## Non-equilibrium physics in quantum materials

One of the most exciting frontiers in condensed matter physics is the study of quantum many-particle systems out-of-equilibrium. A natural experimental scenario is the “pump-probe” situation where a “pump” laser takes a material out-of-equilibrium and a “probe” laser is used to measure the properties of the excited system after some time delay with respect to the “pump”. In the limit of a long pump pulse width, the systems experiences an approximately time-periodic Hamiltonian and a Floquet description is relevant. Hence, the study of Floquet physics is central to understanding an important class of non-equilibrium phenomena in condensed matter physics.

## New formalism for time-evolution in non-equilibrium many-body systems

When the Hamiltonian is time-dependent, computing the time-evolution of a system is substantially more difficult, particularly for an interacting, many-body system. An important special case is that of a time-periodic Hamiltonian. When the period of the drive is small (so the frequency of the drive is large) compared to other relevant scales, one can use a high-frequency expansion (Magnus expansion). However, this expansion typically breaks down in the low-frequency regime. By applying ideas from the renormalization group, and Wegner flow in particular, our group has developed a powerful approach to computing the time-evolution of quantum many-body systems. Our “flow equation approach” is based on an infinite sequence of infinitesimal unitary transformations. In addition to providing access to accurate time evolution in lower frequency regimes, the method also provides a flexible starting point for a large variety of approximation schemes for the time evolution.

## Optical control of magnetism and band structure via selective excitation of phonons

When one illuminates a material with a laser a choice is made regarding the frequency of the light. When the frequency is in the visible range (electron-volt energy scale), then electronic excitations can be resonantly excited. However, if one uses lower frequency light, typically in the far-infrared (milielectron-volt energy scale), then lattice vibrations – phonons – are can be resonantly excited. These phonons can couple to one another if their amplitude is large enough (from a laser of sufficiently large intensity) and this has an impact on the electronic degrees of freedom, including the magnetism and the band structure. In a recent study, our group has investigated bilayer CrI3 which has a ferromagnetic order within the planes, but antiferromagnetic order between the planes. We have shown that selectively targeting infra-red active vibrational modes that couple non-linearly to Raman active modes can induce a new inter-plane magnetic order: ferromagnetic so that the entire bilayer undergoes a magnetic transition from antiferromagnetic (with zero net moment) to ferromagnetic (with a finite net moment). In another recent work, our group has extended this idea to the candidate axion insulator, MnBi2Te4.

## Floquet physics in twisted bilayer graphene

Turning from a focus on the magnetism to the band structure, we have been investigating how the band structure of twisted bilayer graphene can be modified in interesting ways using a Floquet drive. Twisting two single layers with respect to one another creates a moire lattice which can have a lattice constant substantially larger the than the atomic lattice of either layer. This means that the magnetic flux in the moire lattice unit cell can be substantially larger, and the corresponding Brillouin zone substantially smaller, than that of the layer constituents. An important special case is when the inter-layer twist angle is around 1.1 degrees. Then, the band structure becomes becomes very flat, signifying quenched kinetic energy and enhanced electron-electron interaction effects. The equilibrium phase diagrams of these systems show Mott insulating phases and superconductivity. The flat band physics turns out to be highly sensitive to the inter-layer electron hopping. Our group has proposed a way that the band structure can be reversibly tuned in-situ using light emanating from a waveguide. We have also developed an accurate formalism to capture the bandstructure under a low-frequency drive and determined the effective low-energy Hamiltonian of twisted bilayer graphene under general drives. Recent extensions of this work by the group have shown that driving twisted *double bilayer graphene can* bring in an additional control knob: valley control.

## Spin and energy transport in non-collinear magnets

Another way that a system can be taken out-of-equilibrium is through the application of a temperature gradient. The second law of thermodynamics tells us that energy will flow from a hot region to a colder region. In a magnetic insulator (lattice with local moments on the lattice sites) magnetic fluctuations known as magnons will carry energy (heat) and also spin. Our group has shown that different classes of magnets with non-collinear orders have *topological magnon bands*, including Y2Ir2O7 and the iron jarosites. Recently, our group has studied how efficiently spin can be injected from a non-collinear magnetic into a neighbor metal. The results can depend sensitively on the interfacial magnetic exchange and crystallographic orientation.