## Semiconductors

**Low-Dimensional III-V semiconductors** are investigated by scanning tunneling spectroscopy, photolectron spectroscopy and transport measurements. In particular, two dimensional systems in magnetic field are probed as prototypes of tunable quantum phase transitions.

**Central goal** is the determination of fingerprints of the different electron phases and its transitions in real space.

#### Methods

- Angle-resolved photoemission spectroscopy (ARPES)
- Scanning tunneling microscopy (STM) and spectroscopy (STS)

#### RecentÂ Projects

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Surface accumulation and inversion layers are induced on the surface of InSb(110) and InAs(110) by a few % of adsorbates. The two dimensional electron system (2DES) is characterized by ARPES and by Fourier transformation imaging of standing electron waves in the STS data. The tip-induced band bending is carefully minimized.

###### Related Publications

- M. Morgenstern, A. Georgi, C. StraĂźer, C. R. Ast, S. Becker, and M. Liebmann Scanning tunneling microscopy of two-dimensional semiconductors: Spin properties and disorder Physica E: Low-dimensional Systems and Nanostructures 44, 1795-1814 (2012); doi:10.1016/j.physe.2012.06.006

[BibTeX] [Abstract] [Download PDF]

The interrelation between spin and charge in semiconductors leads to interesting effects, e.g., the Rashba-type spinâ€“orbit splitting or the exchange enhancement. These properties are proposed to be used in applications such as spin transistors or spin qubits. Probing them on the local scale with the ultimate spatial resolution of the scanning tunneling microscope addresses their susceptibility to disorder directly. Here we review the results obtained on two-dimensional electron systems (2DESs) in semiconductors. We describe the preparation and characterization of an adequate 2DES which can be probed by scanning tunneling microscopy. It is shown how the electron density and the disorder within the 2DES can be tuned and measured. The observed local density of states of weakly and strongly disordered systems is discussed in detail. It is shown that the weakly disordered 2DES exhibits quantum Hall effect in magnetic field. The corresponding local density of states across a quantum Hall transition is mapped showing the development from localized states to extended states and back to localized states in real space. Decoupling the 2DES from screening electrons of the bulk of the IIIâ€“V semiconductor leads to a measurable exchange enhancement of up to 0.7 meV which depends on the local spin polarization of the 2DES. At stronger confinement potential, i.e. larger doping, the Rashba spin splitting with a as large as 7Ă—10-11 eV m is observed as a beating in the density of states in magnetic field. The Rashba spin splitting varies with position by about Â±50% being largest at potential hills.

`@article{Morgenstern20121795, abstract = {The interrelation between spin and charge in semiconductors leads to interesting effects, e.g., the Rashba-type spinâ€“orbit splitting or the exchange enhancement. These properties are proposed to be used in applications such as spin transistors or spin qubits. Probing them on the local scale with the ultimate spatial resolution of the scanning tunneling microscope addresses their susceptibility to disorder directly. Here we review the results obtained on two-dimensional electron systems (2DESs) in semiconductors. We describe the preparation and characterization of an adequate 2DES which can be probed by scanning tunneling microscopy. It is shown how the electron density and the disorder within the 2DES can be tuned and measured. The observed local density of states of weakly and strongly disordered systems is discussed in detail. It is shown that the weakly disordered 2DES exhibits quantum Hall effect in magnetic field. The corresponding local density of states across a quantum Hall transition is mapped showing the development from localized states to extended states and back to localized states in real space. Decoupling the 2DES from screening electrons of the bulk of the IIIâ€“V semiconductor leads to a measurable exchange enhancement of up to 0.7 meV which depends on the local spin polarization of the 2DES. At stronger confinement potential, i.e. larger doping, the Rashba spin splitting with a as large as 7Ă—10-11 eV m is observed as a beating in the density of states in magnetic field. The Rashba spin splitting varies with position by about Â±50% being largest at potential hills. }, added-at = {2015-03-17T00:21:40.000+0100}, author = {Morgenstern, M. and Georgi, A. and StraĂźer, C. and Ast, C.R. and Becker, S. and Liebmann, M.}, biburl = {http://www.bibsonomy.org/bibtex/26cc8457f0d4cff5caee6e5be330d0b3d/institut2b}, description = {Scanning tunneling microscopy of two-dimensional semiconductors: Spin properties and disorder}, doi = {10.1016/j.physe.2012.06.006}, interhash = {8bbdcfbaa672ba5b864d6a1e91da262a}, intrahash = {6cc8457f0d4cff5caee6e5be330d0b3d}, issn = {1386-9477}, journal = {Physica E: Low-dimensional Systems and Nanostructures }, keywords = {morgenstern}, number = 9, pages = {1795 - 1814}, timestamp = {2015-03-17T00:21:40.000+0100}, title = {Scanning tunneling microscopy of two-dimensional semiconductors: Spin properties and disorder }, url = {http://www.sciencedirect.com/science/article/pii/S1386947712002263}, volume = 44, year = 2012 }`

- M. Morgenstern, J. Klijn, C. Meyer, M. Getzlaff, R. Adelung, R. A. RĂ¶mer, K. Rossnagel, L. Kipp, M. Skibowski, and R. Wiesendanger Direct Comparison between Potential Landscape and Local Density of States in a Disordered Two-Dimensional Electron System Phys. Rev. Lett. 89, 136806 (2002); doi:10.1103/PhysRevLett.89.136806

[BibTeX] [Download PDF]`@article{PhysRevLett.89.136806, added-at = {2015-03-17T01:09:16.000+0100}, author = {Morgenstern, M. and Klijn, J. and Meyer, Chr. and Getzlaff, M. and Adelung, R. and R\"omer, R. A. and Rossnagel, K. and Kipp, L. and Skibowski, M. and Wiesendanger, R.}, biburl = {http://www.bibsonomy.org/bibtex/226428e10c13c787932610bb8cdc1693b/institut2b}, description = {Phys. Rev. Lett. 89, 136806 (2002) - Direct Comparison between Potential Landscape and Local Density of States in a Disordered Two-Dimensional Electron System}, doi = {10.1103/PhysRevLett.89.136806}, interhash = {ff060acd7655047364fc2c66ba5a2bbf}, intrahash = {26428e10c13c787932610bb8cdc1693b}, journal = {Phys. Rev. Lett.}, keywords = {morgenstern}, month = sep, number = 13, numpages = {4}, eid = {136806}, publisher = {American Physical Society}, timestamp = {2015-03-17T01:09:16.000+0100}, title = {Direct Comparison between Potential Landscape and Local Density of States in a Disordered Two-Dimensional Electron System}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.89.136806}, volume = 89, year = 2002 }`

- M. Morgenstern, J. Wiebe, A. Wachowiak, M. Getzlaff, J. Klijn, L. Plucinski, R. L. Johnson, and R. Wiesendanger Co on \textitp -InAs(110): An island-induced two-dimensional electron system consisting of electron droplets Phys. Rev. B 65, 155325 (2002); doi:10.1103/PhysRevB.65.155325

[BibTeX] [Download PDF]`@article{PhysRevB.65.155325, added-at = {2015-03-17T01:09:19.000+0100}, author = {Morgenstern, M. and Wiebe, J. and Wachowiak, A. and Getzlaff, M. and Klijn, J. and Plucinski, L. and Johnson, R. L. and Wiesendanger, R.}, biburl = {http://www.bibsonomy.org/bibtex/26bf4968b47b02eaffd2a5f0b0e5a4b3b/institut2b}, description = {Phys. Rev. B 65, 155325 (2002) - Co on p-InAs(110): An island-induced two-dimensional electron system consisting of electron droplets}, doi = {10.1103/PhysRevB.65.155325}, interhash = {8b7a1e19417ca159dd9a4f3f62f0dcbf}, intrahash = {6bf4968b47b02eaffd2a5f0b0e5a4b3b}, journal = {Phys. Rev. B}, keywords = {morgenstern}, month = apr, number = 15, numpages = {8}, eid = {155325}, publisher = {American Physical Society}, timestamp = {2015-03-17T01:09:19.000+0100}, title = {Co on \textit{p} -InAs(110): An island-induced two-dimensional electron system consisting of electron droplets}, url = {http://link.aps.org/doi/10.1103/PhysRevB.65.155325}, volume = 65, year = 2002 }`

- M. Getzlaff, M. Morgenstern, C. Meyer, R. Brochier, R. L. Johnson, and R. Wiesendanger Nb-induced two-dimensional electron gas on Anomalous coverage dependence Phys. Rev. B 63, 205305 (2001); doi:10.1103/PhysRevB.63.205305

[BibTeX] [Download PDF]`@article{PhysRevB.63.205305, added-at = {2015-03-17T01:11:02.000+0100}, author = {Getzlaff, M. and Morgenstern, M. and Meyer, Chr. and Brochier, R. and Johnson, R. L. and Wiesendanger, R.}, biburl = {http://www.bibsonomy.org/bibtex/2b1705e3eba46aea78b91cdf6bce9f0c0/institut2b}, description = {Phys. Rev. B 63, 205305 (2001) - Nb-induced two-dimensional electron gas on $n$-${}\mathrm{InAs}(110):$ Anomalous coverage dependence}, doi = {10.1103/PhysRevB.63.205305}, interhash = {75472f21200ec3536dd0e4e64e7c869d}, intrahash = {b1705e3eba46aea78b91cdf6bce9f0c0}, journal = {Phys. Rev. B}, keywords = {morgenstern}, month = apr, number = 20, numpages = {6}, eid = {205305}, publisher = {American Physical Society}, timestamp = {2015-03-17T01:11:02.000+0100}, title = {Nb-induced two-dimensional electron gas on Anomalous coverage dependence}, url = {http://link.aps.org/doi/10.1103/PhysRevB.63.205305}, volume = 63, year = 2001 }`

- M. Morgenstern, M. Getzlaff, D. Haude, R. Wiesendanger, and R. L. Johnson Coverage dependence of the Fe-induced Fermi-level shift and the two-dimensional electron gas on InAs(110) Phys. Rev. B 61, 13805-13812 (2000); doi:10.1103/PhysRevB.61.13805

[BibTeX] [Download PDF]`@article{PhysRevB.61.13805, added-at = {2015-03-17T01:14:33.000+0100}, author = {Morgenstern, M. and Getzlaff, M. and Haude, D. and Wiesendanger, R. and Johnson, R. L.}, biburl = {http://www.bibsonomy.org/bibtex/231db086d7eba77bb3545ea7686a2c52d/institut2b}, description = {Phys. Rev. B 61, 13805 (2000) - Coverage dependence of the Fe-induced Fermi-level shift and the two-dimensional electron gas on InAs(110)}, doi = {10.1103/PhysRevB.61.13805}, interhash = {9e7f5ec35dc8e54ba4db3beda581228f}, intrahash = {31db086d7eba77bb3545ea7686a2c52d}, journal = {Phys. Rev. B}, keywords = {morgenstern}, month = may, number = 20, numpages = {0}, pages = {13805--13812}, publisher = {American Physical Society}, timestamp = {2015-03-17T01:14:33.000+0100}, title = {Coverage dependence of the Fe-induced Fermi-level shift and the two-dimensional electron gas on InAs(110)}, url = {http://link.aps.org/doi/10.1103/PhysRevB.61.13805}, volume = 61, year = 2000 }`

- R. Dombrowski, C. Steinebach, C. Wittneven, M. Morgenstern, and R. Wiesendanger Tip-induced band bending by scanning tunneling spectroscopy of the states of the tip-induced quantum dot on InAs(110) Phys. Rev. B 59, 8043-8048 (1999); doi:10.1103/PhysRevB.59.8043

[BibTeX] [Download PDF]`@article{PhysRevB.59.8043, added-at = {2015-03-17T01:16:36.000+0100}, author = {Dombrowski, R. and Steinebach, Chr. and Wittneven, Chr. and Morgenstern, M. and Wiesendanger, R.}, biburl = {http://www.bibsonomy.org/bibtex/21dd28b4753e831d5358b824f8bee7565/institut2b}, description = {Phys. Rev. B 59, 8043 (1999) - Tip-induced band bending by scanning tunneling spectroscopy of the states of the tip-induced quantum dot on InAs(110)}, doi = {10.1103/PhysRevB.59.8043}, interhash = {68793c43918f11241d8c04aef281bfd9}, intrahash = {1dd28b4753e831d5358b824f8bee7565}, journal = {Phys. Rev. B}, keywords = {morgenstern}, month = mar, number = 12, numpages = {0}, pages = {8043--8048}, publisher = {American Physical Society}, timestamp = {2015-03-17T01:16:36.000+0100}, title = {Tip-induced band bending by scanning tunneling spectroscopy of the states of the tip-induced quantum dot on InAs(110)}, url = {http://link.aps.org/doi/10.1103/PhysRevB.59.8043}, volume = 59, year = 1999 }`

Landau and spin levels are probed with sub-nanometer spatial resolution in magnetic fields up to 12 T by scanning tunneling spectroscopy (STS).

###### Related Publications

- S. Becker, C. Karrasch, T. Mashoff, M. Pratzer, M. Liebmann, V. Meden, and M. Morgenstern Probing Electron-Electron Interaction in Quantum Hall Systems with Scanning Tunneling Spectroscopy Phys. Rev. Lett. 106, 156805 (2011); doi:10.1103/PhysRevLett.106.156805

[BibTeX] [Download PDF]`@article{PhysRevLett.106.156805, added-at = {2015-03-17T00:22:48.000+0100}, author = {Becker, S. and Karrasch, C. and Mashoff, T. and Pratzer, M. and Liebmann, M. and Meden, V. and Morgenstern, M.}, biburl = {http://www.bibsonomy.org/bibtex/2d108d9f2f45962afccb8863869e5280c/institut2b}, description = {Phys. Rev. Lett. 106, 156805 (2011) - Probing Electron-Electron Interaction in Quantum Hall Systems with Scanning Tunneling Spectroscopy}, doi = {10.1103/PhysRevLett.106.156805}, interhash = {c6f089ad944129bb580ebe042fb668ac}, intrahash = {d108d9f2f45962afccb8863869e5280c}, journal = {Phys. Rev. Lett.}, keywords = {morgenstern}, month = apr, number = 15, numpages = {4}, eid = {156805}, publisher = {American Physical Society}, timestamp = {2015-03-17T00:22:48.000+0100}, title = {Probing Electron-Electron Interaction in Quantum Hall Systems with Scanning Tunneling Spectroscopy}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.106.156805}, volume = 106, year = 2011 }`

- K. Hashimoto, J. Wiebe, T. Inaoka, Y. Hirayama, R. Wiesendanger, and M. Morgenstern Real-space mapping of a disordered two-dimensional electron system in the quantum Hall regime Journal of Physics: Conference Series 334, 012008 (2011);

[BibTeX] [Abstract] [Download PDF]

By using scanning tunnelling spectroscopy, we study the influence of potential disorder on an adsorbate-induced two-dimensional electron system in the integer quantum Hall regime. The real-space imaged local density of states exhibits transition from localized drift states encircling the potential minima to another type of localized drift states encircling the potential maxima. While the former states show regular round shapes, the latter have irregular-shaped patterns. This difference is induced by different sources for the potential minima and maxima, i.e., substrate donors and an inhomogeneous distribution of the adsorbates, respectively.

`@article{1742-6596-334-1-012008, abstract = {By using scanning tunnelling spectroscopy, we study the influence of potential disorder on an adsorbate-induced two-dimensional electron system in the integer quantum Hall regime. The real-space imaged local density of states exhibits transition from localized drift states encircling the potential minima to another type of localized drift states encircling the potential maxima. While the former states show regular round shapes, the latter have irregular-shaped patterns. This difference is induced by different sources for the potential minima and maxima, i.e., substrate donors and an inhomogeneous distribution of the adsorbates, respectively.}, added-at = {2015-03-17T00:24:19.000+0100}, author = {Hashimoto, K and Wiebe, J and Inaoka, T and Hirayama, Y and Wiesendanger, R and Morgenstern, M}, biburl = {http://www.bibsonomy.org/bibtex/258858a94cfd827bd5e884ff75e49325f/institut2b}, description = {Real-space mapping of a disordered two-dimensional electron system in the quantum Hall regime - Abstract - Journal of Physics: Conference Series - IOPscience}, interhash = {38d2ccddb7aceef83147d0fd8f2ff2a0}, intrahash = {58858a94cfd827bd5e884ff75e49325f}, journal = {Journal of Physics: Conference Series}, keywords = {morgenstern}, number = 1, eid = {012008}, timestamp = {2015-03-17T00:24:19.000+0100}, title = {Real-space mapping of a disordered two-dimensional electron system in the quantum Hall regime}, url = {http://stacks.iop.org/1742-6596/334/i=1/a=012008}, volume = 334, year = 2011 }`

- K. Hashimoto, C. Sohrmann, J. Wiebe, T. Inaoka, F. Meier, Y. Hirayama, R. A. RĂ¶mer, R. Wiesendanger, and M. Morgenstern Quantum Hall Transition in Real Space: From Localized to Extended States Phys. Rev. Lett. 101, 256802 (2008); doi:10.1103/PhysRevLett.101.256802

[BibTeX] [Download PDF]`@article{PhysRevLett.101.256802, added-at = {2015-03-17T00:33:10.000+0100}, author = {Hashimoto, K. and Sohrmann, C. and Wiebe, J. and Inaoka, T. and Meier, F. and Hirayama, Y. and R\"omer, R. A. and Wiesendanger, R. and Morgenstern, M.}, biburl = {http://www.bibsonomy.org/bibtex/20196b77a4ad2600332e91742823ac66d/institut2b}, description = {Phys. Rev. Lett. 101, 256802 (2008) - Quantum Hall Transition in Real Space: From Localized to Extended States}, doi = {10.1103/PhysRevLett.101.256802}, interhash = {5bf8fd67f249c9390a00208c9443df7f}, intrahash = {0196b77a4ad2600332e91742823ac66d}, journal = {Phys. Rev. Lett.}, keywords = {morgenstern}, month = dec, number = 25, numpages = {4}, eid = {256802}, publisher = {American Physical Society}, timestamp = {2015-03-17T00:33:10.000+0100}, title = {Quantum Hall Transition in Real Space: From Localized to Extended States}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.101.256802}, volume = 101, year = 2008 }`

- M. Morgenstern, J. Klijn, C. Meyer, and R. Wiesendanger Real-Space Observation of Drift States in a Two-Dimensional Electron System at High Magnetic Fields Phys. Rev. Lett. 90, 056804 (2003); doi:10.1103/PhysRevLett.90.056804

[BibTeX] [Download PDF]`@article{PhysRevLett.90.056804, added-at = {2015-03-17T01:00:38.000+0100}, author = {Morgenstern, M. and Klijn, J. and Meyer, Chr. and Wiesendanger, R.}, biburl = {http://www.bibsonomy.org/bibtex/2a62f43cfc39d72e436fa852582806c62/institut2b}, description = {Phys. Rev. Lett. 90, 056804 (2003) - Real-Space Observation of Drift States in a Two-Dimensional Electron System at High Magnetic Fields}, doi = {10.1103/PhysRevLett.90.056804}, interhash = {9a86369f402593cf4c415095720cd334}, intrahash = {a62f43cfc39d72e436fa852582806c62}, journal = {Phys. Rev. Lett.}, keywords = {morgenstern}, month = feb, number = 5, numpages = {4}, eid = {056804}, publisher = {American Physical Society}, timestamp = {2015-03-17T01:00:38.000+0100}, title = {Real-Space Observation of Drift States in a Two-Dimensional Electron System at High Magnetic Fields}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.90.056804}, volume = 90, year = 2003 }`

Transitions from localized to extended states and back to localized states are mapped in the integer quantum Hall regime by STS. Multifractal analysis of the extended local density of states (LDOS) has been performed, but is limited by the finite energy resolution, thus, non-universal.

###### Related Publications

- K. Hashimoto, C. Sohrmann, J. Wiebe, T. Inaoka, F. Meier, Y. Hirayama, R. A. RĂ¶mer, R. Wiesendanger, and M. Morgenstern Quantum Hall Transition in Real Space: From Localized to Extended States Phys. Rev. Lett. 101, 256802 (2008); doi:10.1103/PhysRevLett.101.256802

[BibTeX] [Download PDF]`@article{PhysRevLett.101.256802, added-at = {2015-03-17T00:33:10.000+0100}, author = {Hashimoto, K. and Sohrmann, C. and Wiebe, J. and Inaoka, T. and Meier, F. and Hirayama, Y. and R\"omer, R. A. and Wiesendanger, R. and Morgenstern, M.}, biburl = {http://www.bibsonomy.org/bibtex/20196b77a4ad2600332e91742823ac66d/institut2b}, description = {Phys. Rev. Lett. 101, 256802 (2008) - Quantum Hall Transition in Real Space: From Localized to Extended States}, doi = {10.1103/PhysRevLett.101.256802}, interhash = {5bf8fd67f249c9390a00208c9443df7f}, intrahash = {0196b77a4ad2600332e91742823ac66d}, journal = {Phys. Rev. Lett.}, keywords = {morgenstern}, month = dec, number = 25, numpages = {4}, eid = {256802}, publisher = {American Physical Society}, timestamp = {2015-03-17T00:33:10.000+0100}, title = {Quantum Hall Transition in Real Space: From Localized to Extended States}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.101.256802}, volume = 101, year = 2008 }`

- M. Morgenstern, J. Klijn, C. Meyer, and R. Wiesendanger Real-Space Observation of Drift States in a Two-Dimensional Electron System at High Magnetic Fields Phys. Rev. Lett. 90, 056804 (2003); doi:10.1103/PhysRevLett.90.056804

[BibTeX] [Download PDF]`@article{PhysRevLett.90.056804, added-at = {2015-03-17T01:00:38.000+0100}, author = {Morgenstern, M. and Klijn, J. and Meyer, Chr. and Wiesendanger, R.}, biburl = {http://www.bibsonomy.org/bibtex/2a62f43cfc39d72e436fa852582806c62/institut2b}, description = {Phys. Rev. Lett. 90, 056804 (2003) - Real-Space Observation of Drift States in a Two-Dimensional Electron System at High Magnetic Fields}, doi = {10.1103/PhysRevLett.90.056804}, interhash = {9a86369f402593cf4c415095720cd334}, intrahash = {a62f43cfc39d72e436fa852582806c62}, journal = {Phys. Rev. Lett.}, keywords = {morgenstern}, month = feb, number = 5, numpages = {4}, eid = {056804}, publisher = {American Physical Society}, timestamp = {2015-03-17T01:00:38.000+0100}, title = {Real-Space Observation of Drift States in a Two-Dimensional Electron System at High Magnetic Fields}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.90.056804}, volume = 90, year = 2003 }`

It is shown that the Fourier transformation decouples disorder related LDOS from the nodal structure of the Landau level functions. The nodes in the Fourier space are identified experimentally. Adequate Fourier filter leads to an appearanceÂ of some nodal structures in the LDOS images (slightly less disorder required).

###### Related Publications

- K. Hashimoto, T. Champel, S. Florens, C. Sohrmann, J. Wiebe, Y. Hirayama, R. A. RĂ¶mer, R. Wiesendanger, and M. Morgenstern Robust Nodal Structure of Landau Level Wave Functions Revealed by Fourier Transform Scanning Tunneling Spectroscopy Phys. Rev. Lett. 109, 116805 (2012); doi:10.1103/PhysRevLett.109.116805

[BibTeX] [Download PDF]`@article{PhysRevLett.109.116805, added-at = {2015-03-17T00:21:44.000+0100}, author = {Hashimoto, K. and Champel, T. and Florens, S. and Sohrmann, C. and Wiebe, J. and Hirayama, Y. and R\"omer, R. A. and Wiesendanger, R. and Morgenstern, M.}, biburl = {http://www.bibsonomy.org/bibtex/2f310bf9f1bbfbd1c6b7911ad29bccb7e/institut2b}, description = {Phys. Rev. Lett. 109, 116805 (2012) - Robust Nodal Structure of Landau Level Wave Functions Revealed by Fourier Transform Scanning Tunneling Spectroscopy}, doi = {10.1103/PhysRevLett.109.116805}, interhash = {ebb23392c6072fead7be1ffabab95385}, intrahash = {f310bf9f1bbfbd1c6b7911ad29bccb7e}, journal = {Phys. Rev. Lett.}, keywords = {morgenstern}, month = sep, number = 11, numpages = {5}, eid = {116805}, publisher = {American Physical Society}, timestamp = {2015-03-17T00:21:44.000+0100}, title = {Robust Nodal Structure of Landau Level Wave Functions Revealed by Fourier Transform Scanning Tunneling Spectroscopy}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.109.116805}, volume = 109, year = 2012 }`

The beating of spatially averaged Landau levels determines an averaged Rashba parameter. The highest value in semiconductors are found at an InSb inversion layer: 0.07 eVnm ! The measured spin splitting reveals a local variation of the Rashba parameter of up to 300%.

###### Related Publications

- S. Becker, M. Liebmann, T. Mashoff, M. Pratzer, and M. Morgenstern Scanning tunneling spectroscopy of a dilute two-dimensional electron system exhibiting Rashba spin splitting Phys. Rev. B 81, 155308 (2010); doi:10.1103/PhysRevB.81.155308

[BibTeX] [Download PDF]`@article{PhysRevB.81.155308, added-at = {2015-03-17T00:24:34.000+0100}, author = {Becker, S. and Liebmann, M. and Mashoff, T. and Pratzer, M. and Morgenstern, M.}, biburl = {http://www.bibsonomy.org/bibtex/2f3a0256dbddd57bb15c7641e312e9492/institut2b}, description = {Phys. Rev. B 81, 155308 (2010) - Scanning tunneling spectroscopy of a dilute two-dimensional electron system exhibiting Rashba spin splitting}, doi = {10.1103/PhysRevB.81.155308}, interhash = {5d9c04766928861fcd1e9c460e696f6a}, intrahash = {f3a0256dbddd57bb15c7641e312e9492}, journal = {Phys. Rev. B}, keywords = {morgenstern}, month = apr, number = 15, numpages = {9}, eid = {155308}, publisher = {American Physical Society}, timestamp = {2015-03-17T00:24:34.000+0100}, title = {Scanning tunneling spectroscopy of a dilute two-dimensional electron system exhibiting Rashba spin splitting}, url = {http://link.aps.org/doi/10.1103/PhysRevB.81.155308}, volume = 81, year = 2010 }`

The measured exchange enhancement in the lowest Landau level (~0.7meV at 7T) is in excellent agreement with the result of the random phase approximation (RPA) which shows that short range interactions are barely perturbed. The Coulomb gap reveals a screening length of 8.6 nm probably caused by tip screening.

###### Related Publications

- S. Becker, C. Karrasch, T. Mashoff, M. Pratzer, M. Liebmann, V. Meden, and M. Morgenstern Probing Electron-Electron Interaction in Quantum Hall Systems with Scanning Tunneling Spectroscopy Phys. Rev. Lett. 106, 156805 (2011); doi:10.1103/PhysRevLett.106.156805

[BibTeX] [Download PDF]`@article{PhysRevLett.106.156805, added-at = {2015-03-17T00:22:48.000+0100}, author = {Becker, S. and Karrasch, C. and Mashoff, T. and Pratzer, M. and Liebmann, M. and Meden, V. and Morgenstern, M.}, biburl = {http://www.bibsonomy.org/bibtex/2d108d9f2f45962afccb8863869e5280c/institut2b}, description = {Phys. Rev. Lett. 106, 156805 (2011) - Probing Electron-Electron Interaction in Quantum Hall Systems with Scanning Tunneling Spectroscopy}, doi = {10.1103/PhysRevLett.106.156805}, interhash = {c6f089ad944129bb580ebe042fb668ac}, intrahash = {d108d9f2f45962afccb8863869e5280c}, journal = {Phys. Rev. Lett.}, keywords = {morgenstern}, month = apr, number = 15, numpages = {4}, eid = {156805}, publisher = {American Physical Society}, timestamp = {2015-03-17T00:22:48.000+0100}, title = {Probing Electron-Electron Interaction in Quantum Hall Systems with Scanning Tunneling Spectroscopy}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.106.156805}, volume = 106, year = 2011 }`

###### Review ArticleÂ Prof. Morgenstern

- M. Morgenstern, A. Georgi, C. StraĂźer, C. R. Ast, S. Becker, and M. Liebmann Scanning tunneling microscopy of two-dimensional semiconductors: Spin properties and disorder Physica E: Low-dimensional Systems and Nanostructures 44, 1795-1814 (2012); doi:10.1016/j.physe.2012.06.006

[BibTeX] [Abstract] [Download PDF]

The interrelation between spin and charge in semiconductors leads to interesting effects, e.g., the Rashba-type spinâ€“orbit splitting or the exchange enhancement. These properties are proposed to be used in applications such as spin transistors or spin qubits. Probing them on the local scale with the ultimate spatial resolution of the scanning tunneling microscope addresses their susceptibility to disorder directly. Here we review the results obtained on two-dimensional electron systems (2DESs) in semiconductors. We describe the preparation and characterization of an adequate 2DES which can be probed by scanning tunneling microscopy. It is shown how the electron density and the disorder within the 2DES can be tuned and measured. The observed local density of states of weakly and strongly disordered systems is discussed in detail. It is shown that the weakly disordered 2DES exhibits quantum Hall effect in magnetic field. The corresponding local density of states across a quantum Hall transition is mapped showing the development from localized states to extended states and back to localized states in real space. Decoupling the 2DES from screening electrons of the bulk of the IIIâ€“V semiconductor leads to a measurable exchange enhancement of up to 0.7 meV which depends on the local spin polarization of the 2DES. At stronger confinement potential, i.e. larger doping, the Rashba spin splitting with a as large as 7Ă—10-11 eV m is observed as a beating in the density of states in magnetic field. The Rashba spin splitting varies with position by about Â±50% being largest at potential hills.

`@article{Morgenstern20121795, abstract = {The interrelation between spin and charge in semiconductors leads to interesting effects, e.g., the Rashba-type spinâ€“orbit splitting or the exchange enhancement. These properties are proposed to be used in applications such as spin transistors or spin qubits. Probing them on the local scale with the ultimate spatial resolution of the scanning tunneling microscope addresses their susceptibility to disorder directly. Here we review the results obtained on two-dimensional electron systems (2DESs) in semiconductors. We describe the preparation and characterization of an adequate 2DES which can be probed by scanning tunneling microscopy. It is shown how the electron density and the disorder within the 2DES can be tuned and measured. The observed local density of states of weakly and strongly disordered systems is discussed in detail. It is shown that the weakly disordered 2DES exhibits quantum Hall effect in magnetic field. The corresponding local density of states across a quantum Hall transition is mapped showing the development from localized states to extended states and back to localized states in real space. Decoupling the 2DES from screening electrons of the bulk of the IIIâ€“V semiconductor leads to a measurable exchange enhancement of up to 0.7 meV which depends on the local spin polarization of the 2DES. At stronger confinement potential, i.e. larger doping, the Rashba spin splitting with a as large as 7Ă—10-11 eV m is observed as a beating in the density of states in magnetic field. The Rashba spin splitting varies with position by about Â±50% being largest at potential hills. }, added-at = {2015-03-17T00:21:40.000+0100}, author = {Morgenstern, M. and Georgi, A. and StraĂźer, C. and Ast, C.R. and Becker, S. and Liebmann, M.}, biburl = {http://www.bibsonomy.org/bibtex/26cc8457f0d4cff5caee6e5be330d0b3d/institut2b}, description = {Scanning tunneling microscopy of two-dimensional semiconductors: Spin properties and disorder}, doi = {10.1016/j.physe.2012.06.006}, interhash = {8bbdcfbaa672ba5b864d6a1e91da262a}, intrahash = {6cc8457f0d4cff5caee6e5be330d0b3d}, issn = {1386-9477}, journal = {Physica E: Low-dimensional Systems and Nanostructures }, keywords = {morgenstern}, number = 9, pages = {1795 - 1814}, timestamp = {2015-03-17T00:21:40.000+0100}, title = {Scanning tunneling microscopy of two-dimensional semiconductors: Spin properties and disorder }, url = {http://www.sciencedirect.com/science/article/pii/S1386947712002263}, volume = 44, year = 2012 }`

- M. MORGENSTERN PROBING THE LOCAL DENSITY OF STATES OF DILUTE ELECTRON SYSTEMS IN DIFFERENT DIMENSIONS Surface Review and Letters 10, 933-962 (2003); doi:10.1142/S0218625X0300575X

[BibTeX] [Abstract] [Download PDF]

<p class="first">Scanning tunneling spectroscopy at T = 6 K is used to investigate the local density of states (LDOS) of electron systems belonging to the bulk conduction band of InAs. In particular, the three-dimensional electron system (3DES) of the n-doped material, an adsorbate-induced two-dimensional electron system (2DES) and the tip-induced quantum dot (0DES) are investigated at B = 0 T and B = 6 T. It is found that the 3DES at B = 0 T can be described by Bloch states weakly interacting with the potential disorder provided by ionized dopants. The 2DES at B = 0 T exhibits much stronger LDOS corrugations, stressing the tendency for weak localization in the potential disorder. In a magnetic field, 3DES and 2DES show drift states, which are expected in 2D, but are surprising in 3D, where they point to a new electron phase consisting of droplets of quasi-2D systems.</p> <p class="last">The 0DES at B = 0 T reveals quantized states in accordance with Hartree calculations. At B = 6 T it exhibits Landau states with exchange enhanced spin splitting. These states are used to investigate the influence of potential disorder on the exchange enhancement, which visualizes the nonlocality of the exchange interaction.</p>

`@article{doi:10.1142/S0218625X0300575X, abstract = { <p class="first">Scanning tunneling spectroscopy at T = 6 K is used to investigate the local density of states (LDOS) of electron systems belonging to the bulk conduction band of InAs. In particular, the three-dimensional electron system (3DES) of the n-doped material, an adsorbate-induced two-dimensional electron system (2DES) and the tip-induced quantum dot (0DES) are investigated at B = 0 T and B = 6 T. It is found that the 3DES at B = 0 T can be described by Bloch states weakly interacting with the potential disorder provided by ionized dopants. The 2DES at B = 0 T exhibits much stronger LDOS corrugations, stressing the tendency for weak localization in the potential disorder. In a magnetic field, 3DES and 2DES show drift states, which are expected in 2D, but are surprising in 3D, where they point to a new electron phase consisting of droplets of quasi-2D systems.</p> <p class="last">The 0DES at B = 0 T reveals quantized states in accordance with Hartree calculations. At B = 6 T it exhibits Landau states with exchange enhanced spin splitting. These states are used to investigate the influence of potential disorder on the exchange enhancement, which visualizes the nonlocality of the exchange interaction.</p> }, added-at = {2015-03-17T01:00:58.000+0100}, author = {MORGENSTERN, MARKUS}, biburl = {http://www.bibsonomy.org/bibtex/22f079edcc64eb30a74ea2ba25ffcce09/institut2b}, description = {PROBING THE LOCAL DENSITY OF STATES OF DILUTE ELECTRON SYSTEMS IN DIFFERENT DIMENSIONS (World Scientific)}, doi = {10.1142/S0218625X0300575X}, eprint = {http://www.worldscientific.com/doi/pdf/10.1142/S0218625X0300575X}, interhash = {21c01b4940cd2b63e553feeb32d48d9d}, intrahash = {2f079edcc64eb30a74ea2ba25ffcce09}, journal = {Surface Review and Letters}, keywords = {morgenstern}, number = 06, pages = {933-962}, timestamp = {2015-03-17T01:00:58.000+0100}, title = {PROBING THE LOCAL DENSITY OF STATES OF DILUTE ELECTRON SYSTEMS IN DIFFERENT DIMENSIONS}, url = {http://www.worldscientific.com/doi/abs/10.1142/S0218625X0300575X}, volume = 10, year = 2003 }`