Terahertz Laser Spectroscopy of Two- and Three-Dimensional Topological Insulators based on HgTe Nanostructures

In the framework of this thesis, two- and three-dimensional topological insulators (TI) are investigated with opto-electronic effects in the terahertz range. It is demonstrated that in both cases, photogalvanic effects can be utilized for the detection and the analysis of Dirac fermion states. In the three-dimensional case, a cyclotron-resonance-enhanced photocurrent is observed by exciting 80 nm strained HgTe films with terahertz radiation. The arising resonances could be clearly attributed to the topologically protected top and bottom surface states of the system. Studying these resonant responses in a gated sample, the behaviour of the photocurrent is observed upon a modification of the Fermi energy, which allows the extraction of the cyclotron masses of the top and bottom surface states as a function of the Fermi energy. For larger gate voltages, an additional cyclotron resonance is detected, which is caused by bulk carriers and corresponds to a mass about two times larger than that obtained for the surface states. These results are in full agreement with the band structure of the strained HgTe films, calculated by the k•p method. The cyclotron masses of the surface states estimated from this calculation fit well with the experimental ones. Based on the experimental results, a microscopic theory of the resonant photocurrent is developed. It is shown that an orbital effect emerges due to an asymmetric scattering of non-equilibrium surface electrons, resulting in a fully spin-polarized direct electric current, which exhibits a resonant behaviour due to the cyclotron-resonance-enhanced absorbance. Photogalvanic spectroscopy is also used for the investigation of two-dimensional topological insulators. There spin-polarized photogalvanic currents flowing mainly in the edges of the sample are observed by exciting 2D HgTe QWs with circularly polarized terahertz radiation. These currents exhibit a strong helicity-dependence, meaning that the reversal of the radiation helicity reverses the direction of the photocurrent. Moreover, the sign of the photosignal for a fixed helicity is opposite for the opposite edge, which demonstrates that the current indeed flows in the edges of the sample. Such chiral edge photocurrents are detected in a wide range of applied gate voltages, in which they change their sign twice, which allows a division into three different regions. The mechanisms responsible for the generation of the photocurrent strongly depend on the location of the Fermi level within the band structure. For a Fermi level in the conduction band, the helicity-sensitive photocurrent flowing in the bulk can be attributed to the circular photogalvanic effect, whereas the part generated in the edges is attributed to diffusive scattering at the boundaries of the sample together with the action of the electric field of the circularly polarized radiation on the carrier. In contrast to this, in the TI-regime, the photocurrent is caused by a photoionization of helical edge electrons into the conduction band. For this effect, a microscopic model and the microscopic theory are developed simultaneous to the experiments. It is shown that due to spin-dependent selection rules, the photoionization from spin-up and spin-down branches induced by right- and left-handed circularly polarized radiation is different, which leads to an imbalance of the edge state population and thus to an electric net current. A similar effect is expected for a Fermi level near the valence band region. The photocurrent generation is attributed to transitions from the valence band to the edge sates. However, no full theory could be given till now, as this would require a full understanding of the complex band structure of HgTe near the valence band. To conclude, this work clearly demonstrated that opto-electronic methods present a convenient tool for the investigation of two- and three-dimensional topological insulators and can even be suitable for the search for new topological insulators. An important feature of this kind of investigation is that it can be applied to diverse geometries and states of samples. Thus, opto-electronic effects can be utilised for micrometre-sized samples where pure optical methods can no longer be performed. Furthermore, the CR-assisted investigation of 3D TI can even be carried out in samples where classical dc transport is hardly possible. For example, it can be used in samples with a high residual carrier density of the bulk or in samples with a Fermi energy lying in the conduction band

Quantum Oscillations of Photocurrents in HgTe Quantum Wells with Dirac and Parabolic Dispersions

We report on the observation of magneto-oscillations of terahertz radiation induced photocurrent in HgTe/HgCdTe quantum wells (QWs) of different widths, which are characterized by a Dirac-like, inverted and normal parabolic band structure. The photocurrent data are accompanied by measurements of photoresistance (photoconductivity), radiation transmission, as well as magneto-transport. We develop a microscopic model of a cyclotron-resonance assisted photogalvanic effect, which describes main experimental findings. We demonstrate that the quantum oscillations of the photocurrent are caused by the crossing of Fermi level by Landau levels resulting in the oscillations of spin polarization and electron mobilities in spin subbands. Theory explains a photocurrent direction reversal with the variation of magnetic field observed in experiment. We describe the photoconductivity oscillations related with the thermal suppression of the Shubnikov-de Haas effect.Comment: 16 pages, 13 figure

Cyclotron Resonance Assisted Photocurrents in Surface States of a 3D Topological Insulator Based on a Strained High Mobility HgTe Film

We report on the observation of cyclotron resonance induced photocurrents, excited by continuous wave terahertz radiation, in a 3D topological insulator (TI) based on an 80 nm strained HgTe film. The analysis of the photocurrent formation is supported by complimentary measurements of magneto-transport and radiation transmission. We demonstrate that the photocurrent is generated in the topologically protected surface states. Studying the resonance response in a gated sample we examined the behavior of the photocurrent, which enables us to extract the mobility and the cyclotron mass as a function of the Fermi energy. For high gate voltages we also detected cyclotron resonance (CR) of bulk carriers, with a mass about two times larger than that obtained for the surface states. The origin of the CR assisted photocurrent is discussed in terms of asymmetric scattering of TI surface carriers in the momentum space. Furthermore, we show that studying the photocurrent in gated samples provides a sensitive method to probe the effective masses and the mobility of 2D Dirac surface states, when the Fermi level lies in the bulk energy gap or even in the conduction band

Photogalvanic probing of helical edge channels in two-dimensional HgTe topological insulators

We report on the observation of a circular photogalvanic current excited by terahertz laser radiation in helical edge channels of two-dimensional (2D) HgTe topological insulators (TIs). The direction of the photocurrent reverses by switching the radiation polarization from a right-handed to a left-handed one and, for fixed photon helicity, is opposite for the opposite edges. The photocurrent is detected in a wide range of gate voltages. With decreasing the Fermi level below the conduction band bottom, the current emerges, reaches a maximum, decreases, changes its sign close to the charge neutrality point (CNP), and again rises. Conductance measured over a approximate to 3 mu m distance at CNP approaches 2e(2)/ h, the value characteristic for ballistic transport in 2D TIs. The data reveal that the photocurrent is caused by photoionization of helical edge electrons to the conduction band. We discuss the microscopic model of this phenomenon and compare calculations with experimental data

Photocurrent spectroscopy on nanocontacts : tunnel and single molecule junctions under femtosecond illumination

In dieser Arbeit wurde der lichtinduzierte Ladungstransfer in Nanokontakten untersucht. Dabei wurden sowohl Tunnel- als auch Molekülkontakte eingesetzt. Zur Präparation der Tunnelkontakte standen zwei verschiedene Methoden zur Verfügung: mechanisch kontrollierte Bruchkontakte und elektromigrierte Nanokontakte. Die Bruchkontakttechnik bietet die Möglichkeit, den Abstand der Elektroden mit Sub-AA-Genauigkeit zu verändern, während die elektromigrierten Kontakte einen durch die Präparationsbedingungen fest vorgegebenen Abstand haben. Bei den hier untersuchten Molekülen handelt es sich um Dithiole, die über eine Schwefel-Gold-Bindung an die Elektroden gebunden sind. Die Beleuchtung erfolgte im Fall der Bruchkontakte mit ultrakurzen Laserpulsen bei 800 nm und durch Frequenzverdopplung bei 400 nm. Durch Fokussierung auf einen Radius von ca. 100 mum wurden Spitzenintensitäten von 10^7 Wcm^-2 (800 nm) bzw. 10^6 Wcm^-2 (400 nm) erreicht. Die Bruchkontakte (Tunnel- und Molekülkontakte) waren bis zu den auftretenden Maximalintensitäten von 10^7 Wcm^-2 stabil. Für alle untersuchten Tunnelkontakte konnte eine lichtinduzierte Stromkomponente von bis zu 1 nA nachgewiesen werden. Sie ist proportional zum jeweils fließenden mittleren DC-Strom und beträgt typischerweise einige Prozent davon. Dieser Strom wurde auf die thermische Ausdehnung der Elektroden auf Grund der dort durch Absorption deponierten Lichtenergie zurückgeführt. Aus der relativen Größe des lichtinduzierten Signals und einem Wert der Austrittsarbeit von Gold von ca. 4,7 eV ergibt sich eine Expansion jeder Elektrode um etwa 1 pm. Dies ist in guter Überinstimmung mit einem einfachen thermischen Modell der freitragenden Elektroden. Bei einigen Kontakten wurde noch eine weitere lichtinduzierte Stromkomponente in der Größenordnung einiger pA gefunden, die nicht von der angelegten Biasspannung abhängt, aber linear mit der Laserleistung zunimmt. Ein Modell, das diese Befunde erklärt, geht von einer asymmetrischen Anregung in den beiden Elektroden aus. Somit ergibt sich ein Nettostrom angeregter Elektronen in eine Richtung. Die dazugehörige gemessene Quanteneffizienz liegt nahe bei 1, was ein Indiz auf einen Beitrag von sekundären heißen Elektronen zum Strom ist. Auch bei den Molekülkontakten konnte eine lichtinduzierte Stromkomponente identifiziert werden, die linear von der Laserintensität abhängt. Sie wird, ähnlich wie im Fall der Tunnelkontakte, der thermisch verursachten Expansion der Elektroden zugeschrieben, allerdings ließ sich der genaue Prozess bisher noch nicht erklären. Es ist anzunehmen, dass die Zunahme der Elektrodenlänge durch eine Umordnung auf atomarer Längenskala in der vordersten Spitze der Goldelektrode kompensiert wird, da dies der duktilste Bereich des gesamten Kontakts ist. Der genaue Prozess konnte jedoch noch nicht geklärt werden. Messungen, die den Elektrodenabstand um einige AA veränderten, lieferten weitere Indizien für die Komplexität der Molekülkontakte. So trat in manchen Fällen eine starke Korrelation zwischen Veränderungen des mittleren DC-Stroms und des lichtinduzierten Signals auf, was auf einen einzelnen Transportpfad für beide Signale hindeutet. Andererseits veränderten sich die beiden Ströme teilweise aber auch unabhängig voneinander, was nur durch mehrere parallele Transportkanäle im Kontakt erklärt werden kann. Zusätzlich zum thermisch verursachten lichtinduzierten Signal wurden, wie im Fall der Tunnelkontakte, biasspannungsunabhängige Ströme identifiziert. Sie sind in der gleichen Größenordnung wie in Tunnelkontakten und werden somit der gleichen Ursache zugeschrieben, nämlich einer asymmetrischen Anregung in den Metallelektroden, die zu einem Nettostrom in einer Richtung führt. Im zweiten Teil der Arbeit wurden elektromigrierte Tunnelkontakte untersucht. Da diese Kontakte einen sehr großen Elektrodenabstand in der Größenordnung von 30 nm aufwiesen, konnte nur bei Kombination von einer Biasspannung von mehreren Volt mit Femtosekundenbeleuchtung ein Strom im Bereich von 100 fA detektiert werden. Durch Verbesserung der Fokussierung im Vergleich zu den Experimenten an den Bruchkontakten wurden Spitzenintensitäten von 10^11 Wcm^-2 erreicht. Die lichtinduzierten Tunnelströme zeigen eine quadratische Intensitätsabhängigkeit, was einem Zwei-Photonen-Prozess entspricht, sowie eine ebenfalls nichtlineare Spannungsabhängigkeit. Zur Beschreibung der Daten wurde das Modell einer Multiphotonen-Photofeldemission verwendet, das auf der Fowler-Nordheim-Formel für Feldemission basiert. Durch geeignete Wahl der Modellparameter (Elektrodenabstand, Krümmungsradius der Elektrodenspitze und Barrierenhöhe im Tunnelkontakt) war es möglich, die Spannungsabhängigkeit des lichtinduzierten Signals zu reproduzieren.The goal of the present work was the investigation of light induced charge transfer in nano contacts. In this context, tunnel and molecular contacts were employed. Tunnel contacts were prepared by two different methods: the mechanically controlled break-junction technique (MCBJ) and the electromigration of nano junctions. The MCBJs make it possible to vary the distance of the electrodes with sub-AA precision while the gap width of the electromigrated contacts has a fixed value which is determined by the preparation conditions. All molecules under investigation are dithiols that bind to the metallic electrode by a strong gold-sulfur bonding. In the experiments with the MCBJs the contacts were illuminated with ultrashort laser pulses at 800 nm and its second harmonic at 400 nm. Focussing on a spot radius of approximately 100 mum resulted in peak intensities of 10^7 Wcm^-2 for 800 nm and 10^6 Wcm^-2 for 400 nm. The MCBJs (tunnel and molecular junctions) were stable up to the maximum intensities of 10^7 Wcm^-2. For all investigated tunnel junctions a light induced current of up to 1 nA could be detected. This current is proportional to the respective average DC current through the junction (caused by an applied bias voltage) and typically amounts to some percent of it. The light induced current component was attributed to a thermal expansion of the electrodes due to photon absorption. From its relative magnitude and the work function of gold of 4.7 eV an expansion of each electrode of about 1 pm could be deduced. This is in good agreement with a simple thermal model for the freestanding electrodes. For some contacts an additional light induced current component in the range of some pA was identified. It is independent of the applied bias, but increases linearily with the laser power. A model that accounts for these findings is based on an asymmetric excitation in the two electrodes. Thus, a net current of excited electrons in one particular direction is generated. The corresponding measured quantum efficiency is approximately 1 indicating a significant contribution of secondary hot charge carriers to the current. Also, for the molecular contacts a light induced current component could be identified that depends linearily on the laser intensity. Like in the case of the tunnel contacts it is accounted for by the thermal expansion of the electrodes. However, it has not yet been possible to explain the precise mechanism. The increase of the electrode length is presumably compensated by a rearrangement on the atomic scale in the foremost part of the tip since this is the most ductile region of the whole contact. A detailed explanation however is still missing. Measurements where the electrode separation is varied by some AA provide further evidence for the complexity of the molecular junctions. In some cases a strong correlation between changes in the average DC current and the light induced signal could be observed. This suggests a single transport path for the two signals. On the other hand the signals sometimes changed independently of each other. This can only be explained by several parallel transport channels in the contact. In addition to the thermally caused light induced signal also a bias independent current could be identified, like in the case of tunnel junctions. These currents are in the same order of magnitude as in tunnel contacts and are therefore attributed to the same origin, i.e. an asymmetric excitation in the metal electrodes that causes a net current in one direction. For bias voltages up to +/- 1 V this current contribution is constant and in particular doesn't exhibit any spectral features. In the second part of the present work electromigrated tunnel contacts were investigated. These junctions exhibited a very large electrode separation of around 30 nm. Therefore, only the combination of a bias voltage of some volts and illumination with femtosecond laser pulses yielded a detectable current in the range of 100 fA. By improving the focussing with respect to the MCBJ experiments peak intensities up to 10^11 Wcm^-2 were reached. The light induced tunnel currents exhibit a quadratic intensity dependence that corresponds to a two-photon process. Moreover, the bias dependence is non-linear as well. For the description of the data a model of a multi-photon photo-field emission was used that is based on the Fowler-Nordheim equation of field emission. By a suitable choice of the model parameters (electrode separation, radius of curvature of the electrode tips and barrier height in the tunnel junction) it was possible to reproduce the bias dependence of the light-induced signal