We study the Wigner crystal melting in a two dimensional quantum system of particles interacting via the 1/r Coulomb potential. We use quantum Monte Carlo methods to calculate its phase diagram, locate the Wigner crystal region, and analyze its instabilities towards the liquid phase. We discuss the role of quantum effects in the critical behavior of the system, and compare our numerical results with the classical theory of melting, and the microemulsion theory of frustrated Coulomb systems. We find a Pomeranchuk effect much larger then in solid helium. In addition, we find that the exponent for the algebraic decay of the hexatic phase differs significantly from the Kosterilitz-Thouless theory of melting. We search for the existence of mesoscopic phases and find evidence of metastable bubbles but no mesoscopic phase that is stable in equilibrium.
Persistent current is a small but perpetual electric current that flows in metallic rings in the absence of any applied source. We compute the persistent currents of one-dimensional disordered metallic rings of interacting electrons in the presence of impurity on lattices up to 8-sites at half-filling and also away from half-filling using the Lanczos algorithm. For the case of half-filling, we observe that both interaction and disorder suppress the amplitude of the persistent currents by localizing the electrons. However, in the presence of disorder and away from half-filling, the Coulomb inte…
Motivated by the recently developed duality between elasticity of a crystal and a symmetric tensor gauge theory by Pretko and Radzihovsky, we explore its classical analog, that is a dual theory of the dislocation-mediated melting of a two-dimensional crystal, formulated in terms of a higher derivative vector sine-Gordon model. It provides a transparent description of the continuous two-stage melting in terms of the renormalization-group relevance of two cosine operators that control the sequential unbinding of dislocations and disclinations, respectively corresponding to the crystal-to-hexatic…
Mesoscopic behavior of the transmission phase through confined correlated electronic systems
研究了电子关联对量子相干散射体传输相位的影响，考虑了库仑阻塞机制下的量子点与两个单通道导线的连接。我们专注于传输零点和相关的π-相位已经在干涉实验中观察到的失误。我们用数值方法研究了量子点的两种模型：（i）具有多达八个位点的晶格模型，以及（ii）具有多达六个能级的共振能级模型。我们确定了不同的制度的参数，其中存在的电子相关性是负责的传输零点与电化学电位的点的数量的增加或减少。然而，我们表明，相互作用的影响不能再现的普遍行为的交替共振和相位滞后，实验观察到的多电子库仑阻塞点。我们的数值计算结果强烈表明，主要的实验观察到的特征是由莫利纳等人的混沌弹道点理论捕获，[Phys. Rev. Lett. 108，076803（2012）]，其结合了单粒子波函数相关性，但忽略了多粒子电子相关性。
We study crystal melting in two-dimensional antiferromagnets, by analyzing the statistical mechanics of the six-state clock model on a lattice in which defects (dislocations and disclinations) are allowed to appear. We show that the elementary dislocations bind to fractional magnetic vortices. We compute the phase diagram by mapping the system into a Coulomb gas model. Surprisingly, we find that in the limit of dominant magnetic interactions, antiferromagnetism can survive even in the hexatic and liquid phases. The ensuing molten antiferromagnets are topologically ordered and are characterized…
The carbon monolayer band structure calculated in the approximation of weakly interacting π electrons corresponds to massless electron excitations known as Dirac fermions not previously observed in any other material. However, if strong Coulomb and exchange interactions between π electrons are taken into account, another picture of the π electron state emerges. These interactions result in π electron localization and electron crystal formation. The atomically flat layer can be regarded as a simplest quasi-two-dimensional mesoscopic quantum system consisting of a carbon ion plane and two π elec…
A novel mesoscopic electron spectrometer allows for the probing of relaxation processes in quantum Hall edge channels. The device is composed of an emitter quantum dot that injects energy-resolved electrons into the channel closest to the sample edge, to be subsequently probed downstream by a detector quantum dot of the same type. In addition to inelastic processes in the sample that stem from interactions inside the region between the quantum dot energy filters (inner region), anomalous signals are measured when the detector energy exceeds the emitter energy. Considering finite range Coulomb …
This review illustrates how Local Fermi Liquid (LFL) theories describe the strongly correlated and coherent low-energy dynamics of quantum dot devices. This approach consists in an effective elastic scattering theory, accounting exactly for strong correlations. Here, we focus on the mesoscopic capacitor and recent experiments achieving Coulomb-induced quantum state transfer. Extending to out-of-equilibrium regimes, aiming at triggered single electron emission, we illustrate how inelastic effects become crucial, requiring approaches beyond LFLs, shedding new light on past experimental data, by …
