Frequency correlations in reflection from random media

We present a theoretical study of frequency correlations of light backscattered from a random scattering medium. This statistical quantity provides insight into the dynamics of multiple scattering processes accessible both, in theoretical and experimental investigations. For frequency correlations between field amplitudes, we derive a simple expression in terms of the path length distribution of the underlying backscattering processes. In a second step, we apply this relation to describe frequency correlations between intensities in the regime of weak disorder. Since, with increasing disorder strength, an unexplained breakdown of the angular structure of the frequency correlation function has recently been reported in experimental studies, we explore extensions of our model to the regime of stronger disorder. In particular, we show that closed scattering trajectories tend to suppress the angular dependence of the frequency correlation function.Comment: 10 pages, 8 figure

Phase diagram of a graphene bilayer in the zero-energy Landau level

Bilayer graphene under a magnetic field has an octet of quasidegenerate levels due to spin, valley, and orbital degeneracies. This zero-energy Landau level is resolved into several incompressible states whose nature is still elusive. We use a Hartree-Fock treatment of a realistic tight-binding four-band model to understand the quantum ferromagnetism phenomena expected for integer fillings of the octet levels. We include the exchange interaction with filled Landau levels below the octet states. This Lamb-shift-like effect contributes to the orbital splitting of the octet. We give phase diagrams as a function of applied bias and magnetic field. Some of our findings are in agreement with experiments. We discuss the possible appearance of phases with orbital coherence

Edge structure of graphene monolayers in the {\nu} = 0 quantum Hall state

Monolayer graphene at neutrality in the quantum Hall regime has many competing ground states with various types of ordering. The outcome of this competition is modified by the presence of the sample boundaries. In this paper we use a Hartree-Fock treatment of the electronic correlations allowing for space-dependent ordering. The edge influence is modeled by a simple perturbative effective magnetic field in valley space. We find that all phases found in the bulk of the sample, ferromagnetic, canted antiferromagnetic, charge-density wave and Kekul$\'e$ distortion are smoothly connected to a Kekul$\'e$-distorted edge. The single-particle excitations are computed taking into account the spatial variation of the order parameters. An eventual metal-insulator transition as a function of the Zeeman energy is not simply related to the type of bulk order.Comment: 18 pages, 11 figures, corresponds to published versio

Flux conservation in coherent backscattering and weak localisation of light

The standard theoretical description of coherent backscattering, accord- ing to which maximally crossed diagrams accounting for interference between counter- propagating path amplitudes are added on top of the incoherent background, violates the fundamental condition of flux conservation. In contrast to predictions of previous theories, we show that including maximally crossed diagrams with one additional scat- tering event does not restore flux conservation. Instead, we propose that the latter is recovered when treating the effects of coherent backscattering and weak localisation in a unified framework. On the basis of this framework, we demonstrate explicitly flux conservation in leading order of the weak disorder parameter 1/(kl).Comment: 18 page

Semimetallic features in quantum transport through a gate-defined point contact in bilayer graphene

We demonstrate that, at the onset of conduction, an electrostatically defined quantum wire in bilayer graphene (BLG) with an interlayer asymmetry gap may act as a 1D semimetal, due to the multiple minivalley dispersion of its lowest subband. Formation of a non-monotonic subband coincides with a near-degeneracy between the bottom edges of the lowest two subbands in the wire spectrum, suggesting an $8e^2/h$ step at the conduction threshold, and the semimetallic behaviour of the lowest subband in the wire would be manifest as resonance transmission peaks on an $8e^2/h$ conductance plateau.Comment: 9 pages, 8 figures (including appendices

Kagome network of miniband-edge states in double-aligned graphene–hexagonal boron nitride structures

Twistronic heterostructures have recently emerged as a new class of quantum electronic materials with properties determined by the twist angle between the adjacent two-dimensional materials. Here we study moir\'e superlattice minibands in graphene (G) encapsulated in hexagonal boron nitride (hBN) with an almost perfect alignment with both the top and bottom hBN crystals. We show that, for such an orientation of the unit cells of the hBN layers that locally breaks inversion symmetry of the graphene lattice, the hBN/G/hBN structure features a Kagom\'e network of topologically protected chiral states with energies near the miniband edge, propagating along the lines separating the areas with different miniband Chern numbers.Comment: 6 pages, 3 figures (Supplemental Material: 7 pages, 5 figures, 1 table

Engineering of the topological magnetic moment of electrons in bilayer graphene using strain and electrical bias

Topological properties of electronic states in multivalley two-dimensional materials, such as mono- and bilayer graphene, or thin films of rhombohedral graphite, give rise to various unusual magneto-transport regimes. Here, we investigate the tunability of the topological magnetic moment (related to the Berry curvature) of electronic states in bilayer graphene using strain and vertical bias. We show how one can controllably vary the valley $g$-factor of the band-edge electrons, $g_v^*$, across the range $10 < |g_v^*| < 200$, and we discuss the manifestations of the topological magnetic moment in the anomalous contribution towards the Hall conductivity and in the Landau level spectrum.Comment: 6 pages, 5 figure

Tunneling theory for a bilayer graphene quantum dot's single- and two-electron states

The tuneability and control of quantum nanostructures in two-dimensional materials offer promising perspectives for their use in future electronics. It is hence necessary to analyze quantum transport in such nanostructures. Material properties such as a complex dispersion, topology, and charge carriers with multiple degrees of freedom, are appealing for novel device functionalities but complicate their theoretical description. Here, we study quantum tunnelling transport across a few-electron bilayer graphene quantum dot. We demonstrate how to uniquely identify single- and two-electron dot states' orbital, spin, and valley composition from differential conductance in a finite magnetic field. Furthermore, we show that the transport features manifest splittings in the dot's spin and valley multiplets induced by interactions and magnetic field (the latter splittings being a consequence of bilayer graphene's Berry curvature). Our results elucidate spin- and valley-dependent tunnelling mechanisms and will help to utilize bilayer graphene quantum dots, e.g., as spin and valley qubits.Comment: 18 pages, 12 figure

Tuning‐Confined States and Valley G‐Factors by Quantum Dot Design in Bilayer Graphene

Electrostatically confined quantum dots in bilayer graphene have shown potential as building blocks for quantum technologies. To operate the dots, e.g., as qubits, a precise understanding and control of the confined states and their properties is required. Herein, a large-scale numerical characterization of confined quantum states in bilayer graphene dots is performed over an extensive range of gate-tunable parameters such as the dot size, depth, shape, and the bilayer graphene gap. The dot states’ orbital degeneracy, wave function distribution, and valley g-factor are established and the parametric dependencies to achieve different regimes are provided. It is found that the dot states are highly susceptible to gate-dependent confinement and material parameters, enabling efficient tuning of confined states and valley g-factor modulation by quantum dot design