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Topological Insulators investigated by real- and momentum space microscopy

Fig. 1: k-space picture of a surface state dispersion connecting the valence and conduction band. Image taken from Hasan and Kane
Topological insulators are one of the hot topics in condensed matter physics. These are materials that are (ideally) insulating in the bulk of the material, but have metallic surfaces. The presence of conducting surface states in insulators is nothing new, but in the recently discovered alloys BiSb, Bi2Se3, Bi2Te3 and some intercalated versions of these materials the surface states are robust against the effects of impurity scattering on adatoms at the surface.

The origin of this robustness lies in the notion of topological invariance. The hamiltonian describing the energetics of most insulators, including the vacuum, can be characterized with a topological invariant known as a Chern number. The Chern number can take on different values, depending of the class to which the insulator belongs, and the recently discovered topolgical insulators turn out to have a Chern number different from ordinary insulators. The surface of such a material now acts as the boundary between two quantum systems, say the topological insulator and the vacuum, with differing Chern numbers. As a result new states emerge that live on the surface between the two insulators (see fig. 1). These states bridge the valance and conduction bands, thereby crossing the Fermi level and hence are metallic. Moreover, because they arise from the difference in Chern number they are not easily destroyed by impurities at the surface. It is the robustness of the metallic states which attracted much attention. Here we have a quantum system, protected from scattering and other decoherence-effects that seems - at first glance - very attractive for people concerned with spintronics and quantum computing. Understanding the nature of the surface states and how they can be manipulated is of crucial importance for developing them into a new kind of electronics.

 

Fig. 2 (clockwise) a):Crystal structure of Bi2Te3, adapted from Alpichshev. b): Typical crystals grown from melt, cleaved sample mounted on the cold finger and typical LEED picture. 3D compilation from first measurements. c): Constant energy contours emphasizing the Dirac like dispersion.
Our group has started a project aimed at developing and investigating new materials that fall in the class of topological insulators. Our first efforts in this direction has been to investigate two known alloys, Bi2Se3 and Bi2Te3. The synthesis of these materials was done at the crystal growth lab in Amsterdam by Dr. Yingkai Huang. We have also grown systems in which some of the Bi atoms are replaced by Cu. It has been shown that if the Cu atoms mainly occupy the interstitial sites the topological insulator becomes a superconductor with a critical temperature of 3.8 K. We have investigated these materials using ARPES and scanning tunneling microscopy. One of the often cited disadvantages of angle resolved photoemission spectroscopy (ARPES), namely its surface sensitivity, is turned into a huge advantage in these kind of systems. A typical He discharge lab source emits photons with specific energies of 21.2 eV and 41.8 eV, right around the minimum in the universal electron escape depth vs. kinetic energy curve.

Initial ARPES characterization of our crystals was carried out in Amsterdam using the Fom Amsterdam MOmentum Space microscope (FAMoS). Together with Bachelor project student Jiri Oen, we investigated Cu-doped crystals of Bi2Se3 and Bi2Te3. In a relatively short period of time he succeeded in repeating some of the initial measurements performed by world leading groups. Exploiting the strengths of our 6 axis manipulator, we were able to derive high resolution k-space maps showing the unique energy dispersion, known as a Dirac cone. The observed surface state dispersion is not perfectly conical, but rather reflects the 6-fold symmetry of the lattice (fig. 2). These experiments show that the valence band has a maximum at a binding energy around 0.36 eV, while the conduction band dips below the Fermi energy with a bottom at 0.1 eV. As a consequence the bulk of this material is not a perfect insulator, which is one of the shortcomings of these alloys.

Our initial, lab-based measurements leave space for more advanced experiments at the synchrotron. At this point we are analyzing measurements performed at the "13" beamline at the BESSY2 synchrotron. General benefits of the synchrotron source are the availability of continuous photon energies, different polarizations and high flux. The 13 beamline in particular offers 1 meV beamline resolution, 1 meV analyzer resolution and base temperature below 1 K. Fig. 3 shows some valence band pictures measured at 800 mK.

Fig. 3: ARPES measurements performed at the 13 beamline at BESSY2, Berlin.

Fig. 4 shows a comparison of an integrated ARPES energy distribution map (EDM) and an average tunneling density of states measured on Cu doped Bi2Se3. The binding energy of the Dirac point is determined from an MDC analysis to be -0.36 eV. Just below the Dirac point we observe a minimum in the integrated intensity The tunneling density of states shows a similar structure at this energy, but interestingly has almost no DOS at the Fermi energy. We are currently investigating whether this is an effect of specific tunneling matrix elements or arises from another source.

Fig. 4: comparison of integrated photoemission DOS (top right) and tunneling DOS (bottom right). The ARPES DOS is derived from the EDM shown on the left, measured at the 13 beamline.
For more information, please contact Erik van Heumen or Mark Golden