薄介观超导环中的涡旋电荷分布

本文用Ginzburg-Landau理论研究在薄介观超导环中的涡旋电荷分布．对于巨涡旋态，我们发现随着外场的增加，内半径附近的电荷会从负号变为正号．本文表明，是顺磁迈斯纳效应和抗磁迈斯纳效应的竞争决定了涡旋电荷的分布．     

Coulomb-induced positive current-current correlations in normal conductors

In the white-noise limit current correlations measured at different contacts of a mesoscopic conductor are negative due to the antisymmetry of the wave function (Pauli principle). We show that current fluctuations at capacitive contacts induced via the long range Coulomb interaction due to charge fluctuations in the mesoscopic sample can be positively correlated. The positive correlations are a consequence of the extension of the wave functions into areas near both contacts. As an example we investigate in detail a quantum point contact in a high magnetic field under conditions in which transport is along an edge state.     

Effects of geometrical symmetry on the vortex in mesoscopic superconductors

We first systematically study the multivortex states in mesoscopic superconductors via self-consistent Bogoliubov-de Gennes equations. Our work focuses on how the geometrical symmetry affects the penetration and arrangement of vortices in mesoscopic superconductors and find that the key parameter determining the entrance of the vortex is the current density at the hot spots on the edge of sample. Through determining the spatial distribution of hot spots, the geometrical symmetry of the superconducting sample influences the nucleation and entrance of vortices. Our results propose one possible experimental approach to control and manipulate the quantum states of mesoscopic superconductors with their topological geometries, and they can be easily generalized to the confined superfluids and Bose-Einstein condensates.     

用热场动力学理论研究介观电路的Wigner函数

利用热场动力学及相干热态表象理论,重构了有限温度下介观RLC电路的Wigner函数,研究了有限温度下介观RLC电路的量子涨落.借助于Weyl-Wigner理论讨论了有限温度下介观RLC电路Wigner函数的边缘分布,并进一步阐明了Wigner函数边缘分布统计平均的物理意义.结果表明: 有限温度下介观RLC电路中电荷和电流的量子涨落随着温度和电阻值的增加而增加,回路中的电荷和电流之间存在着压缩效应,这种量子效应是由于系统零点振动的涨落而引起的; 有限温度下介观RLC电路Wigner函数边缘分布的统计平均正好是储存在介观RLC电路中电容和电感上的能量.     

用热场动力学理论研究介观电路的Wigner函数

利用热场动力学及相干热态表象理论,重构了有限温度下介观RLC电路的Wigner函数,研究了有限温度下介观RLC电路的量子涨落.借助于Weyl-Wigner理论讨论了有限温度下介观RLC电路Wigner函数的边缘分布,并进一步阐明了Wigner函数边缘分布统计平均的物理意义.结果表明:有限温度下介观RLC电路中电荷和电流的量子涨落随着温度和电阻值的增加而增加,回路中的电荷和电流之间存在着压缩效应,这种量子效应是由于系统零点振动的涨落而引起的;有限温度下介观RLC电路Wigner函数边缘分布的统计平均正好是储存在介观RLC电路中电容和电感上的能量.     

Analytic solutions to Maxwell–London equations and levitation force for a general magnetic source in the presence of a long type-II superconducting cylinder

The interaction between a general magnetic source and a long type-II superconducting cylinder in the Meissner or mixed state is studied within the London theory. We first study the Meissner state and solve the Maxwell–London equations when the source is a magnetic monopole located at an arbitrary position. Then the field and supercurrent for a more complicated magnetic charge distribution can be obtained by superposition. A magnetic point dipole with arbitrary direction is studied in detail. It turns out that the levitation force on the dipole contains in general an angular as well as a radial component. By integration we obtain the field and supercurrent when the source is a two-dimensional monopole (a magnetically charged long thread along the axial direction), from which the results for a two-dimensional point dipole easily follow. In the latter case the levitation force points in the radial direction regardless of the orientation of the dipole. The case for a current carrying long straight wire parallel to the cylindrical axis is solved separately. The limit of ideal Meissner state is discussed in most cases. The case of mixed state is discussed briefly. It turns out that vortex lines along the axial direction and vortex rings concentric with the cylinder have no effect outside the cylinder and the levitation forces remain the same as in the case of the Meissner state.     

Electrodynamics of spin currents in superconductors

In recent work we formulated a new set of electrodynamic equations for superconductors as an alternative to the conventional London equations, compatible with the prediction of the theory of hole superconductivity that superconductors expel negative charge from the interior towards the surface. Charge expulsion results in a macroscopically inhomogeneous charge distribution and an electric field in the interior, and because of this a spin current is expected to exist. Furthermore, we have recently shown that a dynamical explanation of the Meissner effect in superconductors leads to the prediction that a spontaneous spin current exists near the surface of superconductors (spin Meissner effect). In this paper we extend the electrodynamic equations proposed earlier for the charge density and charge current to describe also the space and time dependence of the spin density and spin current. This allows us to determine the magnitude of the expelled negative charge and interior electric field as well as of the spin current in terms of other measurable properties of superconductors. We also provide a `geometric' interpretation of the difference between type I and type II superconductors, discuss how superconductors manage to conserve angular momentum, discuss the relationship between our model and Slater's seminal work on superconductivity, and discuss the magnitude of the expected novel effects for elemental and other superconductors.     

Electron waiting times in mesoscopic conductors

Electron transport in mesoscopic conductors has traditionally involved investigations of the mean current and the fluctuations of the current. A complementary view on charge transport is provided by the distribution of waiting times between charge carriers, but a proper theoretical framework for coherent electronic systems has so far been lacking. Here we develop a quantum theory of electron waiting times in mesoscopic conductors expressed by a compact determinant formula. We illustrate our methodology by calculating the waiting time distribution for a quantum point contact and find a crossover from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off. Even when the low-frequency transport is noiseless, the electrons are not equally spaced in time due to their inherent wave nature. We discuss the implications for renewal theory in mesoscopic systems and point out several analogies with level spacing statistics and random matrix theory.     

Mesoscopic one-way channels for quantum state transfer via the quantum Hall effect

We show that the one-way channel formalism of quantum optics has a physical realization in electronic systems. In particular, we show that magnetic edge states form unidirectional quantum channels capable of coherently transporting electronic quantum information. Using the equivalence between one-way photonic channels and magnetic edge states, we adapt a proposal for quantum state transfer to mesoscopic systems using edge states as a quantum channel, and show that it is feasible with reasonable experimental parameters. We discuss how this protocol may be used to transfer information encoded in number, charge, or spin states of quantum dots, so it may prove useful for transferring quantum information between parts of a solid-state quantum computer.     

Charge densities and charge noise in mesoscopic conductors

We introduce a hierarchy of density of states to characterize the charge distribution in a mesoscopic conductor. At the bottom of this hierarchy are the partial density of states which represent the contribution to the local density of states if both the incident and the out-going scattering channel is prescribed. The partial density of states play a prominent role in measurements with a scanning tunneling microscope on multiprobe conductors in the presence of current flow. The partial density of states determine the degree of dephasing generated by a weakly coupled voltage probe. In addition the partial density of states determine the frequency-dependent response of mesoscopic conductors in the presence of slowly oscillating voltages applied to the contacts of the sample. The partial density of states permit the formulation of a Friedel sum rule which can be applied locally. We introduce the off-diagonal elements of the partial density of states matrix to describe charge fluctuation processes. This generalization leads to a local Wigner-Smith life-time matrix.     

相干介观系统中散粒噪声的Monte Carlo模拟方法研究

根据电荷通过低温量子导体时具有的二项分布导致散粒噪声这一结论,结合Landauer电流公式的物理内涵建立了相干介观系统中的散粒噪声模型,并通过Monte Carlo模拟方法产生了散粒噪声时间序列.介观系统中散粒噪声的抑制来源于电子输运时的相关性,传输本征值双峰分布导致量子混沌腔和无序金属中的散粒噪声抑制.根据这两个结论,通过Monte Carlo模拟定性地分析了传输本征值分布与电子输运相关性之间的关系. 关键词： 散粒噪声 Landauer公式 介观系统     

Contact effect in the dynamic electron transport of a two-probe mesoscopic conductor

Based on the self-consistent electron dynamic transport theory for multi-probe mesoscopic systems, we calculate the distribution of internal potential, charge density, and ac conductance of a two-probe mesoscopic conductor with wide trapezoid reservoirs, and study the contact effect. The results show that including the contact effect can make a significant difference to the frequency-dependent electron transport properties. In the nonzero frequency case, the internal potential and the charge density are complex with extremely small imaginary parts. Importantly, the imaginary part of the charge density gives rise to a real ac conductance (admittance), which corresponds to the charge-relaxation resistance.     

Charge redistribution between cyclotron-resolved edge states at high imbalance

We use a quasi-Corbino sample geometry with independent contacts to different edge states in the quantum Hall effect regime to investigate a charge redistribution between cyclotron-split edge states at high imbalance. We also modify the Büttiker formalism by introducing local transport characteristics in it and use this modified Büttiker picture to describe the experimental results. We find that charge transfer between cyclotron-split edge states at high imbalance can be described by a single parameter, which is a transferred between edge states portion of the available for transfer part of the electrochemical potential imbalance. This parameter is found to be independent of the particular sample characteristics, describing fundamental properties of the interedge-state scattering. From the experiment we obtain it in the dependence on the voltage imbalance between edge states and propose a qualitative explanation to the experimental findings.     

Magnetic field analysis in a diamond anvil cell for Meissner effect measurement by using the diamond NV~- center

Diamond negatively charged nitrogen-vacancy(NV-) centers provide an opportunity for the measurement of the Meissner effect on extremely small samples in a diamond anvil cell(DAC) due to their high sensitivity in detecting the tiny change of magnetic field. We report on the variation of magnetic field distribution in a DAC as a sample transforms from normal to superconducting state by using finite element analysis. The results show that the magnetic flux density has the largest change on the sidewall of the sample, where NV-centers can detect the strongest signal variation of the magnetic field. In addition, we study the effect of magnetic coil placement on the magnetic field variation. It is found that the optimal position for the coil to generate the greatest change in magnetic field strength is at the place as close to the sample as possible.     

三维介观超导环涡旋态的研究

通过数值求解非线性金兹堡-朗道(G-L)方程组,研究了三维介观超导环中的涡旋态。发现了在细环中只能存在巨涡旋态,以及存在顺磁、抗磁迈斯纳效应和间隙性超导现象。在粗环中,发现了多涡旋态和巨涡旋态共存的混合态。相应讨论有助于理解介观超导环中涡旋态相变。     

热克尔态下介观LC电路的量子涨落

基于介观电容可看作介观隧道结的物理事实，利用旋波近似方法，对介观LC电路进行量子化处理，量子化后介观LC电路系统等效为一个克尔系统.再利用热场动力学理论方法 研究了介观LC电路在有限温度时热克尔态下电荷和磁通的量子涨落，并对结果进行了讨 论. 关键词： 介观LC电路 热克尔态 量子涨落     

Charge distribution in graphene from quantum calculation

The local charge distributions of different shape graphene sheets are investigated by using the quantum calculations.It is found that the charge distribution on carbon atom is not uniform, strongly depending on its position in the graphene and its local atomic environment condition. The symmetrical characteristic and geometrical structures of graphene also have an important influence on the charge distribution. The charges of atom at the graphene edge are strongly related to their surrounding bonds. It is found that the charges of double-bonded atom at the zigzag edge are closely related to the bond angle, but the charges of double-bonded atom at the armchair edge are mainly influenced by the area of triangle. The charges of triple-bonded atom at the edge are mainly affected by the standard deviation of the length of the associated triple bonds.     

Fermi-edge singularities in the mesoscopic x-ray edge problem

We study the x-ray edge problem for a chaotic quantum dot or nanoparticle displaying mesoscopic fluctuations. In the bulk, x-ray physics is known to produce Fermi-edge singularities-deviations from the naively expected photoabsorption cross section in the form of a peaked or rounded edge. For a coherent system with chaotic dynamics, we find substantial changes; in particular, a photoabsorption cross section showing a rounded edge in the bulk will change to a slightly peaked edge on average as the system size is reduced to a mesoscopic (coherent) scale.     

Interaction effects on counting statistics and the transmission distribution

We investigate the effect of weak interactions on the full counting statistics of charge transfer through an arbitrary mesoscopic conductor. We show that the main effect can be incorporated into an energy dependence of the transmission eigenvalues and study this dependence in a nonperturbative approach. An unexpected result is that all mesoscopic conductors behave at low energies such as either a single or a double tunnel junction, which divides them into two broad classes.     

电荷不连续时电容耦合介观电路的量子回路方程及其能谱

考虑电荷具有不连续性的事实对双LC介观电路进行量子化,给出耦合形式的量子回路方程以及无相互作用Hamilton本征基矢下的电路能谱.结果表明,计及电荷离散性将使回路方程的形式发生明显变化;介观电路的能谱除与电路参数相关外,还明显地依赖于电荷的量子化性质.