Electron Transport And Waiting Time Distribution In Topological Superconductors

Majorana bound states can be utilized to achieve topological quantum computa-tion due to their non-Abelian statistics.In recent years,Majorana bound states have attracted a lot of interest in the condensed matter physics.The experimental signals of Majorana bound states in condensed matter systems,such as hybrid superconductor-semiconductor nanowires,chains of magnetic adatoms on the surface of a superconductor,and iron-based superconductors,have been reported.However,both experiments and the-ories have shown that the signatures of Majorana bound states in hybrid superconductor-semiconductor nanowires may have a non-Majorana origin.This makes the experimental confirmation of the existence of Majorana bound states still under debate.In this disser-tation,we mainly investigate electron transport and waiting time distributions of systems with Majorana bound states.The contents are shown as follows:1.Waiting time distributions and current correlations in a Majorana single-charge transistor are investigated by using the T-matrix based master equation.The transition rates between Majorana island charge states due to the sequential and cotunneling pro-cesses are obtained from the generalized Fermi’s golden rule.By constructing current matrices,we evaluate the electrical current,the differential conductance and the noise Fano factor.It’s found that the super-Poissonian shot noise could be induced when the Majorana energy splitting is larger than the charging energy.In the large charging energy limit,the waiting time distribution for electron transport through two Majorana bound states has the same form as that of a single resonant level,which is a manifestation of the electron teleportation in a Majorana island.For comparison,we also discuss the waiting time distribution in a non-Majorana nanowire island.It is found that the waiting time dis-tributions sensitively depend on the length of the nanowire island and exhibit oscillatory behaviors.The particular behaviors of waiting time distributions in a Majorana island device may be useful in identifying the existence of Majorana bound states.2.Waiting time distributions of electron transport through a quantum dot coupled to a Majorana bound state are studied by using a quantum master equation.The waiting time distribution reveals the internal dynamics of the system,including the coherent transfer of electrons between the dot and the topological superconductor,the splitting and forming of Cooper pairs.The two coherent processes give rise to complicated oscillatory behaviors of the waiting time distributions.We find that the waiting time distribution is an even function of the energy level of the dot and the Majorana energy splitting,respectively.As a comparison,we also consider the case that a quantum dot is side coupled to an ordinary fermionic state.In this case,the waiting time distributions are different when the dot energy level is tuned to have an opposite sign.Moreover,we calculate the g^（2）function of two systems and find that they exhibit quite different behaviors.Our work also shows that waiting time distributions may be another scenario to detect Majorana energy splitting.3.We investigate theoretically the finite-time full counting statistics in a quantum dot coupled to a Majorana bound state and a metallic lead.In the long-time limit,as the de-tunings increase,the sub-Poissonian shot noise becomes Poissonian or super-Poissonian.The Fano factor with a value of 2 indicates the Poissonian processes of the formation of Cooper pairs.The ordinary and factorial cumulants at finite times exhibit oscillations,which is originated from coherent transfer of electrons in the system.The factorial cumu-lants show a violation of the sign criterion due to superconducting correlations generated by the quantum dot coupled to a Majorana bound state,which indicates the presence of correlation between the tunneling electrons.4.We study the noise and the waiting time distribution in a double-dot Cooper pair splitter with electrons emitted from a superconducting island.The island is Josephson cou-pled to a bulk superconductor which acts as the source of Cooper pairs.A small Josephson coupling strength could create a bottleneck for Cooper pair splitting,leading to a strongly enhanced Fano factor of the cross correlation even when elastic cotunneling processes are favorable.Moreover,a finite Josephson coupling strength could give rise to the os-cillations of the waiting time distributions.Finally,by evaluating the branching ratio of spins,it is found that,with decreasing Josephson coupling,the time to obtain nonlocal entangled electron pairs with near-unity probability increases.Our findings show that splitting Cooper pairs from a superconducting island could be a useful mechanism to optimize Cooper pair splitting properties.