Janusz Jacak

Hierarchy of fillings for the FQHE in monolayer graphene

In this paper, the commensurability conditions, which originated from the unique topology of two-dimensional systems, are applied to determine the quantum Hall effect hierarchy in the case of a monolayer graphene. The fundamental difference in a definition of a typical semiconductor and a monolayer graphene filling factor is pointed out. The calculations are undertaken for all spin-valley branches of two lowest Landau levels, since only they are currently experimentally accessible. The obtained filling factors are compared with the experimental data and a very good agreement is achieved. The work also introduces a concept of the single-loop fractional quantum Hall effect.

Cyclotron braid group structure for composite fermions

Although they describe properties of 2D Hall systems in the fractional quantum regime well, composite fermions suffer from the unexplained character of the localized magnetic field flux-tubes attached to each particle in order to reproduce the Laughlin correlations via Aharonov-Bohm phase shifts. The identification of the cyclotron trajectories of 2D charged particles as accessible classical trajectories within the braid group approach at the magnetic field presence, allows, however, for the avoidance of the construction with fluxes. We introduce cyclotron braid subgroups for charged 2D systems at the fractional Landau-level filling associated in a more natural way with composite fermions without invoking field flux-tubes. The Aharonov-Bohm phase shifts caused by fluxes are replaced with the phase gain due to multi-loop cyclotron trajectories unavoidably occurring at the fractional filling of 1/p (p is an odd integer). Another approach to composite particles, using so-called vortices, is also discussed from the point of view of the cyclotron braid group description (for both odd and even p integers).

Application of Braid Groups in 2D Hall System Physics: Composite Fermion Structure

Introduction Elements of Hall System Physics in 2D Spaces Topological Methods of Describing Systems of Many Particles at Various Manifolds Cyclotron Braids for Multi-Particle Charged 2D Systems in a Strong Magnetic Field Recent Progress in FQHE Field Summary Comments and Supplements.

Mechanism of plasmon-mediated enhancement of photovoltaic efficiency

Metallic nanospheres (Au, Ag, Cu) deposited on a photovoltaic (PV)-active semiconductor surface can act as light converters, collecting energy of incident photons in plasmon oscillations. This energy can be next transferred to a semiconductor substrate via a near-field channel, in a more efficient manner in comparison with the direct photo-effect. We explain this enhancement by inclusion of indirect interband transitions in a semiconductor layer due to the near-field coupling with plasmon radiation in nanoscale of the metallic components, where the momentum is not conserved as the system is not translationally invariant. The model of the nanosphere plasmons is developed (random phase approximation, analytical version, adjusted to description of large metallic clusters, with a radius of 10–60 nm) including surface and volume modes. Damping of plasmons is analysed via Lorentz friction, and irradiation losses in the far- and near-field regimes. Resulting resonance shifts are verified experimentally for Au and Ag colloidal water solutions with respect to particle size. Probability of the electron interband transition (within the Fermi golden rule) in the substrate semiconductor induced by coupling to plasmons in the near-field regime turns out to be significantly larger than for coupling of electrons to planar-wave photons. This is of practical importance for enhancement of thin-film solar cell efficiency, both for semiconductor type (such as III–V semiconductor based cells) and for conjugate-polymer-based or dye organic plastic cells, intensively developed at present. We have described also a non-dissipative collective mode of surface plasmons in a chain of near-field-coupled metallic nanospheres, for particular size, separation parameters and wavelengths. This would find an application in sub-diffraction electro-photonic circuit arrangement and for possible energy transport in solar cells, in particular in organic materials with low mobility of carriers.

Commensurability condition and hierarchy of fillings for FQHE in higher Landau levels in conventional 2DEG systems and in graphene—monolayer and bilayer

The structure of the filling rate hierarchy referred to as the fractional quantum Hall effect is studied in higher Landau levels using the commensurability condition. The hierarchy of fillings that are derived in this manner is consistent with the experimental observations of the first three Landau levels in conventional semiconductor Hall systems. The relative poverty of the fractional structure in higher Landau levels compared with the lowest Landau level is explained using commensurability topological arguments. The commensurability criterion for correlated states for higher Landau levels (with ) including the paired states at half fillings of the spin-subbands of these levels is formulated. The commensurability condition is applied to determine the hierarchy of the fractional fillings of Landau levels in the monolayer and bilayer graphene. Good agreement with current experimental observations of fractional quantum Hall effect in the graphene monolayer and bilayer is achieved. The presence of even denominator rates in the hierarchy for fractional quantum Hall effect in the bilayer graphene is also explained.

Unconventional fractional quantum Hall effect in monolayer and bilayer graphene

The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling fractions in the hierarchy for FQHE in bilayer graphene is explained. Experimentally observed hierarchy of FQHE in the first and second Landau levels in monolayer graphene and in the zeroth Landau level in bilayer graphene is beyond the conventional composite fermion interpretation but fits to the presented nonlocal topology commensurability condition. Graphical Abstract

Ultra-Quantum 2D Materials: Graphene, Bilayer Graphene, and Other Hall Systems—New Non-Local Quantum Theory of Hall Physics

We present a brief introduction of the fractional quantum Hall effect—a description of the phenomenon is provided and basic requirements for its formation are discussed. We recall assumptions of the standard composite fermion theory. Additionally, we present a list of the fractional quantum Hall effect puzzles. The chapter also introdu‐ ces the non-local approach to quantum Hall physics, which is entirely based on a mathematical concept of braid groups and their reduction stimulated by an external magnetic field (in two-dimensional spaces). We emphasize the connection between a one-dimensional unitary representation of the system braid group and the particle statistics (unavoidable for any correlated Hall-like states). We implement our topolog‐ ical approach to construct hierarchies of FQHE fillings for various two-dimensional structures, including multi-layers. We show the remarkable agreement of our results with experimental findings.

Quantum cryptography: Theoretical protocols for quantum key distribution and tests of selected commercial QKD systems in commercial fiber networks

The overview of the current status of quantum cryptography is given in regard to quantum key distribution (QKD) protocols, implemented both on nonentangled and entangled flying qubits. Two commercial R&D platforms of QKD systems are described (the Clavis II platform by idQuantique implemented on nonentangled photons and the EPR S405 Quelle platform by AIT based on entangled photons) and tested for feasibility of their usage in commercial TELECOM fiber metropolitan networks. The comparison of systems efficiency, stability and resistivity against noise and hacker attacks is given with some suggestion toward system improvement, along with assessment of two models of QKD.

Stability assessment of QKD procedures in commercial quantum cryptography systems versus quality of dark channel

In order to assess the susceptibility of the quantum key distribution (QKD) systems to the hacking attack including simultaneous and frequent system self-decalibrations, we analyze the stability of the QKD transmission organized in two commercially available systems. The first one employs non-entangled photons as flying qubits in the dark quantum channel for communication whereas the second one utilizes the entangled photon pairs to secretly share the cryptographic key. Applying standard methods of the statistical data analysis to the characteristic indicators of the quality of the QKD communication (the raw key exchange rate [RKER] and the quantum bit error rate [QBER]), we have estimated the pace of the self-decalibration of both systems and the repeatability rate in the case of controlled worsening of the dark channel quality.

Mechanism of plasmon enhancement of PV efficiency for metallic nano-modified surface of semiconductor photo-cell

Metallic nanospheres (Au, Ag, Cu) deposited on PV-active semiconductor surface can act as light converters, collecting energy of incident photons in plasmon oscillations. This energy can be next transferred to semiconductor substrate via a near-field channel, in a more efficient manner in comparison to the direct photo-effect. We explain this enhancement by inclusion of all indirect inter-band transitions in semiconductor layer due to near-field coupling with plasmon radiation in nanoscale of the metallic components, where the momentum is not conserved as the system is not translationally invariant. The model of nano-sphere plasmon is formulated (RPA, analytical version, adjusted to description of large metallic clusters, with radius of 10-100 nm) including surface and volume modes. Damping of plasmons is analyzed including Lorentz friction, and irradiation losses in far- and near-field regimes. Resulting resonance shifts are verified experimentally for Au and Ag (10-80 nm) colloidal water solutions with respect to particle size. Probability of interband transition (within the Fermi golden rule) caused by coupling to plasmons in near-field regime turns out to be 4-order larger than for coupling of electrons to planar-wave photons. Inclusion of proximity effects (for type of deposition of nano-components and their shape) allows for explanation of photo-current growth experimentally measured. We describe also a non-dissipative collective mode of surface plasmons in a chain of near-field-coupled metallic nanospheres, for particular size/separation parameters and wave-lengths.