Geometry effects in the magnetoconductance of normal and Andreev Sinai billiards

Fractal Magneto-conductance Fluctuations in Mesoscopic Semiconductor Billiards

Negatively biased surface-gates allow electrostatic depletion of selected regions of a 2DEG, forming confined regions of specific geometry called billiards, in which ballistic transport occurs. At millikelvin temperatures, the electron phase coherence length is sufficient that quantum interference effects produce reproducible magneto-conductance fluctuations (MCF) that act as a 'magneto-fingerprint' of the scattering dynamics in the billiard. It has been predicted that billiard MCF are fractal. Fractal MCF in mesoscopic semiconductor billiards are investigated experimentally. The MCF of a Sina…

Nonlinear Effects on Quantum Interference in Electron Billiards

Magnetoconductance fluctuations are used to study the effect of an applied bias on an electron billiard. At lower bias, nonlinear effects can be well described by electron heating alone, while at higher bias (V > 2mV, ~5% of the electron Fermi energy) non-equilibrium effects become significant. At high bias, we also observe that the spectral content of the MCF is sensitive to the nonequilibrium effects. Spectral behavior is consistent with a fractal scaling of the conductance fluctuations with magnetic field, resulting in the first observation of fractal conductance fluctuations outside of the…

Reaction matrix for Dirichlet billiards with attached waveguides

The reaction matrix of a cavity with attached waveguides connects scattering properties to properties of a corresponding closed billiard for which the waveguides are cut off by straight walls. On the one hand this matrix is directly related to the S-matrix, on the other hand it can be expressed by a spectral sum over all eigenfunctions of the closed system. However, in the physically relevant situation where these eigenfunctions vanish on the impenetrable boundaries of the closed billiard, the spectral sum for the reaction matrix, as it was used before, fails to converge and does not reliably …

Multifractal Magnetoconductance Fluctuations in Mesoscopic Systems

We perform a multifractal detrended fluctuation analysis of the magnetoconductance data of two standard types of mesoscopic systems: a disordered nanowire and a ballistic chaotic billiard, with two different lattice structures. We observe in all cases that multifractality is generally present and that it becomes stronger in the quantum regime of conduction, i.e., when the number of open scattering channels is small. We argue that this behavior originates from correlations induced by the magnetic field, which can be characterized through the distribution of conductance increments in the corresp…

Effect of proximity-induced spin-orbit coupling in graphene mesoscopic billiards

Van der Waals heterostructures based on two-dimensional materials have recently become a very active topic of research in spintronics, both aiming at a fundamental description of spin dephasing processes in nanostructures and as a potential element in spin-based information processing schemes. Here, we theoretically investigate the magnetoconductance of mesoscopic devices built from graphene proximity-coupled to a high spin-orbit coupling material. Through numerically exact tight-binding simulations, we show that the interfacial breaking of inversion symmetry generates robust weak antilocaliza…

Effective Random Matrix Theory description of chaotic Andreev billiards

An effective random matrix theory description is developed for the universal gap fluctuations and the ensemble averaged density of states of chaotic Andreev billiards for finite Ehrenfest time. It yields a very good agreement with the numerical calculation for Sinai-Andreev billiards. A systematic linear decrease of the mean field gap with increasing Ehrenfest time $τ_E$ is observed but its derivative with respect to $τ_E$ is in between two competing theoretical predictions and close to that of the recent numerical calculations for Andreev map. The exponential tail of the density of states is …

量子混沌在声子极化子腔体中的特征

Signatures of quantum chaos in phonon-polariton billiards

研究通过扫描近场光学显微镜成像六方氮化硼（hBN）腔体中超声子极化子的特征，发现非混沌的一维边界模式与量子疤痕共存，并通过数值框架和理论分析揭示了腔体混沌动力学的广泛特性。

Quantum stress in chaotic billiards

This article reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor $T_{αβ}(x,y)$ for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as $ψ= u+iv$. With the assumption that $u$ and $v$ are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components $T_{αβ}$. The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained …

Is it the boundaries or disorder that dominates electron transport in semiconductor `billiards'?

Semiconductor billiards are often considered as ideal systems for studying dynamical chaos in the quantum mechanical limit. In the traditional picture, once the electron's mean free path, as determined by the mobility, becomes larger than the device, disorder is negligible and electron trajectories are shaped by specular reflection from the billiard walls alone. Experimental insight into the electron dynamics is normally obtained by magnetoconductance measurements. A number of recent experimental studies have shown these measurements to be largely independent of the billiards exact shape, and …

Magnetic-field dependence of transport in normal and Andreev billiards: a classical interpretation to the averaged quantum behavior

We perform a comparative study of the quantum and classical transport probabilities of low-energy quasiparticles ballistically traversing normal and Andreev two-dimensional open cavities with a Sinai-billiard shape. We focus on the dependence of the transport on the strength of an applied magnetic field $B$. With increasing field strength the classical dynamics changes from mixed to regular phase space. Averaging out the quantum fluctuations, we find an excellent agreement between the quantum and classical transport coefficients in the complete range of field strengths. This allows an overall …

Interaction effects in a chaotic graphene quantum billiard

We investigate the local electronic structure of a Sinai-like, quadrilateral graphene quantum billiard with zigzag and armchair edges using scanning tunneling microscopy at room temperature. It is revealed that besides the $(\sqrt{3}\times\sqrt{3})R30$° superstructure, which is caused by the intervalley scattering, its overtones also appear in the STM measurements, which are attributed to the Umklapp processes. We point out that these results can be well understood by taking into account the Coulomb interaction in the quantum billiard, accounting for both the measured density of state values a…