@phdthesis{Winnerlein2020,
  author    = {Winnerlein, Martin},
  title     = {Molecular Beam Epitaxy and Characterization of the Magnetic Topological Insulator (V,Bi,Sb)\(_2\)Te\(_3\)},
  doi       = {10.25972/OPUS-21166},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-211666},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2020},
  abstract  = {The subject of this thesis is the fabrication and characterization of magnetic topological insulator layers of (V,Bi,Sb)\(_2\)Te\(_3\) exhibiting the quantum anomalous Hall effect. A major task was the experimental realization of the quantum anomalous Hall effect, which is only observed in layers with very specific structural, electronic and magnetic properties. These properties and their influence on the quantum anomalous Hall effect are analyzed in detail. First, the optimal conditions for the growth of pure Bi\(_2\)Te\(_3\) and Sb\(_2\)Te\(_3\) crystal layers and the resulting structural quality are studied. The crystalline quality of Bi\(_2\)Te\(_3\) improves significantly at higher growth temperatures resulting in a small mosaicity-tilt and reduced twinning defects. The optimal growth temperature is determined as 260\(^{\circ}\)C, low enough to avoid desorption while maintaining a high crystalline quality. The crystalline quality of Sb\(_2\)Te\(_3\) is less dependent on the growth temperature. Temperatures below 230\(^{\circ}\)C are necessary to avoid significant material desorption, though. Especially for the nucleation on Si(111)-H, a low sticking coefficient is observed preventing the coalescence of islands into a homogeneous layer. The influence of the substrate type, miscut and annealing sequence on the growth of Bi\(_2\)Te\(_3\) layers is investigated. The alignment of the layer changes depending on the miscut angle and annealing sequence: Typically, layer planes align parallel to the Si(111) planes. This can enhance the twin suppression due to transfer of the stacking order from the substrate to the layer at step edges, but results in a step bunched layer morphology. For specific substrate preparations, however, the layer planes are observed to align parallel to the surface plane. This alignment avoids displacement at the step edges, which would cause anti-phase domains. This results in narrow Bragg peaks in XRD rocking curve scans due to long-range order in the absence of anti-phase domains. Furthermore, the use of rough Fe:InP(111):B substrates leads to a strong reduction of twinning defects and a significantly reduced mosaicity-twist due to the smaller lattice mismatch. Next, the magnetically doped mixed compound V\(_z\)(Bi\(_{1-x}\)Sb\(_x\))\(_{2-z}\)Te\(_3\) is studied in order to realize the quantum anomalous Hall effect. The addition of V and Bi to Sb\(_2\)Te\(_3\) leads to efficient nucleation on the Si(111)-H surface and a closed, homogeneous layer. Magneto-transport measurements of layers reveal a finite anomalous Hall resistivity significantly below the von Klitzing constant. The observation of the quantum anomalous Hall effect requires the complete suppression of parasitic bulklike conduction due to defect induced carriers. This can be achieved by optimizing the thickness, composition and growth conditions of the layers. The growth temperature is observed to strongly influence the structural quality. Elevated temperatures result in bigger islands, improved crystallographic orientation and reduced twinning. On the other hand, desorption of primarily Sb is observed, affecting the thickness, composition and reproducibility of the layers. At 190\(^{\circ}\)C, desorption is avoided enabling precise control of layer thickness and composition of the quaternary compound while maintaining a high structural quality. It is especially important to optimize the Bi/Sb ratio in the (V,Bi,Sb)\(_2\)Te\(_3\) layers, since by alloying n-type Bi\(_2\)Te\(_3\) and p-type Sb\(_2\)Te\(_3\) charge neutrality is achieved at a specific mixing ratio. This is necessary to shift the Fermi level into the magnetic exchange gap and fully suppress the bulk conduction. The Sb content x furthermore influences the in-plane lattice constant a significantly. This is utilized to accurately determine x even for thin films below 10 nm thickness required for the quantum anomalous Hall effect. Furthermore, x strongly influences the surface morphology: with increasing x the island size decreases and the RMS roughness increases by up to a factor of 4 between x = 0 and x = 1. A series of samples with x varied between 0.56-0.95 is grown, while carefully maintaining a constant thickness of 9 nm and a doping concentration of 2 at.\% V. Magneto-transport measurements reveal the charge neutral point around x = 0.86 at 4.2 K. The maximum of the anomalous Hall resistivity of 0.44 h/e\(^2\) is observed at x = 0.77 close to charge neutrality. Reducing the measurement temperature to 50 mK significantly increases the anomalous Hall resistivity. Several samples in a narrow range of x between 0.76-0.79 show the quantum anomalous Hall effect with the Hall resistivity reaching the von Klitzing constant and a vanishing longitudinal resistivity. Having realized the quantum anomalous Hall effect as the first group in Europe, this breakthrough enabled us to study the electronic and magnetic properties of the samples in close collaborations with other groups. In collaboration with the Physikalisch-Technische Bundesanstalt high-precision measurements were conducted with detailed error analysis yielding a relative de- viation from the von Klitzing constant of (0.17 \(\pm\) 0.25) * 10\(^{-6}\). This is published as the smallest, most precise value at that time, proving the high quality of the provided samples. This result paves the way for the application of magnetic topological insulators as zero-field resistance standards. Non-local magneto-transport measurements were conducted at 15 mK in close collaboration with the transport group in EP3. The results prove that transport happens through chiral edge channels. The detailed analysis of small anomalies in transport measurements reveals instabilities in the magnetic phase even at 15 mK. Their time dependent nature indicates the presence of superparamagnetic contributions in the nominally ferromagnetic phase. Next, the influence of the capping layer and the substrate type on structural properties and the impact on the quantum anomalous Hall effect is investigated. To this end, a layer was grown on a semi-insulating Fe:InP(111)B substrate using the previously optimized growth conditions. The crystalline quality is improved significantly with the mosaicity twist reduced from 5.4\(^{\circ}\) to 1.0\(^{\circ}\). Furthermore, a layer without protective capping layer was grown on Si and studied after providing sufficient time for degradation. The uncapped layer on Si shows perfect quantization, while the layer on InP deviates by about 5\%. This may be caused by the higher crystalline quality, but variations in e.g. Sb content cannot be ruled out as the cause. Overall, the quantum anomalous Hall effect seems robust against changes in substrate and capping layer with only little deviations. Furthermore, the dependence of the quantum anomalous Hall effect on the thickness of the layers is investigated. Between 5-8 nm thickness the material typically transitions from a 2D topological insulator with hybridized top and bottom surface states to a 3D topological insulator. A set of samples with 6 nm, 8 nm, and 9 nm thickness exhibits the quantum anomalous Hall effect, while 5 nm and 15 nm thick layers show significant bulk contributions. The analysis of the longitudinal and Hall conductivity during the reversal of magnetization reveals distinct differences between different thicknesses. The 6 nm thick layer shows scaling consistent with the integer quantum Hall effect, while the 9 nm thick layer shows scaling expected for the topological surface states of a 3D topological insulator. The unique scaling of the 9 nm thick layer is of particular interest as it may be a result of axion electrodynamics in a 3D topological insulator. Subsequently, the influence of V doping on the structural and magnetic properties of the host material is studied systematically. Similarly to Bi alloying, increased V doping seems to flatten the layer surface significantly. With increasing V content, Te bonding partners are observed to increase simultaneously in a 2:3 ratio as expected for V incorporation on group-V sites. The linear contraction of the in-plane and out-of-plane lattice constants with increasing V doping is quantitatively consistent with the incorporation of V\(^{3+}\) ions, possibly mixed with V\(^{4+}\) ions, at the group-V sites. This is consistent with SQUID measurements showing a magnetization of 1.3 \(\mu_B\) per V ion. Finally, magnetically doped topological insulator heterostructures are fabricated and studied in magneto-transport. Trilayer heterostructures with a non-magnetic (Bi,Sb)\(_2\)Te\(_3\) layer sandwiched between two magnetically doped layers are predicted to host the axion insulator state if the two magnetic layers are decoupled and in antiparallel configuration. Magneto-transport measurements of such a trilayer heterostructure with 7 nm undoped (Bi,Sb)\(_2\)Te\(_3\) between 2 nm thick layers doped with 1.5 at.\% V exhibit a zero Hall plateau representing an insulating state. Similar results in the literature were interpreted as axion insulator state, but in the absence of a measurement showing the antiparallel magnetic orientation other explanations for the insulating state cannot be ruled out. Furthermore, heterostructures including a 2 nm thin, highly V doped layer region show an anomalous Hall effect of opposite sign compared to previous samples. A dependency on the thickness and position of the doped layer region is observed, which indicates that scattering at the interfaces causes contributions to the anomalous Hall effect of opposite sign compared to bulk scattering effects. Many interesting phenomena in quantum anomalous Hall insulators as well as axion insulators are still not unambiguously observed. This includes Majorana bound states in quantum anomalous Hall insulator/superconductor hybrid systems and the topological magneto-electric effect in axion insulators. The limited observation temperature of the quantum anomalous Hall effect of below 1 K could be increased in 3D topological insulator/magnetic insulator heterostructures which utilize the magnetic proximity effect. The main achievement of this thesis is the reproducible growth and characterization of (V,Bi,Sb)2Te3 layers exhibiting the quantum anomalous Hall effect. The detailed study of the structural requirements of the quantum anomalous Hall effect and the observation of the unique axionic scaling behavior in 3D magnetic topological insulator layers leads to a better understanding of the nature of this new quantum state. The high-precision measurements of the quantum anomalous Hall effect reporting the smallest deviation from the von Klitzing constant are an important step towards the realization of a zero-field quantum resistance standard.},
  subject      = {Bismutverbindungen},
  language  = {en}
}
@phdthesis{Koenig2007,
  author    = {K{\"o}nig, Markus},
  title     = {Spin-related transport phenomena in HgTe-based quantum well structures},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-27301},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2007},
  abstract  = {Within the scope of this thesis, spin related transport phenomena have been investigated in HgTe/HgCdTe quantum well structures. This material exhibits peculiar band structure properties, which result in a strong spin-orbit interaction of the Rashba type. An inverted band structure, i.e., a reversed ordering of the energy states in comparison to common semiconductors, is obtained for quantum well layers above a critical thickness. Furthermore, the band structure properties can be controlled in the experiments by moderate gate voltages. Most prominently, the type of carriers in HgTe quantum wells can be changed from n to p due to the narrow energy gap. Along with the inverted band structure, this unique transition is the basis for the demonstration of the Quantum Spin Hall state, which is characterized by the existence of two one-dimensional spin-polarized edge states propagating in opposite directions, while the Fermi level in the bulk is in the energy gap. Since elastic scattering is suppressed by time reversal symmetry, a quantized conductance for charge and spin transport is predicted. Our experiments provide the first experimental demonstration of the QSH state. For samples with characteristic dimensions below the inelastic mean free path, charge conductance close to the expected value of 2e^2/h has been observed. Strong indication for the edge state transport was found in the experiments as well. For large samples, potential fluctuations lead to the appearance of local n-conducting regions which are considered to be the dominant source of backscattering. When time reversal symmetry is broken in a magnetic field, elastic scattering becomes possible and conductance is significantly suppressed. The suppression relies on a dominant orbital effect in a perpendicular field and a smaller Zeeman-like effect present for any field direction. For large perpendicular fields, a re-entrant quantum Hall state appears. This unique property is directly related to the non-trivial QSH insulator state. While clear evidence for the properties of charge transport was provided, the spin properties could not be addressed. This might be the goal of future experiments. In another set of experiments, the intrinsic spin Hall effect was studied. Its investigation was motivated by the possibility to create and to detect pure spin currents and spin accumulation. A non-local charging attributed to the SHE has been observed in a p-type H-shaped structure with large SO interaction, providing the first purely electrical demonstration of the SHE in a semiconductor system. A possibly more direct way to study the spin Hall effects opens up when the spin properties of the QSH edge states are taken into account. Then, the QSH edge states can be used either as an injector or a detector of spin polarization, depending on the actual configuration of the device. The experimental results indicate the existence of both intrinsic SHE and the inverse SHE independently of each other. If a spin-polarized current is injected from the QSH states into a region with Rashba SO interaction, the precession of the spin can been observed via the SHE. Both the spin injection and precession might be used for the realization of a spin-FET similar to the one proposed by Datta and Das. Another approach for the realization of a spin-based FET relies on a spin-interference device, in which the transmission is controlled via the Aharonov-Casher phase and the Berry phase, both due to the SO interaction. In the presented experiments, ring structures with tuneable SO coupling were studied. A complex interference pattern is observed as a function of external magnetic field and gate voltage. The dependence on the Rashba splitting is attributed to the Aharonov-Casher phase, whereas effects due to the Berry phase remain unresolved. This interpretation is confirmed by theoretical calculations, where multi-channel transport through the device has been assumed in agreement with the experimental results. Thus, our experiments provide the first direct observation of the AC effect in semiconductor structures. In conclusion, HgTe quantum well structures have proven to be an excellent template for studying spin-related transport phenomena: The QSHE relies on the peculiar band structure of the material and the existence of both the SHE and the AC effect is a consequence of the substantial spin-orbit interaction. While convincing results have been obtained for the various effects, several questions can not be fully answered yet. Some of them may be addressed by more extensive studies on devices already available. Other issues, however, ask, e.g., for further advances in sample fabrication or new approaches by different measurements techniques. Thus, future experiments may provide new, compelling insights for both the effects discussed in this thesis and, more generally, other spin-orbit related transport properties.},
  subject      = {Spin-Bahn-Wechselwirkung},
  language  = {en}
}