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Structural Properties of a Class of Cayley Graphs and their Complements: Well-coveredness and Cohen–Macaulayness
, M.Sc. Thesis Sharif University of Technology ; Pournaki, Mohammad Reza (Supervisor)
Abstract
Let be a field and R= [x0, . . . , xn−1] be the polynomial ring in n variables over the field . Let G be a finite simple graph with the vertex set V(G) ={0, . . . , n − 1} and the edge set E(G). One can associate a square-free quadratic monomial ideal I(G) = (xixj | {i, j} ∈ E(G)) of R to the graph G. The ideal I(G) is called the edge ideal of G in R. The graph G is called Cohen–Macaulay (resp. Buchsbaum, Gorenstein) over if the ring R/I(G) is Cohen–Macaulay (resp. Buchsbaum, Gorenstein).Let n be a positive integer and let Sn be the set of all nonnegative integers less than n which are relatively prime to n. In this thesis, we investigate structural properties of Cayley graphs generated by...
Higgs-mode signature in ultrafast electron dynamics in superconducting graphene
, Article Physical Review B ; Volume 104, Issue 17 , 2021 ; 24699950 (ISSN) ; Goudarzi, H ; Khezerlou, M ; Jafari, S. A ; Sharif University of Technology
American Physical Society
2021
Abstract
We theoretically investigate the effect of superconductivity on the ultrafast electron dynamics in graphene interacting with an ultrashort linearly polarized optical pulse. The optical pulse, with frequency greater than 1 THz, quadratically couples to the Higgs (amplitude) mode and therefore can excite the Higgs-mode oscillations in superconductors, leading to quenching superconducting excitation energy, even in s-wave pairing symmetry. Since the duration of the used pulse is less than the electron scattering time in graphene (10-100 fs), the electron dynamics driven by the electric field of pulse remains coherent and is described within the tight-binding model of graphene. We show that the...