Study Of The Transport Behavior Of Low-dimensional Quantum Systems

For the recent three decades,with the development of CMOS(complementary metal oxide semiconductor) technology and micro-measuring technology,the realization of ultra-low temperature,mesoscopic physics has been formed rapidly and has developed into an important part of condensed matter physics,becomes a new research focus.In one-dimensional electron gas(such as quantum wire),the corresponding component of electronic momentum is discrete quantity arising from the electron confinement in two dimensions,fermi surface becomes discrete fermi level.At low temperatures,even if there is a small electronic interaction,it shows a strong correlation(quantum fluctuations),so one-dimensional structure(such as quantum wire) has a completely different physical properties from the three-dimensional structure.In quasi-zero-dimensional structure(such as quantum dots),since the electrons in quantum dots are completely confined in artificially constructed boxes,the quantum effects become manifest in most striking way. Quantum dots structure have become one of the most active areas in mesoscopic physics in very recent years(Ferry D.K.et al,1997.KouwenhovenL.P.et al,1997). From the point of discrete quantum level and charge,quantum dots closely resemble ordinary atoms,and hence,frequently,quantum dots are called artificial atoms (Kastner M.A.,1993.Ashoori R.C.,1996).The unique properties of electron transport,saying,Coulomb blockade(Stating A.A.M.et al,1991) and single electron tunneling(Meirav U.,1990) in quantum dot structures develop new directions for designing and making devices operating on the principles of quantum effects.Besides, the quantum dots can be used to probe those experimental fields which ever are very difficult to touch for their easily tunable parameters.Most importantly,there are strong correlations between the electrons in quantum dots,the study of electron transport in quantum dots contribute much to further understand the strong correlation behaviors. The research methods that we use in the thesis are the bosonization method and the eigen functional theory.The eigen functional theory was established by Professor Liu Yu-liang in 2002-2005.In the eigen-functional theoretical framework,there explicitly exists a key parameter hidden in the quantum many-particle systems,which represents the fermion correlation strength produced by the particle interaction.This parameter is the most intrinsic quantity of the quantum many particle systems,which is called the phase fields.With the phase fields one may unifiably represent the weakly and strongly correlated systems.In the traditional perturbation theories,there does not appear a parameter used to represent the fermion correlation strength.The two key steps of this method are that under the path integral formulation we first change a D-dimensional quantum many-particle system into an(D+1)-dimensional (time-dependent) effective "single-particle" problem,then by solving the eigen equation of the propagator operator of the particles,we can obtain the ground state energy functional and action,respectively.Under the eigen-functional theory,the problems of quantum many-particle systems end in to solve the equation of phase fields that are completely determined by the electron interaction.In practice this equation of the phase fields can be numerically solved by using Monte Carlo.After replacing the real time by the imaginary time,this method can also be applied for finite temperature cases.Using the bosonization method and the eigen functional theory,we study the following two problems.1,Single Impurity Scattering in One-Channel Spinless Luttinger LiquidIt is very important to rigorously treat backward scattering of electrons on an impurity in one-dimensional systems,because the x-ray absorption and the impurity scattering in a Lutttinger liquid(LL),edge-state tunneling of the fractional quantum Hall effect at a quantum point contact,and quantum Brownian motion of an one-dimensional particle in a periodic potential,all involve the treatment of backward scattering term.As a paradigm for non-Fermi-liquid behaviors,the transport properties of electrons in a LL,especially transmission through single local barrier, have been studied widely.The common characteristic of a single impurity scattering in LL is that there is backward scattering of electrons on impurity,which dramatically changes the low-energy behavior of the system.When the interaction is repulsive,the strength of the barrier is renormalized to infinite even if the potential is arbitrarily weak.Thus with repulsive interaction,electrons are completely reflected on the impurity.The divergence of strength of the barrier makes this problem hard to handle.With the bosonization and phase shift representation,we have rigorously treated the backward scattering induced by a non-magnetic impurity in a spinless Luttinger liquid at zero temperature.In the phase shift representation,the behaviors of the system at ultraviolet and infrared fixed points are very clear.We have explicitly shown the transport properties of the system,especially the tunneling conductance.In low energy region,electrons are completely reflected on the impurity;and in high energy region,they completely transmit through it.We explicitly give the expression of the tunneling conductance,which is a modified Landauer-B(u|¨)ttiker formula.2,Fano resonance in Landau Fermi and Luttinger liquidsRecently the Fano resonance has been clearly observed in quantum dot experiments and carbon nanotube experiments where pure metallic carbon nanotube had been shown to have Luttinger liquid behavior in low energy region experimentally and theoretically,but its some novel properties cannot been completely explained by current theory.The Fano resonance is an important phenomenon,and it takes place in a system composed of a continuous energy band and a local energy level in which quantum mechanical interference between these two channels yields a characteristic asymmetric line shape in the transition probability. Obviously,this interference can be easily influenced by an external magnetic field/flux,and the change of the line shape of the Fano resonance with the external magnetic flux can be clearly observed in experiments.With a two channels model,we study the influence of temperature,external voltage and magnetic flux on the line shape of the Fano resonance,and show that in the Luttinger liquid case the background transmittance and the asymmetric parameter strongly depend upon the temperature and external voltage,while for the Landau Fermi liquid case they are nearly independent of these parameters in low energy region.Moreover,we demonstrate that the asymmetric parameter changes periodically with an external magnetic flux,which is consistent with the recent experimental data.