טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentTenenbaum Katan Yaniv David
SubjectDynamics in Low-Dimensions: Floquet Topological Insulators,
the Higgs Mode and other Tales
DepartmentDepartment of Physics
Supervisor Professor Daniel Podolsky
Full Thesis textFull thesis text - English Version


Abstract

This work studies dynamics in low dimensional condensed matter systems. The study is divided into three parts.

The first part of this work, “Modulated Floquet Topological Insulators”, studies the topological properties that are induced in condensed matter systems by the use of space modulated light.  This work demonstrates that spatial modulation of light allows for remarkable control of the properties in these systems. We find that domain wall configurations of the phase, polarization, and frequency of the light can generate localized modes with zero quasi-energy in the bulk of these systems. In addition, we establish that vortex configurations of the phase of the light can give rise to fractionalized excitations at the vortex core. We explain these results by establishing an analogy to superconductors. We also demonstrate that these systems support photoinduced currents that are the analogous of the superconducting Josephson currents. We demonstrate these results analytically and numerically in a variety of model systems.

The second part of this work, “The Higgs mode in 4-epsilon  Dimensions”, studies the amplitude (Higgs) mode of the O(N)  model near the quantum phase transition in D<4  space-time dimensions. The O(N)  model is a general relativistic field theory with O(N)  symmetry, and has many experimental realizations in condensed matter systems near phase transitions. Until recent years, the common thought was that the Higgs excitation of the O(N)  model is over-damped at low dimensions and cannot be observed in experiment. This was recently changed with the introduction of a new method to probe the Higgs mode, a physical observable named the “scalar susceptibility”. The presented work demonstrates by a perturbative approach, that at D<4  the scalar susceptibility produces a distinct peak which can be identified as the Higgs excitation. We also show that a Higgs like resonance may be present at finite temperatures above the critical point.

The third part of this work, “Dynamics of a One Dimensional Particle in a Random Potential”, studies the motion of classical particles in fluctuating one dimensional systems. This type of potential has been recently shown to be extremely relevant to non linear optical experiments. The presented work focuses on the effect of potentials with finite number of random Fourier components. The study provides a description for the dynamics of such systems as a random walk in phase space.