Topological Quantum Hydrodynamics in Nonmetallic Materials

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NONTECHNICAL SUMMARYThis award supports theoretical research and education with an aim to unravel hidden physical properties and potential utilities of insulating materials. These materials could be chemically natural or judiciously tailored in an atomic layer-by-layer fashion. The dynamic cooperation among the underlying elementary constituents can result in the effectively knotted geometric entities, such as vortices or magnetic textures that resemble the arrangement of spines on a hedgehog, that spur unexpected physical behavior. In certain natural or engineered systems, an intricate geometric character is already woven into the chemical fabric of the homogeneous material itself. While this may not be directly evident, it can be manifested through exotic physics at the material's boundary. The latter, in turn, can be exploited to control the textured inhomogeneous dynamics in the bulk by electrical, thermal, or optical manipulations on the edges. Ultimately, this research aims at establishing new modalities for classical and quantum information transmission by appropriately designed systems and devices, which can exhibit novel types of (out-of-equilibrium) dynamics and (nonelectrical) signal generation as well as yield hidden functionalities.The topics studied here thus have technological implications, while also offering educational opportunities. The PI's collaboration with materials scientists and engineers will promote new device concepts for efficient nanoscale energy storage and quantum communications. The intersection between topology, quantum transport, and quantum information science also offers a terrific departure point for designing modern courses, research topics for training students and postdocs, as well as educational outreach to schools and the public. The PI will team up with the California NanoSystems Institute to carry out outreach activities to Los Angeles public school district, maintain a theoretical nanoscience component at the UCLA summer internship programs, as well as contribute to the physics fairs that are periodically offered to the public by his department. Beyond UCLA, an international conference will be organized for scientists from developing nations, with a broad scope in topological and quantum phenomena in condensed-matter physics.TECHNICAL SUMMARYThis award supports theoretical research and education to investigate novel modes of information flow and the associated quantum correlations in materials with topological character. The latter is generally associated with bulk-boundary correspondence, and provides control handles on the dynamics and transport processes in the interior of a system through the manipulations and measurements on its boundaries. We are primarily interested in insulating magnetic or superconducting systems, which can exhibit spatially-inhomogeneous order-parameter dynamics not hindered by much dissipation. Topological conservation laws underlying such collective textures, like magnetic/superconducting vorticity in 2D or magnetic hedgehog textures in 3D, offers a hydrodynamic framework for developing a systematic field-theoretic formalism for quantum transport. The topological bulk-boundary relations enable the bias and measure the topological texture flow, either thermoelectrically or optically, offering a fundamentally new way to probe transport in wide classes of nonmetallic media. After developing a microscopic quantum response theory, it will be applied to effective descriptions for ordered, disordered, and critical regimes, with a focus on quantum magnets and spin liquids. Even for ordinary ferromagnets and antiferromagnets, our perspective raises new types of questions for interrogating materials. This becomes even more interesting when the material is already topological at the level of its band structure, as in the quantum Hall phases and topological superconductors. Here, we anticipate two interwoven bulk-boundary features, with the robust edge states dictated by the band-structure topology affording us universal means to bias and control real-space topological textures in the bulk. Low-energy quantum degrees of freedom, which are either naturally associated with the topological features (such as skyrmionic vibrations or Majorana fermions in a vortex core) or artificially implanted (such as nitrogen-vacancy centers in diamond), are then studied in concert with the delocalized collective driven-dissipative dynamics.This project will further our understanding of fundamental properties of correlated quantum materials on three fronts: (i) Through the prism of their novel transport properties based on topological conservation laws (which has so far eluded much attention in solid state); (ii) By tuning an ensemble of individually-accessible quantum bits into strong (electromagnetic) coupling with a topological material, and quantifying the induced entanglement; and (iii) Exploring these questions for a driven-dissipative dynamics, where the non-Hermitian character enriches both the topological properties and the associated quantum correlations. The project thus sets out to offer new general-purpose probes of dynamic properties of correlated materials, with an eye on topology, quantum entanglement, and dissipation, along with the interplay thereof.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.