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We theoretically investigate the propagation of heat currents in a three-terminal quantum dot engine. Electron–electron interactions introduce state-dependent processes which can be resolved by energy-dependent tunneling rates. We identify the relevant transitions which define the operation of the system as a thermal transistor or a thermal diode. In the former case, thermal-induced charge fluctuations in the gate dot modify the thermal currents in the conductor with suppressed heat injection, resulting in huge amplification factors and the possible gating with arbitrarily low energy cost. In the latter case, enhanced correlations of the state-selective tunneling transitions redistribute heat flows giving high rectification coefficients and the unexpected cooling of one conductor terminal by heating the other one. We propose quantum dot arrays as a possible way to achieve the extreme tunneling asymmetries required for the different operations.
In this work fluorescence-based single molecule detection at low concetration is investigated, with an emphasis on the usage of active transport and waveguides.
Active transport allows to overcome the limits of diffusion-based systems in terms of the lowest detectable threshold of concentration.
The effect of flow in single molecule experiments is investigated and a theoretical model is derived for laminar flow.
Waveguides on the other hand promise compact detection schemes and show great potential for their possible integration into lab-on-a-chip applications. Their properties in single molecule experiments are analyzed with help of a method based on the reciprocity theorem of electromagnetic theory.
Optical antennas work similar to antennas for the radio-frequency regime and convert electromagnetic radiation into oscillating electrical currents. Charge density accumulations form at the antenna surface leading to strong and localized near-fields. Since most optical antennas have dimensions of a few hundred nanometers, their near-fields allow the focusing of electromagnetic fields to volumes much smaller than the diffraction limit, with intensities several orders of magnitude larger than achievable with classical diffractive and refractive optical elements. The task to maximize the emission of a quantum emitter, a point-like entity capable of reception and emission of single photons, is identical to the task to maximize the field intensity at the position of the quantum emitter. Therefore it is desirable to optimize the capabilities of focusing optical antennas.
Radio-frequency-antenna designs scaled to optical dimensions of several hundred nanometers show already a decent performance. However, optical frequencies lie near the plasma frequency of the metals used for optical antennas and the mass of electrons cannot be neglected anymore. This leads to new physical phenomena. Light can couple to charge density oscillations, yielding a so-called Plasmon. Effects emerge which have no equivalent in the very advanced field of radio-frequency-technology, e.g.~volume currents and shortened effective wavelengths. Additionally the conductivity is not infinite anymore, leading to thermal losses. Therefore, the question for the optimal geometry of a focusing optical antenna is not easy to answer. However, up to now there was no evidence that there exist better alternatives for optical antennas than down-scaled radio-frequency designs.
In this work the optimization of focusing optical antennas is based on an approach, which often proved successful for radio-frequency-antennas in complex applications (e.g.~broadband and isotropic reception): evolutionary algorithms. The first implementation introduced here allows a large freedom regarding particle shape and count, as it arranges cubic voxels on a planar, square grid. The geometries are encoded in a binary matrix, which works as a genome and enables the methods of mutation and crossing as mechanism of improvement. Antenna geometries optimized in this way surpass a comparable dipolar geometry by a factor of 2. Moreover, a new working principle can be deduced from the optimized antennas: a magnetic split-ring resonance can be coupled conductively to dipolar antennas, to form novel and more effective split-ring-antennas, as their currents add up constructively near the focal point.
In a next step, the evolutionary algorithm is adapted so that the binary matrices describe geometries with realistic fabrication constraints. In addition a 'printer driver' is developed which converts the binary matrices into commands for focused ion-beam milling in mono-crystalline gold flakes. It is shown by means of confocal two-photon photo-luminescence microscopy that antennas with differing efficiency can be fabricated reliably directly from the evolutionary algorithm. Besides, the concept of the split-ring antenna is further improved by adding this time two split-rings to the dipole-like resonance.
The best geometry from the second evolutionary algorithm inspires a fundamentally new formalism to determine the power transfer between an antenna and a point dipole, best termed 'three-dimensional mode-matching'. Therewith, for the first time intuitive design rules for the geometry of an focusing optical antenna can be deduced. The validity of the theory is proven analytically at the case of a point dipole in from of a metallic nano sphere.
The full problem of focusing light by means of an optical antenna can, thus, be reduced to two simultaneous mode-matching conditions -- on the one hand with the fields of a point dipole, on the other hand with a plane wave. Therefore, two types of ideal focusing optical antenna mode patterns are identified, being fundamentally different from the established dipolar antenna mode. This allows not only to explain the functionality of the evolutionary antennas and the split-ring antenna, but also helps to design novel plamonic cavity antennas, which lead to an enhanced focusing of light. This is proven numerically in direct comparison to a classical dipole antenna design.
Soft x-ray spectroscopic study of methanol and glycine peptides in different physical environments
(2017)
Ion-specific effects occur in a huge variety of aqueous solutions of electrolytes and larger molecules like peptides, altering properties such as viscosity, enzyme activity, protein stability, and salting-in and salting-out behavior of proteins. Typically, these type of effects are rationalized in terms of the Hofmeister series, which originally orders cations and anions according to their ability to enhance or suppress the solubility of proteins in water. This empirical order, however, is still not understood yet. Quite some effort was made to gain a molecular level understanding of this phenomenon, yet no consensus has been found about the underlying mechanisms and the determination and localization of the interaction sites.
Resonant inelastic soft x-ray scattering (RIXS) combines x-ray emission (XES) and absorption spectroscopies (XAS), probing the partial local density of states of both occupied and unoccupied electronic states and is thus a promising candidate to shed more light onto the issue. The studies presented in this work are directed towards an improved understanding of the interaction between salts and peptides. In order to address this topic, the impact of different physical environments on the electronic structure of small molecules (i.e., methanol and glycine derived peptides) is investigated systematically using soft x-ray spectroscopic methods, corroborated with density functional theory (DFT) calculations.
In a first step, molecules without any interactions to the surrounding are investigated, using gas-phase methanol as a model system. Thereby, the local and element specific character of RIXS is demonstrated and used to separately probe the local electronic structure of methanol’s hydroxyl and methyl group, respectively. The attribution of the observed emission features to distinct molecular orbitals is confirmed by DFT calculations, which also quantitatively explain the different relative intensities of the emission features. For resonant excitation of the O K pre-edge absorption resonance, strong isotope effects are found that are explained by dynamical processes at the hydroxyl group. This serves as an excellent example for possible consequences of a local change in the geometric structure or symmetry of a molecule on its electronic structure.
In the following, the sample system is expanded to the amino acid glycine and its smallest derived peptides diglycine and triglycine. As a first step, they are studied in their crystalline form in solid state. Again, a comprehensive picture of the electronic structure is developed by measuring RIXS maps at the oxygen and nitrogen K absorption edge, corroborated by DFT calculations. Similar to the case of methanol, dynamic processes at the protonated amino group of the molecules after exciting the nitrogen atom have a strong influence on the emission spectra. Furthermore, it is shown that RIXS can be used to selectively excite the peptide nitrogen to probe the electronic structure around it. A simple building block approach for XES spectra is applied to separate the contribution of the emission attributed to transitions into core holes at the peptide and the amino nitrogen, respectively.
In the aqueous solution, the surrounding water molecules slightly change the electronic structure, probably via interactions with the charged functional groups. The effects on the x-ray emission spectra, however, are rather small. Much bigger changes are observed when manipulating the protonation state of the functional groups by adjusting the pH value of the solution. A protonation of the carboxyl group at low pH values, as well as a deprotonation of the amino group at high pH values lead to striking changes in the shape of the RIXS maps. In a comprehensive study of glycine’s XES spectra at varying pH values, changes in the local electronic structure are not only observed in the immediate surrounding of the manipulated functional groups but also in more distant moieties of the molecule.
Finally, the study is extended to mixed aqueous solutions of diglycine and a variety of different salts as examples for systems where Hofmeister effects are observed. To investigate the influence of different cations and anions on the electronic structure of diglycine, two series of chlorine and potassium salts are used. Ion-specific effects are identified for both cases. Some of the changes in the x-ray emission spectra of diglycine in the mixed solutions qualitatively follow the Hofmeister series as a function of the used salt. The observed trends thereby indicate an increased interaction between the electron density around the peptide oxygen with the cations, whereas anions seem to interact with the amino group of the peptide.
Spin- and angle-resolved photoelectron spectroscopy is the prime method to investigate
spin polarized electronic states at solid state surfaces. In how far the spin polarization
of an emitted photoelectron reflects the intrinsic spin character of an electronic state is
the main question in the work at hand. It turns out that the measured spin polarization
is strongly influenced by experimental conditions, namely by the polarization of the
incoming radiation and the excitation energy. The photoemission process thus plays a
non-negligible role in a spin-sensitive measurement. This work is dedicated to unravel
the relation between the result of a spin-resolved measurement and the spin character
in the ground state and, therefore, to gain a deep understanding of the spin-dependent
photoemission process.
Materials that exhibit significant spin-splittings in their electronic structure,
owing to a strong spin-orbit coupling, serve as model systems for the investigations in
this work. Therefore, systems with large Rashba-type spin-splittings as BiTeI(0001)
and the surface alloys BiAg2/Ag(111) and PbAg2/Ag(111) are investigated. Likewise,
the surface electronic structure of the topological insulators Bi2Te2Se(0001) and
Bi2Te3(0001) are analyzed.
Light polarization dependent photoemission experiments serve as a probe of the
orbital composition of electronic states. The knowledge of the orbital structure helps
to disentangle the spin-orbital texture inherent to the different surface states, when
in addition the spin-polarization is probed. It turns out that the topological surface
state of Bi2Te2Se(0001) as well as the Rashba-type surface state of BiTeI(0001) exhibit
chiral spin-textures associated with the p-like in-plane orbitals. In particular, opposite
chiralities are coupled to either tangentially or radially aligned p-like orbitals,
respectively. The results presented here are thus evidence that a coupling between
spin- and orbital part of the wave function occurs under the influence of spin-orbit
coupling, independent of the materials topology.
Systematic photon energy dependent measurements of the out-of-plane spin polarization
of the topological surface state of Bi2Te3(0001) reveal a strong dependence and
even a reversal of the sign of the photoelectron spin polarization with photon energy.
Similarly, the measured spin component perpendicular to the wave vector of the surface
state of BiAg2/Ag(111) shows strong modulations and sign reversals when the photon energy is changed. In BiAg2/Ag(111) the variations in the photoelectron spin
polarization are accompanied by significant changes and even a complete suppression
of the photoemission intensity from the surface state, indicating that the variations of
the spin polarization are strongly related to the photoemission cross section.
This relation is finally analyzed in detail by employing a simple model, which is
based on an evaluation of the transition matrix elements that describe the presented
experiments. The model shows that the underlying cause for the observed photoelectron
spin reversals can be found in the coupling of the spin structure to the spatial part
of the initial state wave function, revealing the crucial role of spin-orbit interaction
in the initial state wave function. The model is supported by ab initio photoemission
calculations, which show strong agreement with the experimental results.
Since the late 20th century, spintroncis has become a very active field of research [ŽFS04]. The prospect of spin based information technology, featuring strongly decreased energy consumption and possibly quantum-computation capabilities, has fueled this interest. Standard materials, like bulk gallium arsenide (GaAs), have experienced new attention in this context by exhibiting extraordinarily long lifetimes for nonequilibrium spin information, which is an important requirement for efficient spin based information storage and transfer. Another important factor is the lengthscale over which spin information can be transported in a given material and the role of external influences. Both aspects have been studied experimentally with innovative optical methods since the late 1990s by the groups of D. D. AWSHALOM and S. A. CROOKER et al. [KA99, CS05, CFL+05]. Although the pioneering experimental approaches presented by these authors led to a variety of insights into spin propagation, some questions were raised as well. Most prominently, the classical Einstein relation, which connects the mobility and diffusivity of a given particle species, seemed to be violated for electron spins in a bulk semiconductor. In essence, nonequilibrium spins appeared to move (diffuse) faster than the electrons that actually carry the spin. However, this contradiction was masked by the fact, that the material of interest was n-type GaAs with a doping concentration directly at the transition between metallic and insulating behavior (MIT). In this regime, the electron mobility is difficult to determine experimentally. Consequently, it was not a priori obvious that the spin diffusion rates determined by the newly introduced optical methods were in contradiction with established electrical transport data.
However, in an attempt to extend the available data of optical spin microscopy, another issue surfaced, concerning the mathematical drift-diffusion model that has been commonly used to evaluate lateral spin density measurements. Upon close investigation, this model appears to have a limited range of applicability, due to systematic discrepancies with the experimental data (chapter 4). These deviations are noticeable in original publications as well, and it is shown in the present work that they originate from the local heating of electrons in the process of optical spin pumping. Based on insights gained during the second half of the 20th century, it is recapitulated why conduction electrons are easily overheated at cryogenic temperatures. The main reason is the poor thermal coupling between electrons and the crystal lattice (chapter 3). Experiments in the present work showed that a significant thermal gradient exists in the conduction band under local optical excitation of electron–hole pairs. This information was used to develop a better mathematical model of spin diffusion, which allowed to derive the diffusivity of the undisturbed system, due to an effective consideration of electron overheating. In this way, spin diffusivities of n-GaAs were obtained as a function of temperature and doping density in the most interesting regime of the metal–insulator-transition.
The experiments presented in this work were performed on a series of n-type bulk GaAs samples, which comprised the transition between metallic conductivity and electrical insulation at low temperatures. Local electron temperature gradients were measured by a hyperspectral photoluminescence imaging technique with subsequent evaluation of the electron–acceptor (e,A$^0$) line shape. The local density of nonequilibrium conduction electron spins was deduced from scanning magneto-optic Kerr effect microscopy. Numerical evaluations were performed using the finite elements method in combination with a least-squares fitting procedure.
Chapter 1 provides an introduction to historical and recent research in the field of spintronics, as far as it is relevant for the understanding of the present work. Chapter 2 summarizes related physical concepts and experimental methods. Here, the main topics are semiconductor optics, relaxation of hot conduction electrons, and the dynamics of nonequilibrium electron spins in semiconductors.
Chapter 3 discusses optical heating effects due to local laser excitation of electron–hole pairs. Experimental evaluations of the acceptor-bound-exciton triplet lines led to the conclusion that the crystal lattice is usually not overheated even at high excitation densities. Here, the heat is efficiently dissipated to the bath, due to the good thermal conductivity of the lattice. Furthermore, the heating of the lattice is inherently limited by the weak heat transfer from the electron system, which on the other hand is also the reason why conduction electrons are easily overheated at temperatures below ≈ 30 K. Spatio-spectral imaging of the electron–acceptor-luminescence line shape allowed to trace the thermal gradient within the conduction band under focused laser excitation. A heat-diffusion model was formulated, which reproduces the experimental electron-temperature trend nicely for low-doped GaAs samples of n- and p-type. For high-doped n-type GaAs samples, it could be shown that the lateral electron-temperature profile is well approximated by a Gaussian. This facilitated easy integration of hot electron influence into the mathematical model of spin diffusion.
Chapter 4 deals with magneto-optical imaging of optically induced nonequilibrium conduction-electron spins in n-GaAs close to the MIT. First, the spectral dependence of the magneto-optic Kerr effect was examined in the vicinity of the fundamental band gap. Despite the marked differences among the investigated samples, the spectral shape of the Kerr rotation could be described in terms of a simple Lorentz-oscillator model in all cases. Based on this model, the linearity of the Kerr effect with respect to a nonequilibrium spin polarization is demonstrated, which is decisively important for further quantitative evaluations.
Furthermore, chapter 4 presents an experimental survey of spin relaxation in n-GaAs at the MIT. Here, the dependence of the spin relaxation time on bath temperature and doping density was deduced from Hanle-MOKE measurements. While all observed trends agree with established literature, the presented results extend the current portfolio by adding a coherent set of data.
Finally, diffusion of optically generated nonequilibrium conduction-electron spins was investigated by scanning MOKE microscopy. First, it is demonstrated that the standard diffusion model is inapplicable for data evaluation in certain situations. A systematic survey of the residual deviations between this model and the experimental data revealed that this situation unfortunately persisted in published works. Moreover, the temperature trend of the residual deviations suggests a close connection to the local overheating of conduction electrons. Consequently, a modified diffusion model was developed and evaluated, in order to compensate for the optical heating effect. From this model, much more reliable results were obtained, as compared to the standard diffusion model. Therefore, it was shown conclusively that the commonly reported anomalously large spin diffusivities were at least in parts caused by overheated conduction electrons.
In addition to these new insights some experimental and technological enhancements were realized in the course of this work. First, the optical resolution of scanning MOKE microscopy was improved by implementing a novel scanning mechanism, which allows the application of a larger aperture objective than in the usual scheme. Secondly, imaging photoluminescence spectroscopy was employed for spatially resolved electron-temperature measurements. Here, two different implementations were developed: One for lattice-temperature measurements by acceptor–bound exciton luminescence and a second for conduction-electron temperature measurements via the analysis of the electron–acceptor luminescence line shape.
It is shown in the present work that the originally stated anomalously high spin diffusivities were caused to a large extent by unwanted optical heating of the electron system. Although an efficient method was found to compensate for the influence of electron heating, it became also evident that the classical Einstein relation was nonetheless violated under the given experimental conditions. In this case however, it could be shown that this discrepancy did not originate from an experimental artifact, but was instead a manifestation of the fermionic nature of conduction electrons.
This thesis aimed at the coherent investigation of the electrical and thermal transport properties of the low-dimensional organic conductor (DCNQI)2M (DCNQI: dicyanoquinonediimine; M: metallic counterion). These radical anion salts present a promising, new material class for thermoelectric applications and hence, a consistent characterization of the key parameters is required to evaluate and to optimize their performance. For this purpose, a novel experimental measurement setup enabling the determination of the electrical conductivity, the Seebeck coefficient and the thermal conductivity on a single crystalline specimen has been designed and implemented in this work. The novel measurement setup brought to operation within this thesis enabled a thorough investigation of the thermal transport properties in the (DCNQI)2M system. The thermal conductivity of (DCNQI-h8)2Cu at RT was determined to κ=1.73 W m^(-1) K^(-1). By reducing of the copper content in isostructural, crystalline (DMe-DCNQI)2CuxLi1-x alloys, the electrical conductivity has been lowered by one order of magnitude and the correlated changes in the thermal conductivity allowed for a verification of the Wiedemann-Franz (WF) law at RT. A room temperature Lorenz number of L=(2.48±0.45)⋅〖10〗^(-8) WΩK^(-2) was obtained in agreement with the standard Lorenz number L_0=2,44⋅〖10〗^(-8) WΩK^(-2) for 3D bulk metals. This value appears to be significantly reduced upon cooling below RT, even far above the Debye temperature of θ_D≈82 K, below which a breakdown of the WF law is caused by different relaxation times in response to thermal and to electric field perturbations. The experimental data enabled the first consistent evaluation of the thermoelectric performance of (DCNQI)$_2$Cu. The RT power factor of 110 μWm^(-1) K^(-2) is comparable to values obtained on PEDOT-based thermoelectric polymers. The RT figure of merit amounts to zT=0.02 which falls short by a factor of ten compared to the best values of zT=0.42 claimed for conducting polymers. It originates from the larger thermal conductivity in the organic crystals of about 1.73 W m^(-1) K^(-1) in (DCNQI)2Cu. Yet, more elaborate studies on the anisotropy of the thermal conductivity in PEDOT polymers assume their figure of merit to be zT=0.15 at most, recently. Therefore, (DCNQI)2Cu can be regarded as thermoelectric material of similar performance to polymer-based ones. Moreover, it represents one of the best organic n-type thermoelectric materials to date and as such, may also become important in hybrid thermoelectrics in combination with conducting polymers. Upon cooling below room temperature, (DCNQI)2Cu reveals its full potential attaining power factors of 50 mW K^(-2) m^(-1) and exceeding values of zT>0.15 below 40 K. These values represent the best thermoelectric performance in this low-temperature regime for organic as well as inorganic compounds and thus, low-dimensional organic conductors might pave the way toward new applications in cryogenic thermoelectrics. Further improvements may be expected from optimizing the charge carrier concentration by taking control over the CT process via the counterion stack of the crystal lattice. The concept has also been demonstrated in this work. Moreover, the thermoelectric performance in the vicinity of the CDW transition in (MeBr-DCNQI)2Cu was found to be increased by a factor of 5. Accordingly, the diversity of electronic ground states accessible in organic conductors provides scope for further improvements. Finally, the prototype of an all-organic thermoelectric generator has been built in combination with the p-type organic metal TTT2I3. While it only converts about 0.02% of the provided heat into electrical energy, the specific power output per active area attains values of up to 5 mW cm^(-2). This power output, defining the cost-limiting factor in the recovery of waste heat, is three orders of magnitude larger than in conducting polymer devices and as such, unrivaled in organic thermoelectrics. While the thermoelectric key parameters of (DCNQI)2Cu still lack behind conventional thermoelectrics made of e.g. Bi2Te3, the promising performance together with its potential for improvements make this novel material class an interesting candidate for further exploration. Particularly, the low-cost and energy-efficient synthesis routes of organic materials highlight their relevance for technological applications.
The issue of quantum mechanical coupling between a semiconductor quantum dot and a quantum well is studied in two families of GaAs- and InP- based structures at cryogenic temperatures. It is shown that by tuning the quantum well parameters one can strongly disturb the 0D-character of the coupled system ground state, initially located in a dot. The out-coupling of either an electron or a hole state from the quantum dot confining potential is viewed by a significant elongation of the photoluminescence decay time constant. Band structure calculations show that in the GaAs-based coupled system at its ground state a hole remains isolated in the dot, whereas an electron gets delocalized towards the quantum well. The opposite picture is built for the ground state of a coupled system based on InP.
The subject of this thesis is the control of strain in HgTe thin-film crystals. Such systems are members of the new class of topological insulator materials and therefore of special research interest. A major task was the experimental control of the strain in the HgTe films. This was achieved by a new epitaxial approach and confirmed by cristallographic analysis and magneto-transport measurements.
In this work, strain was induced in thin films by means of coherent epitaxy on substrate crystals. This means that the film adopts the lattice constant of the substrate in the plane of the substrate-epilayer interface. The level of strain is determined by the difference between the strain-free lattice constants of the substrate and epilayer material (the so-called lattice mismatch). The film responds to an in-plane strain with a change of its lattice constant perpendicular to the interface. This relationship is crucial for both the correct interpretation of high resolution X-ray diffraction (HRXRD) measurements, and the precise determination of the band dispersion. The lattice constant of HgTe is smaller than the lattice constant of CdTe. Therefore, strain in HgTe is tensile if it is grown on a CdTe substrate. In principle, compressive strain can be achieved by using an appropriate \(\text{Cd}_{1-x}\text{Zn}_{x}\text{Te}\) substrate. This concept was modified and applied in this work.
Epilayers have been fabricated by molecular-beam epitaxy (MBE). The growth of thick buffer layers of CdTe on GaAs:Si was established as an alternative to commercial CdTe and \(text{Cd}_{0.96}\text{Zn}_{0.04}\text{Te}\) substrates. The growth conditions have been optimized by an analysis of atomic force microscopy and HRXRD studies. HRXRD measurements reveal a power-law increase of the crystal quality with increasing thickness. Residual strain was found in the buffer layers, and was attributed to a combination of finite layer thickness and mismatch of the thermal expansion coefficients of CdTe and GaAs. In order to control the strain in HgTe epilayers, we have developed a new type of substrate with freely adjustable lattice constant.
CdTe-\(\text{Cd}_{0.5}\text{Zn}_{0.5}\text{Te}\) strained-layer-superlattices have been grown by a combination of MBE and atomic-layer epitaxy (ALE), and have been analyzed by HRXRD. ALE of the \(\text{Cd}_{0.5}\text{Zn}_{0.5}\text{Te}\) layer is self-limiting to one monolayer, and the effective lattice constant can be controlled reproducibly and straightforward by adjusting the CdTe layer thickness. The crystal quality has been found to degrade with increasing Zn-fraction. However, the effect is less drastic compared to single layer \(\text{Cd}_{1-x}\text{Zn}_{x}\text{Te}\) solid solutions. HgTe quantum wells (QWs) sandwiched in between CdHgTe barriers have been fabricated in a similar fashion on superlattices and conventional CdTe and \(\text{Cd}_{0.96}\text{Zn}_{0.04}\text{Te}\) substrates. The lower critical thickness of the CdHgTe barrier material grown on superlattice substrates had to be considered regarding the sample design. The electronic properties of the QWs depend on the strain and thickness of the QW. We have determined the QW thickness with an accuracy of \(\pm\)0.5 nm by an analysis of the beating patterns in the thickness fringes of HRXRD measurements and X-ray reflectometry measurements. We have, for the first time, induced compressive strain in HgTe QWs by an epitaxial technique (i.e. the effective lattice constant of the superlattice is lower compared to the lattice constant of HgTe). The problem of the lattice mismatch between superlattice and barriers has been circumvented by using CdHgTe-ZnHgTe superlattices instead of CdHgTe as a barrier material. Furthermore, the growth of compressively strained HgTe bulk layers (with a thickness of at least 50 nm) was demonstrated as well.
The control of the state of strain adds a new degree of freedom to the design of HgTe epilayers, which has a major influence on the band structure of QWs and bulk layers. Strain in bulk layers lifts the degeneracy of the \(\Gamma_8\) bands at \(\mathbf{k}=0\). Tensile strain opens an energy gap, compressive strain shifts the touching points of the valence- and conduction band to positions in the Brillouin zone with finite \(\mathbf{k}\). Such a situation has been realized for the first time in the course of this work. For QWs in the inverted regime, it is demonstrated that compressive strain can be used to significantly enhance the thermal energy gap of the two-dimensional electron gas (2DEG). In addition, semi-metallic and semiconducting behavior is expected in wide QWs, depending on the state of strain. An examination of the temperature dependence of the subband ordering in QWs revealed that the band gap is only temperature-stable for appropriate sample parameters and temperature regimes. The band inversion is always lifted for sufficiently high temperatures.
A large number of models investigate the influence of the band gap on the stability of the quantum-spin-Hall (QSH) effect. An enhancement of the stability of QSH edge state conductance is expected for enlarged band gaps. Furthermore, experimental studies on the temperature dependence of the QSH conductance are in contradiction to theoretical predictions. Systematic studies of these aspects have become feasible based on the new flexibility of the sample design.
Detailed low-temperature magnetotransport studies have been carried out on QWs and bulk layers. For this purpose, devices have been fabricated lithographically, which consist of two Hall-bar geometries with different dimensions. This allows to discriminate between conductance at the plane of the 2DEG and the edge of the sample. The Fermi energy in the 2DEG has been adjusted by means of a top gate electrode. The strain-induced transition from semi-metallic to semiconducting characteristics in wide QWs was shown. The magnitude of the semi-metallic overlap of valence- and conduction band was determined by an analysis of the two-carrier conductance and is in agreement with band structure calculations. The band gap of the semiconducting sample was determined by measurements of the temperature dependence of the conductance at the charge-neutrality point. Agreement with the value expected from theory has been achieved for the first time in this work. The influence of the band gap on the stability of QSH edge state conductance has been investigated on a set of six samples. The band gap of the set spans a range of 10 to 55 meV. The latter value has been achieved in a highly compressively strained QW, has been confirmed by temperature-dependent conductance measurements, and is the highest ever reported in the inverted regime. Studies of the carrier mobility reveal a degradation of the sample quality with increasing Zn-fraction in the superlattice, in agreement with HRXRD observations. The enhanced band gap does not suppress scattering mechanisms in QSH edge channels, but lowers the conductance in the plane of the 2DEG. Hence, edge state conductance is the dominant conducting process even at elevated temperatures. An increase in conductance with increasing temperature has been found, in agreement with reports from other groups. The increase follows a power-law dependency, the underlying physical mechanism remains open. A cause for the lack of an increase of the QSH edge state conductance with increasing energy gap has been discussed. Possibly, the sample remains insulating even at finite carrier densities, due to localization effects. The measurement does not probe the QSH edge state conductance at the situation where the Fermi energy is located in the center of the energy gap, but in the regime of maximized puddle-driven scattering. In a first set of measurements, it has been shown that the QSH edge state conductance can be influenced by hysteretic charging effects of trapped states in the insulating dielectric. A maximized conductance of \(1.6\ \text{e}^2/\text{h}\) was obtained in a \(58\ \mu\text{m}\) edge channel. Finally, measurements on three dimensional samples have been discussed. Recent theoretical works assign compressively strained HgTe bulk layers to the Weyl semi-metal class of materials. Such layers have been synthesized and studied in magnetotransport experiments for the first time. Pronounced quantum-Hall- and Shubnikov-de-Haas features in the Hall- and longitudinal resistance indicate two-dimensional conductance on the sample surface. However, this conductance cannot be assigned definitely to Weyl surface states, due to the inversion of \(\Gamma_6\) and \(\Gamma_8\) bands. If a magnetic field is aligned parallel to the current in the device, a decrease in the longitudinal resistance is observed with increasing magnetic field. This is a signature of the chiral anomaly, which is expected in Weyl semi-metals.
Measurements of differential cross-sections of top-quark pair production in fiducial phase-spaces are presented as a function of top-quark and \(t\overline{t}\) system kinematic observables in proton-proton collisions at a centre-of-mass energy of \(\sqrt{s}\) = 13 TeV. The data set corresponds to an integrated luminosity of 3.2 fb\(^{−1}\), recorded in 2015 with the ATLAS detector at the CERN Large Hadron Collider. Events with exactly one electron or muon and at least two jets in the final state are used for the measurement. Two separate selections are applied that each focus on different top-quark momentum regions, referred to as resolved and boosted topologies of the \(t\overline{t}\) final state. The measured spectra are corrected for detector effects and are compared to several Monte Carlo simulations by means of calculated \(χ^2\) and \(p\)-values.