Topological Insulators
Topological insulators 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 is 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)
Recent Projects
Please click on the headlines to get more information.
a) STM image of the graphene-like 2D TI layer including a step edge. b) Local density of states image (dI/dV) of the same area revealing a continuous edge mode at the step edge. c) Local dI/dV(V) spectra taken at different position of the sample (marked by respective color in (b)). Edge state visible in the topological band gap of the 2D TI layer.
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 Bi14Rh3I9. The first weak topological insulator Bi14Rh3I9 is a stack of graphene-like 2D topological insulator (TI) layers. Combining these layers into pairs (Bi13Pt3I7), the topological edge states vanish as predicted by theory.
a) Stacked dI/dV images of the 2D TI layer recorded at voltages across the band gap. Edge state is visible throughout the whole band gap region. b) AFM image of Bi14Rh3I9 surface with letters BiRhI scratched into the surface. c) Stacked dI/dV images of the 2D TI layer of Bi13Pt3I7 for energies within the band gaps. No edge state is visible. Same contrast as in (a).
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- 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 }
Left: second derivative (d²I/dE²) of an ARPES spectrum in G-K direction. The valence band maximum is located at the Fermi energy at a k value of 0.15Å-1 vom with respect to the G point. Right: ARPES intensity within the k|| plane at the Fermi energy. Photon energy: 22eV.
The ternary compound Ge2Sb2Te5 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 Sb2Te3. Ge2Sb2Te5 is widely used as storage media in DVDs and RAMs. Using angle-resolved photoemission, we showed that the band structure of epitaxially grown Ge2Sb2Te5 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.
Overlay of ARPES spectra with DFT calculations of the metastable cubic phase. Bulk bands are marked as bright solid lines, states arising from slab calculations are red circles. The size of the circles indicates the extension of the states into the vacuum.
Left: tunneling spectroscopy showing the edges of valence band and conduction band. The Fermi energy is aligned with the top of the valence band. Right: atomically resolved image with contrast variations caused by subsurface defects.
Related Publication
- C. Pauly, M. Liebmann, A. Giussani, J. Kellner, S. Just, J. Sánchez-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 0.27–0.36Å-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 ¯ G ¯ Z 2 ? 0 ? 0
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Left: ARPES spectrum of the lower Dirac cone along the K-G-K direction. Photon energy: 55eV. Spin-polarized measurements yield a spin polarization of 85%. Right: DFT calculations show the Dirac cone overlapping with the upper valence band, and a Rashba-split surface state at lower energy. Bulk states are marked as bright solid lines and states obtained from slab calculations as circles. The size and color of the circles indicate direction and strength of spin polarization.
Using spin- and angle-resolved photoemission on Sb2Te3 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).
Left: ARPES spectrum of the Rashba-type surface state. Photon energy 22eV. Right: energy distribution curves with spin resolution (obtained at k values marked in the left spectrum) showing the spin-splitting of the Rashba band.
Left: STM image of a Sb2Te3 single crystal cleaved in ultrahigh vacuum. The line profile shows a step edge corresponding to the height of a quituple layer. Inset: atomically resolved image with typical defect structures. Right: tunneling spectroscopy showing valence band (VB) and conduction band (CB). The energetic position of the Dirac cone is marked as well.
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- C. Pauly, G. Bihlmayer, M. Liebmann, M. Grob, A. Georgi, D. Subramaniam, M. R. Scholz, J. Sánchez-Barriga, A. Varykhalov, S. Blügel, O. Rader, and M. Morgenstern Probing two topological surface bands of Sb
Te
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 Sb
Te
by spin-polarized photoemission spectroscopy
a) Sb2Te3 large scale STM image with dI/dV(V) spectrum at Bz = 0 T in the inset. b) A series of dI/dV(V) spectra ranging from Bz = 0 to 7 T with Landau levels visible. The spectra are shifted vertically for clarity. c) Landau level energies for Bz = 3 to 7 T plotted against sgn(n)*(nB)1/2. The dotted line is a linear fit to the data and the resulting Fermi velocity vF is marked.
Using scanning tunnelling spectroscopy, Landau levels at varying magnetic fields Bz are measured on the surface of the topological insulator Sb2Te3. 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.
a) STM topographic image revealing typical types of defects at the surface of Sb2Te3. b) Zoom into the marked area of (a) with a close up view of the four different types of defects (marked by different colored ellipses).
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ARPES of (Bix-1Sbx) 2Te3 at hv=21.2 eV, T= 200 K (MBE growth, in-situ transfer): a),b) E(k) dispersion along G – K at different resolution (black: high intensity, white: low intensity), Fermi level is marked as dashed line; c) Momentum distribution curves (MDCs) between E-EF = 250 meV and E-EF = -50 meV; offset for clarity
We were able to synthesize (Bi1-xSbx)2Te3 thin films for 0.95<x<0.96 by molecular beam epitaxy (MBE). These thin films were transferred in-situ in ultrahigh vacuum from the MBE system to the photoemission setup. Angle resolved photoemission spectroscopy (ARPES) shows that the Fermi energy and the Dirac point are congruent and no bulk bands intersect the Fermi energy.
The special electronic properties of the topological insulator can be used, e.g. for creating exotic quasi-particles like Majorana Fermions.
Majorana excitations at the interface of superconductors and topological insulators
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 by DFG SPP 1666: topological insulators.
Scanning tunneling microscopy and spectroscopy image of an electron channel at the step edge of a weak topological insulator.