Research

Research Area: Condensed matter theory, chaos, nonlinear phenomena, exotic ground states, strongly correlated electronic systems, low-dimensional materials

Description of Current Research:

Nonlinear Dynamics of Electrons in Mesoscopic Nanostructures
Quantum dots, quantum wires, and heterojunction layers are of great interest for potential novel electronic devices. We studied the role of nonlinear dynamics in the transport of electrons through various mesoscopic nanostructures, including both vertical and lateral semiconductor superlattices and double-barrier resonance tunneling diodes focusing on effects created by the presence of external driving by both dc- and ac-electric and dc-magnetic fields. Our results include predicting (1) deterministic chaos in the electron current, which would appear experimentally as a substantial increase in the effective noise of the device and (2) symmetry-breaking (i.e., the development of a dc bias in response to a purely ac applied electric field or to a suitably aligned dc magnetic field). We are verifying these predictions through collaborations with several experimental groups.

Quasi-One-dimensional Correlated Electronic Materials
In recent years, increasing computing power and significant progress in numerical algorithms have brought true many-body computational methods to the point at which quantitatively accurate results can be obtained for one-dimensional (1-D) systems involving simultaneously strong electron-electron and electron-phonon interactions. At the same time, significant experimental advances have been made for quasi-1-D electronic materials, such as conjugated polymers, Bechgaard salts, and high Tc cuprate semiconductors, in terms of both materials synthesis and preparation and physical characterization and measurement. Our research, comparing the results of detailed numerical studies with experimental data, focuses on a systematic theoretical investigation of 1-D lattice many-body models, including the important Peierls-Hubbard and spin-Peirels models.

Many-Particle Tunneling Effects and Resonant Processes in Mesoscopic Systems
Remarkable recent advances in materials science permit the construction of new "mesoscopic/nanoscale" materials with structures on the scale of 10–100 nm. These "quantum dots," "wires," and "layers" exhibit many new physical phenomena as nonlinear, quantum, and finite-size effects combine and compete. We have initiated three theoretical studies in this area: (1) correlated electron models for quantum dots and wires; (2) resonant processes in weak and strong electromagnetic fields; and (3) ground states and phase transitions in discrete quantum 1-D and 2-D systems, including the role of many-particle tunneling effects, diffusion, and quantum fluctuations. We will compare our results with experiments and seek applications in the designs of novel electronic devices.

Our research, comparing the results of detailed numerical studies with experimental data, focuses on a systematic theoretical investigation of 1D lattice many-body models, including the important Peierls-Hubbard (PH) and spin-Peierls models.