Traditionally, chemistry has provided the primary route for achieving new properties in materials: to obtain a material with different characteristics, we must change its chemical composition or arrangement of atoms. Inspired by the advent of powerful new experimental techniques for probing and controlling the behavior of quantum systems using coherent microwave and laser driving fields, we are exploring how material properties can be dynamically manipulated in both natural and synthetic (e.g., cold atoms) materials through the application of time-dependent driving fields. Intriguingly, such driven systems can exhibit a variety of novel topological and symmetry-breaking phases with properties that are not possible in equilibrium.

References:

Review paper: "Band structure engineering and non- equilibrium dynamics in Floquet topological insulators," Mark S. Rudner and Netanel H. Lindner, Nature Reviews Physics 2, 229 (2020).

Review paper: "Topology and Broken Symmetry in Floquet Systems," Fenner Harper, Rahul Roy, Mark S. Rudner, and S.L. Sondhi, Annual Reviews of Condensed Matter Physics 11, 345 (2019).

News and Views: "Driving toward hot new phases," Mark S. Rudner, Nature Physics 16, 1008 (2020).

Physics Today: "Cold-atom lattice bends the topological rules," Johanna L. Miller, Physics Today July 23, 2020.

Recent works on Floquet engineering have shown how externally applied ac fields can be used to modify the Bloch band dispersion and geometry (i.e., Berry curvature) that characterize the propagation of electrons through solids and ultracold atoms through optical lattices. In metallic systems, very strong oscillating internal fields can be produced by the electrons within a material itself when plasmonic or other collective modes are excited. In a first proof-of-concept work we explored the nonlinear dynamics resulting from feedback of plasmonic internal fields onto electronic band structure. Remarkably, this feedback can lead to spontaneous non-equilibrium magnetism that is both driven by and helps to sustain a non-vanishing Berry flux that emerges in the steady state.

References:

"Self-induced Berry flux and spontaneous non-equilibrium magnetism," Mark S. Rudner and Justin Song, Nature Physics, 15, 1017 (2019).

News and Views: "A sudden twist," L. E. F. Foa Torres, Nature Physics 15, 988 (2019).

Feature on Phys.org: "Spontaneous magnetization in a non-magnetic interacting metal"

Time-reversal invariant topological insulators are intriguing materials with robust helical surface states that appear due to the nontrivial topological character of the material's underlying band structure. For two-dimensional topological insulators, these helical edge modes are predicted to host quantized transport. On the one hand, the helical edge modes are protected by time-reversal symmetry. On the other hand, a flowing transport current violates time reversal symmetry, and can therefore be expected to cause a breakdown of the topological character of the edge states in the nonlinear transport regime. Specifically, through electron-electron interactions, the spin polarization that accompanies a flowing current produces an internal exchange field that acts back to modify the edge mode band structure (breaking its helical nature). In this work we explore this self-induced modification of the edge mode structure that arises due to the flowing current, and the resulting signatures expected for nonlinear transport in topological insulator devices.

References:

"Current-Induced Gap Opening in Interacting Topological Insulator Surfaces," Ajit C. Balram, Karsten Flensberg, Jens Paaske, and Mark S. Rudner, Phys. Rev. Lett. 123, 246803 (2019).

Related experiment at UW: "Determination of the spin axis in quantum spin Hall insulator monolayer WTe2," Wenjin Zhao et al., arXiv:2010.09986 (2020).

The evolution of an ideal, isolated quantum system is unitary, as described by the Schrödinger equation. In the real world, however, systems of experimental interest exist in the presence of and interact with an environment of additional degrees of freedom (e.g., phonons and electromagnetic fields). The interaction of the system with its environment imparts a nonunitary, or incoherent, character to the system's evolution. We are developing new approaches and methods for studying the dynamics of open quantum many-body systems, and exploring the consequences for emerging quantum hardware.

References:

"Universal Lindblad equation for open quantum systems," Frederik Nathan and Mark S. Rudner, Phys. Rev. B 102, 115109 (2020).