Experiments on collisions of isolated electrons guided along the edges in quantum Hall setups can mimic mixing of photons with the important distinction that electrons are charged fermions. In the so-called electronic Hong-Ou-Mandel (HOM) setup uncorrelated pairs of electrons are injected towards a beamsplitter. If the two electron wave packets were identical, Fermi statistics would force the electrons to scatter to different detectors, yet this quantum antibunching may be confounded by Coulomb repulsion. Here we model an electronic HOM experiment using a quadratic 2D saddle point potential for the beamsplitter and unscreened Coulomb interaction between the two injected electrons subjected to a strong out-of-plane magnetic field. We show that classical equations of motion for the drift dynamics of electrons' guiding centers take on the form of Hamilton equations for canonically conjugated variables subject to the saddle point potential and the Coulomb potential where the dynamics of the center-of-mass coordinate and the relative coordinate separate. We use these equations to determine collision outcomes in terms of a few experimentally tuneable parameters: the initial energies of the uncorrelated electrons, relative time delay of injection and the shape of the saddle point potential. A universal phase diagram of deterministic bunching and antibunching scattering outcomes is presented with a single energy scale characterizing the increase of the effective barrier height due to interaction of coincident electrons. We suggest clear-cut experimental strategies to detect the predicted effects and give analytical estimates of conditions when the classical dynamics is expected to dominate over quantum effects.
We review our recent theoretical results for mesoscopic fluctuations of the local density of states in the presence of electron-electron interaction. We focus on the two specific cases: (i) a vicinity of interacting critical point corresponding to Anderson-Mott transition, and (ii) a vicinity of non-interacting critical point in the presence of a weak electron-electron attraction. In both cases strong mesoscopic fluctuations of the local density of states exist.
We calculate the frequency-dependent equilibrium noise of a mesoscopic capacitor in time-dependent density functional theory (TDDFT). The capacitor is modeled as a single-level quantum dot with on-site Coulomb interaction and tunnel coupling to a nearby reservoir. The noise spectra are derived from linear-response conductances via the fluctuation-dissipation theorem. Thereby, we analyze the performance of a recently derived exchange-correlation potential with time-nonlocal density dependence in the finite-frequency linear-response regime. We compare our TDDFT noise spectra with real-time pertu…
We calculate persistent current of one-dimensional rings of fermions neglecting the spin degrees of freedom considering only nearest-neighbor Coulomb interactions with different electron fillings in both ordered and disordered cases. We treat the interaction exactly and find eigenenergies by exact diagonalization of many-body Hamiltonian and compute persistent current by numerical derivative method. We also determine Drude weight to estimate the conducting nature of the system. From our numerical results, we obtain a metal-insulator transition in half-filled case with increasing correlation st…
Two electrons interacting at a mesoscopic beam splitter
Physikalisch-Technische Bundesanstalt（德国联邦物理技术研究院）；University of Latvia（拉脱维亚大学）；Institut für Mathematische Physik, Technische Universität Braunschweig（布伦瑞克工业大学数学物理研究所）
We consider the full nonequilibrium response of a mesoscopic capacitor in the large transparency limit, exactly solving a model with electron-electron interactions appropriate for a cavity in the quantum Hall regime. For a cavity coupled to the electron reservoir via an ideal point contact, we show that the response to any time-dependent gate voltage $V_{\rm g}(t)$ is strictly linear in $V_{\rm g}$. We analyze the charge and current response to a sudden gate voltage shift, and find that this response is not captured by a simple circuit analogy. In particular, in the limit of strong interaction…
Using the two-loop analysis and the background field method we demonstrate that the local pure scaling operators without derivatives in the Finkel'stein nonlinear sigma model can be constructed by straightforward generalization of the corresponding operators for the noninteracting case. These pure scaling operators demonstrate multifractal behavior and describe mesoscopic fluctuations of the single-particle Green's function. We determine anomalous dimensions of all such pure scaling operators in the interacting theory within the two-loop approximation.
We investigate a mesoscopic spin current for strongly interacting Fermi gases through a quantum point contact. Under the situation where spin polarizations in left and right reservoirs are same in magnitude but opposite in sign, we calculate the contribution of quasiparticles to the current by means of the linear response theory and many-body $T$-matrix approximation. For a small spin-bias regime, the current in the vicinity of the superfluid transition temperature is strongly suppressed due to the formation of pseudogaps. For a large spin-bias regime where the gases become highly polarized, o…
Ensembles of gold nanoparticles present a magnetic behavior which is at odds with the weakly diamagnetic response of bulk gold. In particular, an unusual ferromagnetic order has been unveiled by several experiments. Here we investigate if the combined effect of orbital magnetism of conduction electrons and interparticle dipolar interaction can lead to magnetic ordering. Using different model systems of interacting mesoscopic magnetic dipoles, together with a microscopic description of the electron dynamics within the nanoparticles, we find that a spontaneous magnetic moment may arise in dimers…
We consider an interacting quantum dot working as a coherent source of single electrons. The dot is tunnel coupled to a reservoir and capacitively coupled to a gate terminal with an applied ac potential. At low frequencies, this is the quantum analog of the RC circuit with a purely dynamical response. We investigate the quantized dynamics as a consequence of ac pulses with large amplitude. Within a Keldysh-Green function formalism we derive the time-dependent current in the Coulomb blockade regime. Our theory thus extends previous models that considered either noninteracting electrons in nonli…
When combining lumped mesoscopic electronic components to form a circuit, quantum fluctuations of electrical quantities lead to a non-linear electromagnetic interaction between the components that is not generally understood. The Landauer-Büttiker formalism that is frequently used to describe non-interacting coherent mesoscopic components is not directly suited to describe such circuits since it assumes perfect voltage bias, i.e. the absence of fluctuations. Here, we show that for short coherent conductors of arbitrary transmission, the Landauer-Büttiker formalism can be extended to take into …
Magnetic response of mesoscopic rings: a quantum size effect
我们解析地研究了具有最近邻相互作用（t）和交替位能的双峰势的正常非相互作用介观环中持续电流（PC）的磁响应。结果表明，周长（N）和宽度（M）的环一般表现出弱的抗磁性，打破了电子填充的奇偶规则。特别地，在N=（2 p +1）（M+1），M为奇数，p为整数时，在F0/2周期中，顺磁电流最大，反磁F0/2电流最大，M为偶数时，N=（2 p +1）（M+1）+/-1。电流幅值对N和M都有很强的依赖性，变化幅度至少为1~2个数量级，表现出显著的量子尺寸效应。在N= 2 p（M+1）处，顺磁谐波的电流极限与N和M的大小无关，有利于实验观察。提出了一种新的磁响应机制，即一个电子在一个磁通量子内连续通过环的每个通道，在每个通道间的跃迁中积累一个额外的相位，从而导致顺磁-反磁跃迁和周期减半。结果统一并揭示了PC中理论与实验之间的矛盾，在介观尺度上验证了量子力学。
This work explores different mechanisms that induce thermal rectification in the nanoscale. The presence of interacting energy channels combined with simple asymmetries is sufficient for promoting the desired behavior. We use simple quantum dot configurations, identifying the basic properties that enhance rectification for each case: the size of a quantum dot state space (which suggests the use of scaled up systems with many interacting channels), tunneling asymmetries due to coherent tunneling in a double quantum dot, or quantum interference in a triangular triple quantum dot. An efficient an…
The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations
本文利用Kubo-Landauer方法计算了置于强垂直磁场中的二维电子系统在周期调制和无序势作用下的纵向（两端）电导。散射问题被改写为一组非均匀的，耦合的线性方程组，使我们能够找到从有限大小的系统计算的传输概率;结果是准确的非相互作用的电子。我们的方法充分考虑了无序和周期调制的影响，无论它们的相对强度如何，只要朗道能级混合可以忽略不计。特别是，我们专注于周期性调制和那些无序的影响之间的相互作用。这似乎是理解最近实验的相关机制[S。Melinte { \em et al}，Phys. Rev. Lett. { \bf 92}，036802（2004）]，我们的数值结果与这些实验结果定性一致。我们开发的数值技术可以直接推广到多终端的几何形状，以及其他多通道散射问题。
Two interacting particles in a disordered chain IV: Scaling of level curvatures
数值研究了介观无序环中两粒子能级相对于封闭磁通量的曲率。我们发现，曲率的典型值增加的相互作用在本地化制度和金属制度减少。这证实了Akkermans和Pichard（Eur. J. B 1，223（1998））。在不同的能量和无序强度的相互作用引起的典型曲率的变化表现出单参数标度与电导一样的单参数。这表明相互作用可以类似地影响介观系统的电导。
