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      Fourier Transform Scanning Tunneling Spectroscopy: the possibility to obtain constant energy maps and the band dispersion using a local measurement

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          Abstract

          We present here an overview of the Fourier Transform Scanning Tunneling spectroscopy technique (FT-STS). This technique allows one to probe the electronic properties of a two-dimensional system by analyzing the standing waves formed in the vicinity of defects. We review both the experimental and theoretical aspects of this approach, basing our analysis on some of our previous results, as well as on other results described in the literature. We explain how the topology of the constant energy maps can be deduced from the FT of dI/dV map images which exhibit standing waves patterns. We show that not only the position of the features observed in the FT maps, but also their shape can be explained using different theoretical models of different levels of approximation. Thus, starting with the classical and well known expression of the Lindhard susceptibility which describes the screening of electron in a free electron gas, we show that from the momentum dependence of the susceptibility we can deduce the topology of the constant energy maps in a joint density of states approximation (JDOS). We describe how some of the specific features predicted by the JDOS are (or are not) observed experimentally in the FT maps. The role of the phase factors which are neglected in the rough JDOS approximation is described using the stationary phase conditions. We present also the technique of the T-matrix approximation, which takes into account accurately these phase factors. This technique has been successfully applied to normal metals, as well as to systems with more complicated constant energy contours. We present results recently obtained on graphene systems which demonstrate the power of this technique, and the usefulness of local measurements for determining the band structure, the map of the Fermi energy and the constant-energy maps.

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          Chiral tunneling and the Klein paradox in graphene

          The so-called Klein paradox - unimpeded penetration of relativistic particles through high and wide potential barriers - is one of the most exotic and counterintuitive consequences of quantum electrodynamics (QED). The phenomenon is discussed in many contexts in particle, nuclear and astro- physics but direct tests of the Klein paradox using elementary particles have so far proved impossible. Here we show that the effect can be tested in a conceptually simple condensed-matter experiment by using electrostatic barriers in single- and bi-layer graphene. Due to the chiral nature of their quasiparticles, quantum tunneling in these materials becomes highly anisotropic, qualitatively different from the case of normal, nonrelativistic electrons. Massless Dirac fermions in graphene allow a close realization of Klein's gedanken experiment whereas massive chiral fermions in bilayer graphene offer an interesting complementary system that elucidates the basic physics involved.
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            Confinement of electrons to quantum corrals on a metal surface.

            A method for confining electrons to artificial structures at the nanometer lengthscale is presented. Surface state electrons on a copper(111) surface were confined to closed structures (corrals) defined by barriers built from iron adatoms. The barriers were assembled by individually positioning iron adatoms with the tip of a 4-kelvin scanning tunneling microscope (STM). A circular corral of radius 71.3 A was constructed in this way out of 48 iron adatoms. Tunneling spectroscopy performed inside of the corral revealed a series of discrete resonances, providing evidence for size quantization. STM images show that the corral's interior local density of states is dominated by the eigenstate density expected for an electron trapped in a round two-dimensional box.
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              Imaging standing waves in a two-dimensional electron gas

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                Author and article information

                Journal
                19 July 2011
                Article
                10.1088/0022-3727/44/46/464010
                1107.3648
                1c20b4cb-93c7-4ff6-aaf6-970bed503806

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                33 pages, 15 figures; invited review article, to appear in Journal of Physics D: Applied Physics
                cond-mat.mes-hall

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