Tracing the nonequilibrium topological state of Chern insulators

Chern insulators exhibit fascinating properties, which originate from the topologically nontrivial state characterized by the Chern number. How these properties change if the system is quenched between topologically distinct phases is, however, not fully understood. In this paper, we investigate the quench dynamics of the prototypical massive Dirac model for topological insulators in two dimensions. We consider both dissipationless dynamics and the effect of electron-phonon interactions, and ask how the transient dynamics and nonequilibrium steady states affect simple observables. Specifically, we discuss a time-dependent generalization of the Hall effect and the dichroism of the photoexcitation probability between left and right circularly polarized light. We present optimized schemes based on these observables, which can reveal the evolution of the topological state of the quenched system

Calciumorganic compounds: from curiosity to ubiquity (CalCub)

Zielsetzung der Dissertation ist die Etablierung neuer Synthesemethoden zu calciumorganischen Verbindungen. Einfache Zugangangswege vergrößern das Anwendungsfeld dieser, da die Synthesen auch in Laboratorien ausgeführt werden können, die nur eine grundlegende Inert-Arbeitsweise verfolgen. In der metallorganischen Chemie der s-Blockmetalle spielen „Plattformchemikalien“ eine zentrale Rolle. So sind z. B. n-BuLi, K(hmds) oder Mg(Bu)2 durch ihre kommerzielle Verfügbarkeit in jedem Syntheselabor zu finden. Für die schweren Erdalkalimetalle ist derzeit keine solche Verbindung kommerziell verfügbar. Gleichzeitig ist der Anspruch an die Planung neuer Synthesewege und das Design von breit einsetzbaren metallorganischen Reagenzien gestiegen. Neben rein chemischen Aspekten wie guter Löslichkeit in vielen organischen Lösungsmitteln, einer hohen Basenstärke und Langzeitstabilität sind ökologische Aspekte wie Anzahl der Synthesestufen, Atomeffizienz der Synthese, Toxizität der Metalle und Ressourcenschonung von großer Bedeutung. Die Reaktion von Calciummetall mit Ethylbromid und (H)hmds in THF liefert in sehr guten Ausbeuten (>95%) [(thf)2Ca(hmds)2] und [(thf)4CaBr2]. Aufgrund der angenommenen Bildung einer Calcium-GRIGNARD-Verbindung als intermediäres Metallierungsreagenz wurde die Methode als in situ GRIGNARD-Metallierungsmethode (iGMM) in die Literatur eingeführt. Basierend auf dieser Reaktion wurde das Substratspektrum und die Reaktivität der gebildeten Verbindungen untersucht

Quantum optics measurement scheme for quantum geometry and topological invariants

We show how a quantum optical measurement scheme based on heterodyne detection can be used to explore geometrical and topological properties of condensed matter systems. Considering a 2D material placed in a cavity with a coupling to the environment, we compute correlation functions of the photons exiting the cavity and relate them to the hybrid light-matter state within the cavity. Different polarizations of the intracavity field give access to all components of the quantum geometric tensor on contours in the Brillouin zone defined by the transition energy. Combining recent results based on the metric-curvature correspondence with the measured quantum metric allows us to characterize the topological phase of the material. Moreover, in systems where $S_z$ is a good quantum number, the procedure also allows us to extract the spin Chern number. As an interesting application, we consider a minimal model for twisted bilayer graphene at the magic angle, and discuss the feasibility of extracting the Euler number.Comment: 16 pages, 4 figure

Nonthermal switching of charge order: Dynamical slowing down and optimal control

We investigate the laser-induced dynamics of electronically driven charge-density- wave (CDW) order. A comprehensive mean-field analysis of the attractive Hubbard model in the weak-coupling regime reveals ultrafast switching and ultrafast melting of the order via a nonthermal pathway. The resulting nonequilibrium phase diagram exhibits multiple distinct regimes of the order parameter dynamics upon increasing field strength, indicative of multiple dynamical phase transitions. Using an intuitive pseudospin picture, we show how the distinct dynamical regimes can be connected to the spin precession angle. We furthermore study the effects of electron-electron interactions beyond mean field to show that the main features of the phase diagram are robust against scattering or thermalization processes. For example, the nonthermal state with switched order is characterized by a particularly slow relaxation. The nonthermal phases can be stabilized by tailoring the pulse shape with optimal control theory. We also demonstrate how the dynamics allows to distinguish an electron-electron interaction driven CDW from an electron-phonon interaction driven CDW

One‐Step Synthesis and Schlenk‐Type Equilibrium of Cyclopentadienylmagnesium Bromides

Abstract In the in situ Grignard metalation method (iGMM), the addition of bromoethane to a suspension of magnesium turnings and cyclopentadienes [C 5 H 6 (HCp), C 5 H 5 ‐Si( i Pr) 3 (HCp TIPS )] in diethyl ether smoothly yields heteroleptic [(Et 2 O)Mg(Cp R )(μ‐Br)] 2 (Cp R =Cp ( 1 ), Cp TIPS ( 2 )). The Schlenk equilibrium of 2 in toluene leads to ligand exchange and formation of homoleptic [Mg(Cp R ) 2 ] ( 3 ) and [(Et 2 O)MgBr(μ‐Br)] 2 ( 4 ). Interfering solvation and aggregation as well as ligand redistribution equilibria hamper a quantitative elucidation of thermodynamic data for the Schlenk equilibrium of 2 in toluene. In ethereal solvents, mononuclear species [(Et 2 O) 2 Mg(Cp TIPS )Br] ( 2’ ), [(Et 2 O) n Mg(Cp TIPS ) 2 ] ( 3’ ), and [(Et 2 O) 2 MgBr 2 ] ( 4’ ) coexist. Larger coordination numbers can be realized with cyclic ethers like tetrahydropyran allowing crystallization of [(thp) 4 MgBr 2 ] ( 5 ). The interpretation of the temperature‐dependency of the Schlenk equilibrium constant in diethyl ether gives a reaction enthalpy ΔH and reaction entropy ΔS of −11.5 kJ mol −1 and 60 J mol −1 , respectively.Cyclopentadienylmagnesium bromides are accessible with high yields by a fast and smooth one‐pot synthesis. In hydrocarbons and in ethereal solvents a dissociative Schlenk equilibrium is operative interconverting heteroleptic compounds into homoleptic congeners. imag

Suppression of Heating by Multi-color Driving Protocols in Floquet Engineered Strongly Correlated Systems

Heating effects in Floquet engineered system are detrimental to the control of physical properties. In this work, we show that the heating of periodically driven strongly correlated systems can be suppressed by multi-color driving, i.e., by applying auxiliary excitations which interfere with the absorption processes from the main drive. We focus on the Mott insulating single-band Hubbard model and study the effects of multi-color driving with nonequilibrium dynamical mean-field theory. The main excitation is a periodic electric field with frequency $\Omega$ smaller than the Mott gap, while for the auxiliary excitations, we consider additional electric fields and/or hopping modulations with a higher harmonic of $\Omega$. To suppress the 3-photon absorption of the main excitation, which is a parity-odd process, we consider auxiliary electric-field excitations and a combination of electric-field excitations and hopping modulations. On the other hand, to suppress the 2-photon absorption, which is a parity-even process, we consider hopping modulations. The conditions for an efficient suppression of heating are well captured by the Floquet effective Hamiltonian derived with the high-frequency expansion in a rotating frame. As an application, we focus on the exchange couplings of the spins (pseudo-spins) in the repulsive (attractive) model, and demonstrate that the suppression of heating allows to realize and clearly observe a significant Floquet-induced change of the low energy physics.Comment: 15 pages, 15 figure

Alkaline‐earth metal dimesitylphosphinites and their ether adducts – A structural study in solution and in the crystalline state

Abstract Alkaline‐earth metalation of dimesitylphosphane oxide Mes 2 P(O)H ( 1 ) in ethereal solvents with dialkylmagnesium and alkylmagnesium bromide as well as the homoleptic bis(trimethylsilyl)amides of calcium, strontium, and barium yields [(L)MgR(μ‐OPMes 2 )] 2 (L/R=thf/Et ( 2‐Et ), Et 2 O/Br ( 2‐Br )), [(thf) 3 Ca(hmds)(OPMes 2 )] ( 3‐hmds ), [(thf) 3 Mg(OPMes 2 ) 2 ] ( 2‐thf ) and [(thf) 4 Ae(OPMes 2 ) 2 ] (Ae=Ca ( 3‐thf ), Sr ( 4‐thf ), and Ba ( 5‐thf )), depending on the applied stoichiometry. Exchange of thf ligands in 3‐thf by oligodentate ethers allows isolation of [(thf) 2 (dme)Ca(OPMes 2 ) 2 ] ( 3‐dme ), [(thf) 2 (diglyme)Ca(OPMes 2 ) 2 ] ( 3‐diglyme ) and [(thf)(triglyme)Ca(OPMes 2 ) 2 ] ( 3‐triglyme ). Contrary to this finding, oligodentate amines are unable to substitute ligated thf ligands in 3‐thf . In ethereal solutions, the heteroleptic complexes 2‐Et , 2‐Br and 3‐hmds show Schlenk‐type equilibria, interconverting these compounds into their homoleptic counterparts.imag