Sanjib Kumar Das — Page 2

arXiv2019

Topological crystalline insulators from stacked graphene layers

In principle the stacking of different two-dimensional (2D) materials allows the construction of 3D systems with entirely new electronic properties. Here we propose to realize topological crystalline insulators (TCI) protected by mirror symmetry in heterostructures consisting of graphene monolayers separated by two-dimensional polar spacers. The polar spacers are arranged such that they can induce an alternating doping and/or spin-orbit coupling in the adjacent graphene sheets. When spin-orbit coupling dominates, the non-trivial phase arises due to the fact that each graphene sheet enters a quantum spin-Hall phase. Instead, when the graphene layers are electron and hole doped in an alternating fashion, a uniform magnetic field leads to the formation of quantum Hall phases with opposite Chern numbers. It thus has the remarkable property that unlike previously proposed and observed TCIs, the non-trivial topology is generated by an external time-reversal breaking perturbation.

cond-mat.mes-hall↗

arXiv2009

A real world network pricing game with less severe Braess' Paradox

Internet and graphs are very much related. The graphical structure of internet has been studied extensively to provide efficient solutions to routing and other problems. But most of these studies assume a central authority which controls and manages the internet. In the recent years game theoretic models have been proposed which do not require a central authority and the users are assumed to be routing their flows selfishly. The existence of Nash Equilibria, congestion and the amount of inefficiency caused by this selfish routing is a major concern in this field. A type of paradox in the selfish routing networks, Braess' Paradox, first discovered by Braess, is a major contributor to inefficiency. Several pricing mechanisms have also been provided which give a game theoretical model between users(consumers) and ISPs ({Internet Service Providers} or sellers) for the internet. We propose a novel pricing mechanism, based on real world Internet network architecture, which reduces the severity of Braess' Paradox in selfish routing game theoretic networks. It's a pricing mechanism between combinatorial users and ISPs. We prove that Nash equilibria exists in this network and provide bounds on inefficiency . We use graphical properties of internet to prove our result. Several interesting extensions and future work have also been discussed.

cs.GT↗