This award supports theoretical investigation of the static and time-varying responses of mesoscopic systems. The emphasis is placed on theory applicable to experiments on topological insulators and superconducting nano-circuits. The motivation comes from the recent advances in nanofabrication, synthesis of new materials, and precise experimental techniques of microwave and time-resolved measurements, as well as from the theoretical challenges inherent in the evaluation of the response functions. The common thread of the entire project is the importance of electron interactions and symmetries in the responses of the mesoscopic systems.
The project is composed of three parts on:
(1) Investigation of the finite-temperature conductance of one-dimensional electron channels at the edges of a two-dimensional topological insulator. Here, the conductance evaluation calls for the development of a theory for inelastic electron backscattering in one-dimensional helical electron liquids. The PI and his group aim at deriving a low-energy theory valid for a generic interacting helical edge state which respects time-reversal invariance, but may not conserve any of the electron spin projections
(2) Analysis of the conduction of thin films of three-dimensional topological insulators. The intrinsic disorder in these materials results in their substantial bulk conductivity, which shunts the electron transport within the topologically-protected conducting state at the surface. The aim is to build a comprehensive theory for such experiments.
(3) Addressing the scattering of microwave photons off a weak link in an array of Josephson junctions. This bosonic version of the quantum impurity problem has a number of common traits with its electronic counterpart, but allows one an experimental access to a different set of response functions. Like in the first part of the project, the aim is to develop a theory for inelastic scattering.
The award will also support the PI's educational activities integrated with the above research at the undergraduate, graduate, and postdoctoral levels. The results of the research will be incorporated into the PI's graduate level courses on quantum many-body physics and condensed matter theory. The PI will also organize optical workshops geared towards broad representation of scientists from diverse backgrounds.
NON-TECHNICAL SUMMARY
How matter responds when an electric current passes through it or when electromagnetic waves interact with it depends on the size of the sample. Upon decreasing size new properties that are not observed in bulk materials may emerge. Quantum interference and interaction of electrons or quanta of light, called photons, result in properties emerging on the meso-scale - a scale small enough to preserve coherence, but large compared to the atomic scales. This project aims at theoretical investigation of a number of new experimentally accessible systems which are expected to display unusual mesoscopic behavior.
The systems of interest include two and three-dimensional topological insulators, which do not conduct electricity through the bulk but are perfect conductors for currents passing through their edges or boundaries, photons interacting with scattering centers in small-scale superconducting circuits. All such systems are currently viewed as potential elements of future electronic technology. The theoretical research to be carried out on this project will help in achieving an understanding of real materials exhibiting various exotic properties at the mesoscale and could potentially lead to the design of new technologically important devices.
The award will also support the PI's educational activities integrated with the above research at the undergraduate, graduate, and postdoctoral levels. The results of the research will be incorporated into the PI's graduate level courses on quantum many-body physics and condensed matter theory. The PI will also organize optical workshops geared towards broad representation of scientists from diverse backgrounds.
