The Magnetoresistance And Entanglement In The 1D Two-probe Quantum Device System

Recent experimental and theoretical researches have shown that the combination of the double helix structure,the spin-orbit coupling(SOC)and the dephasing effect will lead to the high spin-selective effect in DNA.The effects of these three factors on spin polarization have also received much attention.However,the magnetoresistance,which is a measurable physical quantity closely related to electron spin,has not been further studied in DNA-related systems.Therefore,the first part of this thesis mainly focuses on the study of magnetoresistance in DNA,including some possible conditions for giant magnetoresistance(GMR).We have discussed the adjustment of DNA structure,voltage bias and DNA length on magnetoresistance,this could be used to help developing the DNA-based quantum magnetic device theoretically.Entanglement is a vital ingredient in quantum system,it has played a key role in dealing with quantum information.The related studies in photonic and electronic systems have shown great application potential.Among the proposed entanglement measures,von Neumann entanglement entropy is the most popular one.Common methods to calculate the entanglement entropy are based on the many-body wave function and density matrix.Since the complexity of these methods is an exponential function of the system size,the related studies are under very small systems.With the rapid development of quantum devices,theoretical studies of large non-equilibrium systems are much needed.Thus,the second part of this thesis mainly focuses on the study of entanglement entropy between the central region and the electrodes in a non-equilibrium 1D two-probe system.The connection between entanglement entropy and quasi-states is studied.As a result,the main points of my thesis are listed as follows:1.Magnetoresistance(Rm)of a double stranded DNA exemplified by a sequence(G:C)N has been studied using transfer matrix method and tight-binding model with the consideration of the double helix structure,the SOC and the dephasing effect.A large Rm=-72.5%is observed under a relatively high voltage bias(Ub).With the analyses of wave functions in the two-probe system,we find the strong Rm originates from the dephasing effect which could allow DNA to absorb electrons from the environment and lead to the growth on wave function.If an extra force is applied on the DNA to change the structure,the SOC will also change because of its close relation to structure parameters and makes Rm vary in a quite large range.This behavior can be modified by Ub.At small Ub,Rm vary from negative to positive with small magnitude.While under large Ub,R n remains negative and could reach close to-100%.Through the comparison of natural B-DNA and plane ladder DNA,we found Rm is stronger in natural B-DNA.In addition,the DNA length could also modify Rm.2.The entanglement entropy in the equilibrium free fermions two-probe system can be determined from the correlation matrix.In this thesis,we have extended this method to a non-equilibrium two-probe electronic system using non-equilibrium Green's function(NEGF).We have studied the entanglement entropy between the central region and the electrodes under different parameters.In cases of different central chain lengths N,the entanglement entropy(S)varies oscillatingly with the increasing voltage bias(Vb).With the analyses of energy bands of electrodes and the quasi states of the central chain,we find that the entanglement entropy will jump up when a quasi state aligns in energy with the band edge.This makes the S-Vb curve an oscillatory form instead of a monotonous decrease one.In addition,in odd lengths cases,the middle quasi state will merge from the band cross and leads to a derivative discontinuity in S-Vb curve.With the study on the occupation of quasi state,we find that for case N=1,the entanglement entropy depends on the deviation from half occupation of the quasi state.When the quasi state is half occupied,the entanglement entropy maximizes.While for case N>1,the entanglement entropy is based on the combination of occupations of all quasi states.Besides,the entanglement entropy dependence of the system scaling is studied and SL?1/3log2N is observed under low bias which fits well with the equilibrium case.This also prove the reliability of our model and method.