Research On Electron Transport Under Generalized Uncertainty Principle

Since the first successful preparation of graphene in the laboratory by British scientist A.K.Geim and others in 2004,graphene has become a research hotspot for many researchers with its unique electromagnetic properties.The successful preparation of graphene has made a great leap in understanding of carbon materials,changed the pattern of the carbon element material world,and is a landmark discovery.Graphene’s two-dimensional monoatomic layer structure makes it show many special properties different from traditional materials.Such as Klein tunneling,non-zero minimum conductivity,and the anticonstant Hall effect,etc.These physical properties exhibited by graphene make it have better electronic properties than other nanomaterials,and provide an important basis for the theoretical research and production applications of nanomaterials.Graphene may become an ideal material for nanoelectronic devices required for the rapid development of the next generation.On the other hand,in recent years,various theories that unify quantum theory and relativity,such as loop quantum gravity theory,superstring theory,and black hole physics,have all shown the existence of a "minimum observable length".This means that in the vicinity of the Planck scale,the Heisenberg uncertainty relationship under quantum mechanics should be modified into the so-called generalized uncertainty principle.The modified generalized uncertainty principle will cause the form of the momentum operator or coordinate operator to change in general quantum mechanics,which will affect the Hamiltonian of the quantum system.In general,under the influence of the generalized uncertainty principle,the Hamiltonian of any quantum system will inevitably be modified.In recent years,various types of generalized uncertainty principles have been proposed one after another,and have been widely used in the study of Schrodinger equation,Dirac equation,Klein Gordon equation and DKP equation,and have achieved many meaningful results.In addition,the generalized uncertainty principle can also be used to explain some black hole residual phenomena,anti-Planck expansion problems,and cosmic constant problems.At present,people have done a lot of research on the electron transport properties of graphene and achieved many meaningful results,but these results are based on the usual quantum theory.And the results based on the analysis of the usual quantum theory are not completely consistent with the experiments,in order to further expand the understanding of the problems related to the electron transport properties of graphene under the generalized uncertainty principle,and to explore the effects of quantum gravitational effects on the problems related to graphene electron transport.Therefore,it is necessary to study the scattering problem of graphene by using the quantum theory under the generalized uncertainty principle.The special properties of graphene make it possible to study its scattering problem under the generalized uncertainty principle.It has positive significance for revealing the rules of electron transport and guiding the design of nanoscale spintronic devices.At the same time,it also provides a reference for experimental verification for some theoretical verifications in the field of highenergy physics.In this article,we first introduce the research status of nanoelectronic devices,spin electronics,and the structure,properties,and applications of graphene.Then describes the background of the generalized uncertainty principle and gives the form of the massless Dirac equation under the generalized uncertainty principle.Based on this,the problem of scattering of graphene is studied.We give expressions of reflection coefficient,transmission coefficient,and resonance conditions.Then,we further study the local state density,scattering cross section,and scattering efficiency in the graphene scattering problem.The conclusion shows that the scattering coefficient,scattering cross section and scattering efficiency of the electrons in graphene are all related to the parameter of the generalized uncertainty principle.In particular,the results when our generalized uncertainty principle parameter 0 is completely consistent with those under ordinary quantum mechanics.