Electron And Transport Properties In Several New Two-dimensional Structures

Since the discovery of graphene,two-dimensional materials with a thickness of only a single or several atomic layers emerge in large numbers,which include the ele-mentary two-dimensional materials with a honeycomb lattice similar to graphene such as silicene,germanene,plumbene,and MXenes composed of transition metal carbides and transition metal nitrides,etc.Due to their planar geometric characteristics,these two-dimensional materials are suitable for current production processes in the semi-conductor industry.Many two-dimensional materials will play an important role in the design and production of ultra-thin electronic devices in future due to their unique elec-tronic structure and transport properties.In addition,experimentally,the electronic properties of two-dimensional materials can be controlled by a variety of tunable meth-ods such as strain and applied field.In such a context,the electronic properties of those two-dimensional materials in response to the tunable methods are necessary to be inves-tigated theoretically.From a fundamental perspective,such investigations can extend the theoretical system of condensed matter physics,while from an application perspec-tive,they can help us to explain or predict the related experimental phenomena,and provide the theoretical support for the application of two-dimensional materials.For such a purpose,we theoretically study the electronic and transport properties of several new two-dimensional materials or structures in this thesis.Especially,the tunability of these properties is of our concern.On the one hand,we focus on the development of new theoretical methods.For example,we firstly use the Lanczos method which is an iterative solution method for the Green function to study the RKKY interaction of two-dimensional structures such as graphene bubble.This provides a new solution for numerically and accurately studying the indirect exchange interaction and magnetic order in two-dimensional structure without periodicity.Meanwhile,we also try to ex-tend the Lanczos method to deal with electron-phonon interaction problems.On the other hand,we have studied the physical properties of several two-dimensional ma-terials governed by electron-phonon interactions through first-principles calculations,such as conventional superconductivity,intrinsic resistivity,and thermoelectric trans-port properties.These studies provide quantitative theoretical information for related experiments focusing on the physical properties of two-dimensional materials at room temperature.Specifically,this thesis is mainly composed of the following parts:Firstly,by means of the Lanczos method,we have performed numerical investiga-tions of the RKKY interaction in a graphene bubble,which is a local eminence of the graphene lattice perpendicular to its plane.We have found that the RKKY interaction in a graphene bubble can either be larger or smaller than the corresponding result in pristine graphene by a few orders of magnitude,depending on the sublattice attribu-tion and pseudomagnetic field strength where two magnetic impurities are positioned,which is due to the sublattice polarization of the low-energy electronic states induced by strong pseudomagnetic field.When the magnetic impurities are both in the bubble region,the^-3decay rate found in pristine graphene breaks down.But it recovers when one magnetic impurity is far away from the bubble center,no matter where an-other impurity is located.Furthermore,our numerical results indicate that Saremi's rule found in pristine graphene still holds in a charge-neutral graphene bubble.Name-ly,the RKKY interaction is ferromagnetic if two magnetic impurities are located on the same sublattice;otherwise,it is antiferromagnetic.However,when the Fermi level deviates from the Dirac point by carrier doping,the antiferromagnetic RKKY interac-tion between two magnetic impurities located on opposite sublattices can be inverted to be ferromagnetic by altering the bubble height.In addition,the strength of the RKKY interaction can be enhanced by more than two orders of magnitude with the increase of the bubble height.The curvature of the graphene bubble can be controlled by applying an electric field experimentally.Therefore,our findings provide a feasible solution to adjust the intensity and switch the magnetic order of the RKKY interaction in the graphene bubble by adjusting the intensity of the electric field.Secondly,we study the RKKY interaction in the one-dimensional topological chan-nel of bilayer graphene by means of the Lanczos method.We suggest that the kink potential can actually be produced by imposing two separate gate electrodes with oppo-site gate voltage on the bilayer graphene.As a result,the one-dimensional topological channel appears between the two gates,where exists the topologically protected one-dimensional electronic states.By computing the RKKY interaction in the topological channel with Lanczos method,we find that the RKKY interaction in the topologi-cal channel is long-range with an^-1decay rate.In comparison,the slowest decay rate of the RKKY interaction in the graphene system is^-2in previous theoretical studies.Such a long-range RKKY interaction implies a distinct magnetic ordering or magnetic phase transition when the bilayer graphene is doped by magnetic impurities,in contrast to conventional dilute magnetic semiconductors.Moreover,our theoretical result indicates that the strength and magnetic ordering of the RKKY interaction in the topological channel of bilayer graphene can be readily controlled by altering the gate voltage or introducing carrier doping.Thirdly,for specific two-dimensional materials,we use first-principles calculations to study the electron-phonon interaction and related physical properties.In this con-tent,the validity of spectral function with the double-function approximation as is used to calculate the intrinsic resistivity of realistic materials has been addressed.We find that the applicability of the double-function approximation requires the follow-ing preconditions.The energy difference between the Fermi energy and the band edge,which is defined as the Fermi energy of the band edge here,must be far larger than the thermal excitation energy and the phonon Debye energy.In addition,a function incorporating the electronic density of states,the electron-phonon interaction matrix element,and the large-angle scattering weight must be slowly-varying around the Fermi energy.However,it is not straightforward to identify whether the double-function ap-proximation is applicable for realistic materials with a multisheet Fermi surface formed by several bands.To exemplify such an issue,we perform first-principles calculations of the intrinsic resistivity of Ti₂N monolayer,a kind of MXenes,by employing the spectral function with the double-function approximation and the spectral function with the Fermi smearing effect respectively.By comparison,we find that the spectral function with the double-function approximation fails to describe correctly the tem-perature dependence of the intrinsic resistivity of Ti₂N monolayer when>250 K.The underlying physical reason is that there are several electronic bands crossing the Fermi surface,with some of the band edges being very close to the Fermi surface.In such a context,it is difficult to identify whether the Fermi energy of the band edge is large enough for the applicability of the double-function approximation.Our results suggest that the spectral function with the Fermi smearing effect is always adequate for studying the intrinsic resistivity of realistic materials on the level of first-principles calculations.In contrast,the validity of the double-function approximation for real-istic materials,particularly those materials with a complicated Fermi surface,should be given a great deal of attention.In addition,we remark briefly on the intrinsic resis-tivity of Ti₂N monolayer,in contrast to other typical two-dimensional materials,which is important from the viewpoint of application and physical property research of the MXene material.Fourthly,by means of the Mc Millian-Allen-Dynes formula and on the level of first-principles calculations,we estimate the conventional superconducting transition tem-perature of high buckled plumbene.A key quantity for estimating the superconducting transition temperature is the electron-phonon coupling strength which measures the electronic band mass enhancement of metals.Usually,the electron-phonon coupling strength can be written as a product of the density of states at the Fermi level and the effective pairing potential.Our numerical simulation indicates that the effective pairing potential in high buckled plumbene varies hardly with the Fermi level,inde-pendent of the spin-orbital coupling.Therefore,the electron-phonon coupling strength and the superconducting transition temperature are mainly determined by the den-sity of states at Fermi level.Firstly,we find that the spin-orbital coupling in high buckled plumbene causes a slight enhancement of the density of states at Fermi level.Hence,the superconducting transition temperature in high buckled plumbene presents an appreciable enhancement as the spin-orbital coupling is taken into account.More interestingly,we find that there are some band edges in the vicinity of the Fermi level of the high buckled plumbene.And it is practically possible to shift the Fermi level to these band edges by carrier doping,which leads to a remarkable increase of density of states at Fermi level.As a result,the superconducting transition temperature of the high buckled plumbene can be sensitively tuned by altering the Fermi level.Ac-cording to our numerical result,the superconducting transition temperature of high buckled plumbene is enhanced from 5.29 K to 17.21 K when the Fermi level is lifted by 0.23 e V from its intrinsic position.In addition,for two-dimensional materials,it is possible to tune the Fermi level by applying a gate voltage on the device region rather than by chemical carrier doping.Therefore,for two-dimensional metal materials with band edges or flat bands near the Fermi level,our study proposes a feasible method to adjust the superconducting transition temperature,thereby achieving the purpose of artificially controlling the superconducting phase transition.Fifthly,we perform first-principles calculations of the thermoelectric properties and tunability of high buckled plumbene.High buckled plumbene is the heaviest mono-layer honeycomb material in the graphene family and expected to show the most pro-nounced spin-orbital coupling effect.We find that the introduction of spin-orbital cou-pling has a nontrivial effect on the thermoelectric properties of high buckled plumbene.It can increase the figure of merit to 5 times.In addition,as mentioned above,many band edges are very close to the Fermi level of high buckled plumbene,hence the van Hove singularity appears in the vicinity of the Fermi level.When the Fermi level is shifted to the nearby van Hove singularity by electron doping from its intrinsic posi-tion,the figure of merit of the high buckled plumbene can be increased by 257 times.Moreover,adjusting the Fermi level of high buckled plumbene can induce the sign re-versal of the Seebeck coefficient.Such a sign reversal of the Seebeck coefficient and the dramatic change in the figure of merit induced by adjusting of the Fermi level indicate a promising device application of high buckled plumbene,such as sensor and cooler.Ad-justing the Fermi level of a two-dimensional material can be achieved by applying a gate voltage in the structure of the electronic transport device,which is a controllable and reversible experimental method.Therefore,our study provides an easy-to-implement solution to improve the thermoelectric performance of two-dimensional materials.Finally,we derive the electron self-energy caused by the electron-phonon interac-tion by Lanczos method.The real part of the electron self-energy is the correction to the eigen energy by the electron-phonon interaction.At finite temperature,the lat-tice vibration changes the potential,and thereupon,the band structure changes with temperature.In particular,it should be noted that for some materials with strong electron-phonon coupling,this effect may cause a non-negligible band correction.For example,an increase in temperature may close the band gap of some topological ma-terials,and band reversal may occur at a critical temperature.This indicates that the electron-phonon interaction may induce a topological phase transition as the tem-perature changes.The existing methods for calculating the electron self-energy only contain the second-order perturbation term,considering the contribution of higher-order terms to be unimportant and can be omitted.However,for some materials with strong electron-phonon coupling,whether the high-order perturbation terms are im-portant remains to be verified.Therefore,we propose a new theoretical scheme,using the Lanczos method to calculate the electron self-energy caused by the electron-phonon interaction to test the contribution of higher-order perturbation terms.The theoretical derivation part of the scheme has been completed,but when we apply the method in realistic materials,it is found that the computational burden is unaffordable.For this difficulty,we are still working on the optimization of the computing scheme.