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Density functional theory (DFT) is applied to study the atomic, electronic, and spin structures of the Au monolayer at the Ge(111) surface. It is found that the theoretically determined most stable atomic geometry is described by the conjugated honeycomb-chained-trimer (CHCT) model, in a very good agreement with experimental data. The calculated electronic structure of the system, being in qualitatively good agreement with the photoemission measurements, shows fingerprints of the many-body effects (self-interaction corrections) beyond the LDA or GGA approximations. The most interesting property of this surface system is the large spin splitting of its metallic surface bands and the undulating spin texture along the hexagonal Fermi contours, which highly resembles the spin texture at the Dirac state of the topological insulator Bi\(_{2}\)Te\(_{3}\). These properties make this system particularly interesting from both fundamental and technological points of view.
Recent theoretical studies employing density-functional theory have predicted BaBiO\(_{3}\) (when doped with electrons) and YBiO\(_{3}\) to become a topological insulator (TI) with a large topological gap (~0.7 eV). This, together with the natural stability against surface oxidation, makes the Bismuth-Oxide family of special interest for possible applications in quantum information and spintronics. The central question, we study here, is whether the hole-doped Bismuth Oxides, i.e. Ba\(_{1-X}\)K\(_{X}\)BiO\(_{3}\) and BaPb\(_{1-X}\)Bi\(_{X}\)O\(_{3}\), which are "high-Tc" bulk superconducting near 30 K, additionally display in the further vicinity of their Fermi energy E\(_{F}\) a topological gap with a Dirac-type of topological surface state. Our electronic structure calculations predict the K-doped family to emerge as a TI, with a topological gap above E\(_{F}\). Thus, these compounds can become superconductors with hole-doping and potential TIs with additional electron doping. Furthermore, we predict the Bismuth-Oxide family to contain an additional Dirac cone below E\(_{F}\) for further hole doping, which manifests these systems to be candidates for both electron-and hole-doped topological insulators.
We study a two-level system controlled in a discrete feedback loop, modeling both the system and the controller in terms of stochastic Markov processes. We find that the extracted work, which is known to be bounded from above by the mutual information acquired during measurement, has to be compensated by an additional energy supply during the measurement process itself, which is bounded by the same mutual information from below. Our results confirm that the total cost of operating an information engine is in full agreement with the conventional second law of thermodynamics. We also consider the efficiency of the information engine as a function of the cycle time and discuss the operating condition for maximal power generation. Moreover, we find that the entropy production of our information engine is maximal for maximal efficiency, in sharp contrast to conventional reversible heat engines.
Accessing topological superconductivity via a combined STM and renormalization group analysis
(2015)
The search for topological superconductors has recently become a key issue in condensed matter physics, because of their possible relevance to provide a platform for Majorana bound states, non-Abelian statistics, and quantum computing. Here we propose a new scheme which links as directly as possible the experimental search to a material-based microscopic theory for topological superconductivity. For this, the analysis of scanning tunnelling microscopy, which typically uses a phenomenological ansatz for the superconductor gap functions, is elevated to a theory, where a multi-orbital functional renormalization group analysis allows for an unbiased microscopic determination of the material-dependent pairing potentials. The combined approach is highlighted for paradigmatic hexagonal systems, such as doped graphene and water-intercalated sodium cobaltates, where lattice symmetry and electronic correlations yield a propensity for a chiral singlet topological superconductor. We demonstrate that our microscopic material-oriented procedure is necessary to uniquely resolve a topological superconductor state.
Many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain "pseudopotential" Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z\(_3\) states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU(n) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.
This Letter presents measurements of correlated production of nearby jets in Pb+Pb collisions at \(\sqrt S_{NN}\)=2.76 TeV using the ATLAS detector at the Large Hadron Collider. The measurement was performed using 0.14 nb\(^{-1}\) of data recorded in 2011. The production of correlated jet pairs was quantified using the rate, R\(_{ΔR}\), of “neighbouring” jets that accompany “test” jets within a given range of angular distance, ΔR , in the pseudorapidity–azimuthal angle plane. The jets were measured in the ATLAS calorimeter and were reconstructed using the anti-k\(_t\) algorithm with radius parameters d=0.2, 0.3, and 0.4. R\(_{ΔR}\) was measured in different Pb+Pb collision centrality bins, characterized by the total transverse energy measured in the forward calorimeters. A centrality dependence of R\(_{ΔR}\) is observed for all three jet radii with R\(_{ΔR}\) found to be lower in central collisions than in peripheral collisions. The ratios formed by the R\(_{ΔR}\) values in different centrality bins and the values in the 40–80% centrality bin are presented.
Pulsars (in short for Pulsating Stars) are magnetized, fast rotating neutron stars. The basic picture of a pulsar describes it as a neutron star which has a rotation axis that is not aligned with its magnetic field axis. The emission is assumed to be generated near the magnetic poles of the neutron star and emitted along the open magnetic field lines. Consequently, the corresponding beam of photons is emitted along the magnetic field line axis. The non-alignment of both, the rotation and the magnetic field axis, results in the effect that the emission of the pulsar is only seen if its beam points towards the observer.
The emission from a pulsar is therefore perceived as being pulsed although its generation is not. This rather simple geometrical model is commonly referred to as Lighthouse Model and has been widely accepted. However, it does not deliver an explanation of the precise mechanisms behind the emission from pulsars (see below for more details).
Nowadays more than 2000 pulsars are known. They are observed at various wavelengths. Multiwavelength studies have shown that some pulsars are visible only at certain wavelengths while the emission from others can be observed throughout large parts of the electromagnetic spectrum. An example of the latter case is the Crab pulsar which is also the main object of interest in this thesis. Originating from a supernova explosion observed in 1054 A.D. and discovered in 1968, the Crab pulsar has been the central subject of numerous studies. Its pulsed emission is visible throughout the whole electromagnetic spectrum which makes it a key figure in understanding the possible mechanisms of multiwavelength emission from pulsars.
The Crab pulsar is also well known for its radio emission strongly varying on long as well as on short time scales. While long time scale behaviour from a pulsar is usually examined through the use of its average profile (a profile resulting from averaging of a large number of individual pulses resulting from single rotations), short time scale behaviour is examined via its single pulses. The short time scale anomalous behaviour of its radio emission is commonly referred to as Giant Pulses and represents the central topic of this thesis.
While current theoretical approaches place the origin of the radio emission from a pulsar like the Crab near its magnetic poles (Polar Cap Model) as already indicated by the Lighthouse model, its emission at higher frequencies, especially its gamma-ray emission, is assumed to originate further away in the geometrical region surrounding a pulsar which is commonly referred to as a pulsar magnetosphere (Outer Gap Model). Consequently, the respective emission regions are usually assumed not to be connected. However, past observational results from the Crab pulsar represent a contradiction to this assumption.
Radio giant pulses from the Crab pulsar have been observed to emit large amounts of energy on very short time scales implying small emission regions on the surface of the pulsar. Such energetic events might also leave a trace in the gamma-ray emission of the Crab pulsar.
The aim of this thesis is to search for this connection in the form of a correlation study between radio giant pulses and gamma-photons from the Crab pulsar.
To make such a study possible, a multiwavelength observational campaign was organized for which radio observations were independently applied for, coordinated and carried out with the Effelsberg radio telescope and the Westerbork Synthesis Radio Telescope and gamma-ray observations with the Major Atmospheric Imaging Cherenkov telescopes. The corresponding radio and gamma-ray data sets were reduced and the correlation analysis thereafter consisted of three different approaches:
1) The search for a clustering in the differences of the times of arrival of radio giant pulses and gamma-photons;
2) The search for a linear correlation between radio giant pulses and gamma-photons using the Pearson correlation approach;
3) A search for an increase of the gamma-ray flux around occurring radio giant pulses.
In the last part of the correlation study an increase of the number of gamma-photons centered on a radio giant pulse by about 17% (in contrast with the number of gamma-photons when no radio giant pulse occurs in the same time window) was discovered. This finding suggests that a new theoretical approach for the emission of young pulsars like the Crab pulsar, is necessary.
The architecture of iso-orientation domains in the primary visual cortex (V1) of placental carnivores and primates apparently follows species invariant quantitative laws. Dynamical optimization models assuming that neurons coordinate their stimulus preferences throughout cortical circuits linking millions of cells specifically predict these invariants. This might indicate that V1's intrinsic connectome and its functional architecture adhere to a single optimization principle with high precision and robustness. To validate this hypothesis, it is critical to closely examine the quantitative predictions of alternative candidate theories. Random feedforward wiring within the retino-cortical pathway represents a conceptually appealing alternative to dynamical circuit optimization because random dimension-expanding projections are believed to generically exhibit computationally favorable properties for stimulus representations. Here, we ask whether the quantitative invariants of V1 architecture can be explained as a generic emergent property of random wiring. We generalize and examine the stochastic wiring model proposed by Ringach and coworkers, in which iso-orientation domains in the visual cortex arise through random feedforward connections between semi-regular mosaics of retinal ganglion cells (RGCs) and visual cortical neurons. We derive closed-form expressions for cortical receptive fields and domain layouts predicted by the model for perfectly hexagonal RGC mosaics. Including spatial disorder in the RGC positions considerably changes the domain layout properties as a function of disorder parameters such as position scatter and its correlations across the retina. However, independent of parameter choice, we find that the model predictions substantially deviate from the layout laws of iso-orientation domains observed experimentally. Considering random wiring with the currently most realistic model of RGC mosaic layouts, a pairwise interacting point process, the predicted layouts remain distinct from experimental observations and resemble Gaussian random fields. We conclude that V1 layout invariants are specific quantitative signatures of visual cortical optimization, which cannot be explained by generic random feedforward-wiring models.
We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling K\(_2\), which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iridate Na\(_2\)IrO\(_3\), and may also play a role in \(\alpha\)-RuCl\(_3\) and Li\(_2\)IrO\(_3\). This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in Na\(_2\)IrO\(_3\). Moreover, the minimal K\(_1\) - K\(_2\) model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.
Over the last decade, the field of topological insulators has become one of the most vivid areas in solid state physics. This novel class of materials is characterized by an insulating bulk gap, which, in two-dimensional, time-reversal symmetric systems, is closed by helical edge states. The latter make topological insulators promising candidates for applications in high fidelity spintronics and topological quantum computing. This thesis contributes to bringing these fascinating concepts to life by analyzing transport through heterostructures formed by two-dimensional topological insulators in contact with metals or superconductors. To this end, analytical and numerical calculations are employed. Especially, a generalized wave matching approach is used to describe the edge and bulk states in finite size tunneling junctions on the same footing.
The numerical study of non-superconducting systems focuses on two-terminal metal/topological
insulator/metal junctions. Unexpectedly, the conductance signals originating from the bulk and
the edge contributions are not additive. While for a long junction, the transport is determined
purely by edge states, for a short junction, the conductance signal is built from both bulk and
edge states in a ratio, which depends on the width of the sample. Further, short junctions show
a non-monotonic conductance as a function of the sample length, which distinguishes the topologically non-trivial regime from the trivial one. Surprisingly, the non-monotonic conductance of the topological insulator can be traced to the formation of an effectively propagating solution, which is robust against scalar disorder.
The analysis of the competition of edge and bulk contributions in nanostructures is extended to transport through topological insulator/superconductor/topological insulator tunneling junctions. If the dimensions of the superconductor are small enough, its evanescent bulk modes
can couple edge states at opposite sample borders, generating significant and tunable crossed
Andreev reflection. In experiments, the latter process is normally disguised by simultaneous
electron transmission. However, the helical edge states enforce a spatial separation of both competing processes for each Kramers’ partner, allowing to propose an all-electrical measurement
of crossed Andreev reflection.
Further, an analytical study of the hybrid system of helical edge states and conventional superconductors in finite magnetic fields leads to the novel superconducting quantum spin Hall effect. It is characterized by edge states. Both the helicity and the protection against scalar disorder of these edge states are unaffected by an in-plane magnetic field. At the same time its superconducting gap and its magnetotransport signals can be tuned in weak magnetic fields, because the combination of helical edge states and superconductivity results in a giant g-factor. This is manifested in a non-monotonic excess current and peak splitting of the dI/dV characteristics as a function of the magnetic field. In consequence, the superconducting quantum spin Hall effect is an effective generator and detector for spin currents.
The research presented here deepens the understanding of the competition of bulk and edge
transport in heterostructures based on topological insulators. Moreover it proposes feasible experiments to all-electrically measure crossed Andreev reflection and to test the spin polarization of helical edge states.