@article{MaCalvoWangetal.2015,
  author    = {Ma, Eric Yue and Calvo, M. Reyes and Wang, Jing and Lian, Biao and M{\"u}hlbauer, Mathias and Br{\"u}ne, Christoph and Cui, Yong-Tao and Lai, Keji and Kundhikanjana, Worasom and Yang, Yongliang and Baenninger, Matthias and K{\"o}nig, Markus and Ames, Christopher and Buhmann, Hartmut and Leubner, Philipp and Molenkamp, Laurens W. and Zhang, Shou-Cheng and Goldhaber-Gordon, David and Kelly, Michael A. and Shen, Zhi-Xun},
  title     = {Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry},
  series = {Nature Communications},
  volume    = {6},
  journal   = {Nature Communications},
  number    = {7252},
  doi       = {10.1038/ncomms8252},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-143185},
  year      = {2015},
  abstract  = {The realization of quantum spin Hall effect in HgTe quantum wells is considered a milestone in the discovery of topological insulators. Quantum spin Hall states are predicted to allow current flow at the edges of an insulating bulk, as demonstrated in various experiments. A key prediction yet to be experimentally verified is the breakdown of the edge conduction under broken time-reversal symmetry. Here we first establish a systematic framework for the magnetic field dependence of electrostatically gated quantum spin Hall devices. We then study edge conduction of an inverted quantum well device under broken time-reversal symmetry using microwave impedance microscopy, and compare our findings to a noninverted device. At zero magnetic field, only the inverted device shows clear edge conduction in its local conductivity profile, consistent with theory. Surprisingly, the edge conduction persists up to 9 T with little change. This indicates physics beyond simple quantum spin Hall model, including material-specific properties and possibly many-body effects.},
  language  = {en}
}
@article{KoenigBaenningerGarciaetal.2013,
  author    = {K{\"o}nig, Markus and Baenninger, Matthias and Garcia, Andrei G. F. and Harjee, Nahid and Pruitt, Beth L. and Ames, C. and Leubner, Philipp and Br{\"u}ne, Christoph and Buhmann, Hartmut and Molenkamp, Laurens W. and Goldhaber-Gordon, David},
  title     = {Spatially Resolved Study of Backscattering in the Quantum Spin Hall State},
  series = {Physical Review X},
  volume    = {3},
  journal   = {Physical Review X},
  number    = {2},
  issn      = {2160-3308},
  doi       = {10.1103/PhysRevX.3.021003},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-127225},
  pages     = {21003},
  year      = {2013},
  abstract  = {The discovery of the quantum spin Hall (QSH) state, and topological insulators in general, has sparked strong experimental efforts. Transport studies of the quantum spin Hall state have confirmed the presence of edge states, showed ballistic edge transport in micron-sized samples, and demonstrated the spin polarization of the helical edge states. While these experiments have confirmed the broad theoretical model, the properties of the QSH edge states have not yet been investigated on a local scale. Using scanning gate microscopy to perturb the QSH edge states on a submicron scale, we identify well-localized scattering sites which likely limit the expected nondissipative transport in the helical edge channels. In the micron-sized regions between the scattering sites, the edge states appear to propagate unperturbed, as expected for an ideal QSH system, and are found to be robust against weak induced potential fluctuations.},
  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}
}