## Topological Insulators

**Topological insulators**Â exhibit surface states which are protected by the symmetry of the insulating bulk. They cannot be detroyed by local defects at the surface. We investigate **weak topological insulators** which provide conducting edge states at the surface. Additionally, we probe whether **phase change materials** (that can be switched between crystalline and amorphous on a ns time scale) are also topological insulators in their crystalline phase. Furthermore, we prepare interfaces which potentially host **Majorana Fermions** (Wikipedia). These investigations are related to quantum Hall systems which also contain topologically protected states.

Central goal isÂ the imaging of topological properties on a local scale.

#### Methods

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

**RecentÂ Projects**

Please click on the headlinesÂ to get more information.

Using scanning tunnelling spectroscopy, we resolved the topological properties of a so-called weak topological insulator for the first time ever, in particular, back-scatter-free electron states (only 0.8 nm in width) which only exist at the step edges of the natural cleavage plane of Bi_{14}Rh_{3}I_{9}. The first weak topological insulator Bi_{14}Rh_{3}I_{9} is a stack of graphene-like 2D topological insulator (TI) layers. Combining these layers into pairs (Bi_{13}Pt_{3}I_{7}), the topological edge states vanish as predicted by theory.

###### Related Publication

- C. Pauly, B. Rasche, K. Koepernik, M. Liebmann, M. Pratzer, M. Richter, J. Kellner, M. Eschbach, B. Kaufmann, L. Plucinski, C. M. Schneider, M. Ruck, J. van den Brink, and M. Morgenstern Subnanometre-wide electron channels protected by topology Nat Phys 11, 338-343 (2015); doi:10.1038/nphys3264

[BibTeX] [Download PDF]`@article{pauly2015subnanometrewide, added-at = {2015-03-16T23:58:42.000+0100}, author = {Pauly, Christian and Rasche, Bertold and Koepernik, Klaus and Liebmann, Marcus and Pratzer, Marco and Richter, Manuel and Kellner, Jens and Eschbach, Markus and Kaufmann, Bernhard and Plucinski, Lukasz and Schneider, Claus M. and Ruck, Michael and van den Brink, Jeroen and Morgenstern, Markus}, biburl = {http://www.bibsonomy.org/bibtex/2c651d215ea047932c8e18942667172bb/institut2b}, description = {Subnanometre-wide electron channels protected by topology : Nature Physics : Nature Publishing Group}, doi = {10.1038/nphys3264}, interhash = {f553c2b6230289ac44ac4ebe385ec823}, intrahash = {c651d215ea047932c8e18942667172bb}, issn = {17452481}, journal = {Nat Phys}, keywords = {morgenstern}, month = mar, number = 4, pages = {338 - 343}, publisher = {Nature Publishing Group}, timestamp = {2015-03-16T23:58:42.000+0100}, title = {Subnanometre-wide electron channels protected by topology}, url = {http://dx.doi.org/10.1038/nphys3264}, volume = {11}, year = 2015 }`

_{2}Sb

_{2}Te

_{5}(STM/STS/ARPES)

The ternary compound Ge_{2}Sb_{2}Te_{5} belongs to the class of phase change materials which can vary their electrical conductivity by several orders of magnitude upon transition between the amorphous and a metastable cubic phase. Some of these materials occur along the pseudobinary line connecting GeTe and the topological insulator Sb_{2}Te_{3}. Ge_{2}Sb_{2}Te_{5} is widely used as storage media in DVDs and RAMs. Using angle-resolved photoemission, we showed that the band structure of epitaxially grown Ge_{2}Sb_{2}Te_{5} on Si(111) in the metastable cubic phase exhibits a valence band minimum at the G point. A comparison with DFT calculations indicates the presence of a topologically non-trivial phase. This combination of phase change material and topological insulator opens up the perspective of switable topological insulators on the time scale of nanoseconds.

###### Related Publication

- C. Pauly, M. Liebmann, A. Giussani, J. Kellner, S. Just, J. SÃ¡nchez-Barriga, E. Rienks, O. Rader, R. Calarco, G. Bihlmayer, and M. Morgenstern Evidence for topological band inversion of the phase change material Ge2Sb2Te5 Applied Physics Letters 103, 243109 (2013); doi:10.1063/1.4847715

[BibTeX] [Abstract] [Download PDF]

We present an angle-resolved photoemission study of a ternary phase change material, namely Ge 2Sb2Te5, epitaxially grown on Si(111) in the metastable cubic phase. The observed upper bulk valence band shows a minimum at being 0.3eV below the Fermi level E F and a circular Fermi contour around with a dispersing diameter of 0.27â€“0.36Ã…-1. This is in agreement with density functional theory calculations of the Petrov stacking sequence in the cubic phase which exhibits a topological surface state. The topologically trivial cubic Kooi-De Hosson stacking shows a valence band maximum at G in line with all previous calculations of the hexagonal stable phase exhibiting the valence band maximum at G for a trivial topological invariant and away from G for non-trivial . Scanning tunneling spectroscopy exhibits a band gap of 0.4eV around E F. G Â¯ G Â¯ Z 2 ? 0 ? 0

`@article{:/content/aip/journal/apl/103/24/10.1063/1.4847715, abstract = {We present an angle-resolved photoemission study of a ternary phase change material, namely Ge 2Sb2Te5, epitaxially grown on Si(111) in the metastable cubic phase. The observed upper bulk valence band shows a minimum at being 0.3eV below the Fermi level E F and a circular Fermi contour around with a dispersing diameter of 0.27â€“0.36Ã…-1. This is in agreement with density functional theory calculations of the Petrov stacking sequence in the cubic phase which exhibits a topological surface state. The topologically trivial cubic Kooi-De Hosson stacking shows a valence band maximum at G in line with all previous calculations of the hexagonal stable phase exhibiting the valence band maximum at G for a trivial topological invariant and away from G for non-trivial . Scanning tunneling spectroscopy exhibits a band gap of 0.4eV around E F. G Â¯ G Â¯ Z 2 ? 0 ? 0}, added-at = {2015-03-17T00:18:27.000+0100}, author = {Pauly, Christian and Liebmann, Marcus and Giussani, Alessandro and Kellner, Jens and Just, Sven and SÃ¡nchez-Barriga, Jaime and Rienks, Emile and Rader, Oliver and Calarco, Raffaella and Bihlmayer, Gustav and Morgenstern, Markus}, biburl = {http://www.bibsonomy.org/bibtex/2d5a7a3ea1c605083e0793291a38bfb37/institut2b}, description = {Evidence for topological band inversion of the phase change material Ge2Sb2Te5}, doi = {10.1063/1.4847715}, eid = {243109}, interhash = {ac6942bc95b9c12011653d942e38ea41}, intrahash = {d5a7a3ea1c605083e0793291a38bfb37}, journal = {Applied Physics Letters}, keywords = {morgenstern}, number = 24, timestamp = {2015-03-17T00:18:27.000+0100}, title = {Evidence for topological band inversion of the phase change material Ge2Sb2Te5}, url = {http://scitation.aip.org/content/aip/journal/apl/103/24/10.1063/1.4847715}, volume = 103, year = 2013 }`

_{2}Te

_{3}(0001) (ARPES/STM/STS)

Using spin- and angle-resolved photoemission on Sb_{2}Te_{3} single crystals cleaved in ultrahigh vacuum, and by comparison with density functional theory calculations we found two topological surfaces states: a spin-polarized Dirac cone with the Dirac point located at the Fermi level and a Rashba-type band with spin-degenerate minimum at the G point. Its spin components each disperse into two different bulk bands. This behavior is the result of a spin-orbit induced band gap in the interior of the Brillouin zone (argument by Pendry and Gurman, 1975, Link: Theory of surface states: General criteria for their existence).

###### Related Publication

- C. Pauly, G. Bihlmayer, M. Liebmann, M. Grob, A. Georgi, D. Subramaniam, M. R. Scholz, J. SÃ¡nchez-Barriga, A. Varykhalov, S. BlÃ¼gel, O. Rader, and M. Morgenstern Probing two topological surface bands of SbTe by spin-polarized photoemission spectroscopy Phys. Rev. B 86, 235106 (2012); doi:10.1103/PhysRevB.86.235106

[BibTeX] [Download PDF]`@article{PhysRevB.86.235106, added-at = {2015-03-17T00:21:14.000+0100}, author = {Pauly, C. and Bihlmayer, G. and Liebmann, M. and Grob, M. and Georgi, A. and Subramaniam, D. and Scholz, M. R. and S\'anchez-Barriga, J. and Varykhalov, A. and Bl\"ugel, S. and Rader, O. and Morgenstern, M.}, biburl = {http://www.bibsonomy.org/bibtex/22a7554bd80f303246c6a3600b597ce7a/institut2b}, description = {Phys. Rev. B 86, 235106 (2012) - Probing two topological surface bands of Sb${}_{2}$Te${}_{3}$ by spin-polarized photoemission spectroscopy}, doi = {10.1103/PhysRevB.86.235106}, interhash = {694812f932b8bf608750202e2c398745}, intrahash = {2a7554bd80f303246c6a3600b597ce7a}, journal = {Phys. Rev. B}, keywords = {morgenstern}, month = dec, number = 23, numpages = {8}, eid = {235106}, publisher = {American Physical Society}, timestamp = {2015-03-17T00:21:14.000+0100}, title = {Probing two topological surface bands of SbTe by spin-polarized photoemission spectroscopy}, url = {http://link.aps.org/doi/10.1103/PhysRevB.86.235106}, volume = 86, year = 2012 }`

_{2}Te

_{3}(STM/STS)

Using scanning tunnelling spectroscopy, Landau levels at varying magnetic fields Bz are measured on the surface of the topological insulator Sb_{2}Te_{3}. A linear dependence of the Landau level energies with the root of the applied magnetic field (B)1/2 confirmed the Dirac fermion nature of the topological surface states as well as the field independent n = 0 Landau level of the Dirac point. Different types and amount of defects lead to local potential fluctuations visible in the Landau level spectroscopy.

###### Related Publication

[bibtex format=”custom” template=”custom-cites” file=”http://www.institut2b.physik.rwth-aachen.de/wp-content/custom_data/mypub.bib” key=PhysRevB.92.085140_{1-x}Sb

_{x})

_{2}Te

_{3}(ARPES)

We were able to synthesize (Bi_{1-x}Sb_{x})_{2}Te_{3}Â thin films for 0.95<x<0.96 by molecularÂ beam epitaxy (MBE). These thin films wereÂ transferred in-situ in ultrahigh vacuum from theÂ MBE system to the photoemission setup. AngleÂ resolved photoemission spectroscopy (ARPES)Â shows that the Fermi energy and the DiracÂ point are congruent and no bulk bands intersectÂ the Fermi energy.

The special electronic properties of theÂ topological insulator can be used, e.g. forÂ creating exotic quasi-particles like MajoranaÂ Fermions.

The interface of strong topological insulators with s-wave superconductors hosts a topological superconductor. This implies Majorana states (quasiparticles which are its own antiparticles) at all boundaries of the interface. Within this project, the boundary is constructed by holes in the superconductor, which are filled with magnetic flux quanta using an external magnetic field. The prediction is that an odd number of flux quanta exhibits a Majorana state within the hole, while an even number leads to coupling of the Majorana states resulting in conventional fermions only.

The Majorana state is visible as a peak in scanning tunneling spectroscopy exactly at the Fermi level.

*Sponsored byÂ DFG SPP 1666: topological insulators.*