scanning transmission x-ray microscopy (STXM), combining magnetic (XMCD) contrast with about 25 nm lateral resolution as well as 70 ps time resolution. Essential progress in the understanding of magnetic vortex dynamics is achieved by vortex core reversal observed by sub-GHz excitation of the vortex gyromode, either by ac magnetic fields or spin transfer torque. The basic switching scheme for this vortex core reversal is the generation of a vortex-antivortex pair. Much faster vortex core reversal is obtained by exciting azimuthal spin wave modes with (multi-GHz) rotating magnetic fields or orthogonal monopolar field pulses in x and y direction, down to 45 ps in duration. In that way unidirectional vortex core reversal to the vortex core 'down' or 'up' state only can be achieved with switching times well below 100 ps. Coupled modes of interacting vortices mimic crystal properties. The individual vortex oscillators determine the properties of the ensemble, where the gyrotropic mode represents the fundamental excitation. By self-organized state formation we investigate distinct vortex core polarization configurations and understand these eigenmodes in an extended Thiele model. Analogies with photonic crystals are drawn. Oersted fields and spin-polarized currents are used to excite the dynamics of domain walls and magnetic bubbles. From the measured phase and amplitude of the displacement of domain walls we deduce the size of the non-adiabatic spin-transfer torque. For sensing applications, the displacement of domain walls is studied and a direct correlation between domain wall velocity and spin structure is found. Finally the synchronous displacement of multiple domain walls using perpendicular field pulses is demonstrated as a possible paradigm shift for magnetic memory and logic applications.

/pdf/imaging-spin-dynamics-on-the-nanoscale-using-x-ray-3qpdcokrry.pdf

Imaging spin dynamics on the nanoscale using X-ray microscopy

In ferromagnetic nanostructures domain walls as emergent entities separate uniformly magnetized regions. They are describable as quasi particles and can be controlled by magnetic fields or spin-polarized currents. Below critical driving forces domain walls are rigid conserving their spin structure. Like other quasi particles internal excitations influence the domain wall dynamics above a critical velocity known as the Walker breakdown. This complex nonlinear motion has not been observed directly. Here we present direct time-resolved x-ray microscopy of structural transformations of domain walls during motion. Although governed by nonlinear dynamics the displacement of the wall on the observed time scale can still be described by an analytical model. Using a reduced dynamical domain-wall width the model enables us to determine the mass of a vortex wall experimentally. Further we observe the creation and the mutual annihilation of domain walls. The intrinsic nanometer length and nanosecond time-scales are determined directly.

/pdf/time-resolved-imaging-of-nonlinear-magnetic-domain-wall-3j0puijrwt.pdf

Time-resolved imaging of nonlinear magnetic domain-wall dynamics in ferromagnetic nanowires

We study the creation and annihilation of domain walls in a permalloy nanowire by local Oersted fields of current pulses passing through a perpendicularly aligned stripline. The occurrence of both processes is investigated for current pulses of different polarities and for various external magnetic fields. Reliable creation and annihilation are achieved for small and zero external fields, while higher externally applied fields lead to the suppression of both processes as well as to the creation of multiple domain walls in the wire.

Falk-Ulrich Stein

Papers

Light-induced anomalous Hall effect in graphene.

Light-induced anomalous Hall effect in graphene

Imaging spin dynamics on the nanoscale using X-ray microscopy

Time-resolved imaging of nonlinear magnetic domain-wall dynamics in ferromagnetic nanowires

Generation and annihilation of domain walls in nanowires by localized fields