We investigate a generalized multiorbital tight-binding model on a triangular lattice, a system prevalent in a wide range of two-dimensional materials and particularly relevant for simulating transition metal dichalcogenide monolayers. We show that the interplay between spin-orbit coupling and different symmetry-breaking mechanisms leads to the emergence of four distinct topological phases [Eck et al., Phys. Rev. B 107, 115130 (2023)]. Remarkably, this interplay also triggers the orbital Hall effect with distinguished characteristics. Furthermore, by employing the Landauer-Büttiker formula, we establish that in the orbital Hall insulating phase, the orbital angular momentum is carried by edge states present in nanoribbons with specific terminations. We also show that they do not have the same topological protection against the disorder of the edge states as a first-order topological insulator.

We investigate the orbital Hall effect through a mesoscopic device with momentum-space orbital texture that is connected to four semi-infinite terminals embedded in the Landauer-Büttiker configuration for quantum transport. We present analytical and numerical evidence that the orbital Hall current exhibits mesoscopic fluctuations, which can be interpreted in the framework of random matrix theory (RMT) (as with spin Hall current fluctuations). The mesoscopic fluctuations of orbital Hall current display two different amplitudes of 0.36 and 0.18 for weak and strong spin-orbit coupling, respectively. The amplitudes are obtained by analytical calculation via RMT and are supported by numerical calculations based on the tight-binding model. Furthermore, the orbital Hall current fluctuations lead to two relationships between the orbital Hall angle and conductivity. Finally, we confront the two relations with experimental data of the orbital Hall angle, which shows good concordance between theory and experiment.

We offer a new perspective on the problem of characterizing mesoscopic fluctuations in the interplateau regions of the integer quantum Hall transition. We found that longitudinal and transverse conductance fluctuations, generated by varying the external magnetic field within a microscopic model, are multifractal and lead to distributions of conductance increments (magnetoconductance) with heavy tails (intermittency) and signatures of a hierarchical structure (cascade) in the corresponding stochastic process, akin to Kolmogorov’s theory of fluid turbulence. We confirm this picture by interpreting the stochastic process of the conductance increments in the framework of $H$ theory, which is a continuous-time stochastic approach that incorporates the basic features of Kolmogorov’s theory. The multifractal analysis of the conductance “time series,” combined with the $H$-theory formalism, provides strong support for the overall characterization of mesoscopic fluctuations in the quantum Hall transition as a multifractal stochastic phenomenon with multiscale hierarchy, intermittency, and cascade effects.

We present analytical results for the leading (weak-localization) quantum interference correction to the shot-noise power in a ballistic chaotic cavity coupled nonideally to two electron reservoirs via leads with an arbitrary number of open scattering channels. The calculations were performed using two independent methods: $S$-matrix diagrammatic perturbation theory and quantum circuit theory. We obtained an unexpected amplification-suppression transition as a function of both the number of open channels and the barriers’ transparencies. The effect results from a subtle combination of temporal and spatial quantum coherence in the electron propagation through the system.

We present complete analytical and numerical results that demonstrate the anomalous universal fluctuations of the spin Hall conductance in chiral materials such as graphene and topological insulators. We investigate both the corresponding fluctuations, the universal fractionated and the universal quantized, and also the open channel orbital number crossover between the two regimes. In particular, we show that the Wigner-Dyson symmetries do not properly describe such conductances and the preponderant role of the chiral classes on the Dirac quantum dots. The results are analytical and solve outstanding issues.