High-order Harmonic Generation In Graphene Nanoribbons

The interaction between light and matter has been an important area of physics for ages.With the development of laser technology,the strong field physics is rapidly developing into the one of the most important fields.Among them,High-order harmonic generation(HHG)is the most popular field as a tool for generating ul-traviolet light as well as ultra-short pulsed coherent light.HHG not only provide a way to generate attosecond pulses,but they are also a tool to help us under-standing the structure of condensed matter.In the past decades,atom HHG have been the focus of attention.In recent years,because of the rapid development of mid-infrared laser technology,one can effectively generate high-order harmonics in solids,whose generation mechanism is much more complex than that of atom HHG.At the same time,many related theoretical models have been greatly devel-oped in order to study solid HHG further.However,at present,people still focus on the study of HHG in bulk crystal,while the study of HHG in low-dimensional materials such as nanoribbons is extremely lacking.Therefore,in this thesis,we will take graphene nanoribbon as an example to study the HHG in low-dimensional nanomaterials.In this thesis,we firstly establish the corresponding tight-binding model and obtain the corresponding band structure based on the spatial structure of graphene nanoribbons,and we discover the corresponding dipole selection law.Then,we successfully calculated the HHG spectrum of the nanoribbons by using the time-dependent evolution.Since we find that the nanoribbons have the properties of both bulk crystal and confined nanosystem,different polarization directions for the linearly polarized laser will lead to drastically different HHG.When the polar-ization is longitudinal,the properties of the HHG are essentially similar to those of the HHG in the bulk crystal.However,we find that for different structures of graphene nanoribbons,presence or no of the band gap affects the transverse HHG response.Also,we find that the edge states of graphene nanoribbons can enhance the transverse response of the HHG.And for the transverse polarization,the cutoff of the HHG spectrum is significantly expanded at a specific nanoribbon width.Subsequently,to reveal the mechanism of the harmonic cutoff expansion at a specific width,we constructed a simplified multi-level model and investigated its electron dynamics.It was found that the HHG are significantly modified be-cause the multi-level resonance is completely different from the dynamic Bloch oscillation that triggers the HHG of the bulk solid.In this case,we propose the conditions of the generation of multi-level resonance: the frequency condition and the field strength condition.Only the satisfaction of both conditions can lead to multi-level resonance,which successfully explains the phenomenon of cutoff ex-pansion.Since,the HHG is influenced by the multi-level resonance,the cutoff law,which varies linearly with the laser field strength,is also adapted.Now the cutoff law of the HHG is not only affected by the laser wavelength and intensity,but also by the laser duration.In this thesis,we have explored the HHG of graphene nanoribbons in detail.We reveal the mechanism of HHG in graphene nanoribbons for the first time.This gives insight into the fact that the solid HHG not only relies on dynamic Bloch oscillation,but multi-energy resonance may also have an effect on it.This will enhance the understanding of HHG in the further.