טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentNahshony Alon
SubjectAnomalous Weyl Points In Three-Dimensional Topological
Quantum Pumps
DepartmentDepartment of Physics
Supervisor Professor Netanel Lindner
Full Thesis textFull thesis text - English Version


Abstract

The Thouless pump is a one dimensional system which exhibits quantized charge transport, due to adiabatic time-periodic changes in the Hamiltonian. We study the three-dimensional analog of this phenomenon.

A three-dimensional gapped Quantum system subjected to adiabatically slow time-periodic potential could be classified topologically, where each topological class is characterized by the second Chern number, defined as an integral over momentum and time of the non-Abelian Berry curvature. Equivalently, the system can be classified by the invariant associated with the third homotopy group of the evolution operator of a full period. A remarkable property of such system is the possibility for existence of Weyl nodes in the Floquet spectrum, with non-zero total chirality. Non-zero total chirality of the Weyl nodes can occur on the three-dimensional surface of a four-dimensional quantum Hall state; here, we obtain this property in a purely three-dimensional system.

For the three-dimensional system, as a result of the topological classification, the change in the magnetoelectric polarization over a full period is quantized (as opposed to the charge in a one-dimensional system). This results in a magnetoelectric effect, i.e., electric current in response to applied magnetic field.

We show the existence of Weyl nodes with non-zero total chirality in the Floquet spectrum of three-dimensional topological pumps, based on topological considerations. In addition, we perform numerical calculation for a tight-binding model, based on an explicit time evolution.

We also show that a similar effect can be obtained by applying time-modulated external fields on a trivial insulator. This is done using a field frequency which is resonant with a transition from the valance to the conduction band, and by changing adiabatically some property of the field, e.g. the polarization, is changed adiabatically. The field frequency and modulation frequency need not be commensurate. We show explicit numerical results for both one-dimensional and three-dimensional models.