Complex quantum materials at their thermal equilibrium already display a huge variety of intriguing properties, like metal-insulator transitions, high-temperature superconductivity, colossal magnetoresistance, topological edge states, or ferromagnetism. These properties can be controlled with external thermodynamic knobs, for instance by changing temperature, pressure, or gate voltages. These thermodynamic knobs have the disadvantage that they are “slow”.
The “New States of Matter” project deals with ultrafast, intrinsically nonequilibrium knobs. Short laser pulses allow us to manipulate quantum matter on the femtosecond time scale. One femtosecond is 0.000000000000001, or one millionth of a billionth, of a second. Therefore, ultrafast optical switching of the above-mentioned states as well as new states with properties beyond the realm of equilibrium thermodynamics come into reach.
New states induced and controlled by lasers are fascinating, but also extremely challenging to theory. In the Theory Department, we use time-dependent density functional theory as well as many-body perturbation theory and Keldysh nonequilibrium Green functions to describe ultrafast processes in molecules and solids. The field of new states of matter is closely related to photon-matter systems, in which the quantum nature of light can hopefully be used to imprint photonic coherence onto electronic states.
Floquet topological states
Light-induced Floquet states of matter provide a new tool of engineering effective Hamiltonians in periodically driven many-body systems. In this project, we are building upon prior work for a model system using Keldysh nonequilibrium Green functions (many-body perturbation theory), in which some of us demonstrated that circularly polarized laser pulses attainable in state-of-the-art pump-probe experiments lead to significant changes in the band structure of graphene as measured by time-resolved photoemission spectroscopy . Importantly, these band structure changes come with ultrafast modifications of the Berry curvature at critical driving parameters where band crossings and gap openings occur.
Ongoing and future work is dedicated to the modeling of novel Floquet topological states in Dirac materials ranging from 2D transition metal dichalcogenides to 3D Dirac semimetals using model calculations as well as ab initio time-dependent density functional theory. A particular focus will be on the impact of phonons both for energy dissipation and for lattice control of electronic properties. The inclusion of the ionic degree of freedom will be particularly relevant when the pump laser is in resonance with infrared active phonons.
In summary, the theory and modeling of Floquet-like states in solids driven by laser pulses in the optical regime (Floquet electronics) and in the mid-IR (Floquet phononics) has the goal of finding new ways of controlling and manipulating interesting and potentially useful quantum states of matter. Moreover, the quantum nature of photons will also be explored in the new field of Floquet quantum-electrodynamical nanoplasmonics. Importantly, besides theory and method developments, this line of work is also geared towards collaborations with the experimental Quantum Condensed Matter Group at MPSD.
 M. A. Sentef, M. Claassen, A. F. Kemper, B. Moritz, T. Oka, J. K. Freericks, and T. P. Devereaux, Nature Communications 6, 7047 (2015)