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Single-Layer and Bilayer Graphene Quantum Dot Devices Single-Layer and Bilayer Graphene Christian Volk Christian Volk Single-layer and bilayer graphene quantum dot devices Single-layer and bilayer graphene This thesis reports low temperature transport experiments on sing- quantum dot devices le-layer and bilayer graphene quantum dot (QD) devices focusing on the analysis of excited state spectra and the investigation of the relaxa- tion dynamics of excited states. Finite-bias spectroscopy measurements unveil the excited state spec- trum of a graphene QD. RF pulsed gate spectroscopy is used to probe the relaxation dynamics of excited state to ground state transitions. Transient current spectroscopy yields an estimate of a lower bound for charge relaxation times on the order of 60 to 100 ns. The experimental results are compared to a basic model regarding electron-phonon coupling as the dominant relaxation mechanism. A bilayer graphene double quantum dot device is characterized. The capacitive interdot coupling can be tuned systematically by a local gate. The electronic excited state spectrum of a features a single-par- ticle level spacing independent on the number of charge carriers on the QDs which is in contrast to single-layer graphene. Graphene nanoribbon based charge sensors are characterized as an important tool to detect individual charging events in close-by QDs. Back action effects of the detector on the probed QD are studied. Dissertation 2015 · 2nd Institute of Physics · RWTH Aachen University Single-layer and bilayer graphene quantum dot devices | Christian Volk graphene quantum and bilayer Single-layer Single-layer and bilayer graphene quantum dot devices Von der Fakult¨atf¨ur Mathematik, Informatik und Naturwissenschaften der RWTH Aachen University zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften genehmigte Dissertation vorgelegt von Diplom-Physiker Christian Volk aus K¨oln Berichter: Universit¨atsprofessorDr. Christoph Stampfer apl. Professor Dr. Thomas Sch¨apers Tag der m¨undlichen Pr¨ufung:26. Februar 2015 Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verf¨ugbar. Abstract Graphene quantum devices, such as single electron transistors and quantum dots, have been a vital field of research receiving increasing attention over the past six years. Quantum dots (QDs) made from graphene have been suggested to be an in- teresting system for implementing spin qubits. Compared to the well-established GaAs-based devices their advantages are the smaller hyperfine interaction and spin-orbit coupling promising more favorable spin coherence times. However, while the preparation, manipulation, and read-out of single spins have been demon- strated in GaAs QDs, research on graphene QDs is still at an early stage. So far, effects like Coulomb blockade, electron-hole crossover and spin-states have been studied in graphene QDs. This thesis reports low temperature transport experiments on single-layer and bilayer graphene quantum dot devices focusing on the analysis of excited state spectra and the investigation of the relaxation dynamics of excited states. Graphene nanoribbon based charge sensors are characterized as an important tool to detect individual charging events in close-by QDs. All devices are fabricated following the concept of width-modulated graphene nanostructures. Carving nanoribbons out of graphene sheets opens an effective band gap and offers the chance to circumvent the limitations originating from the gapless band structure in "bulk" graphene. Shaping graphene into small islands (with typical diameters between 50 and 120 nm) connected to contacts via narrow ribbons (typical widths between 30 and 50 nm) allows the confinement of electrons and the formation of QDs with gate-tunable tunneling barriers. Graphene nanoribbon-based charge detectors coupled to QDs are characterized. They allow the resolution of charging events on the QD even in regimes where the direct current is below the noise floor and excited states of the QD can be i resolved by this technique as well. The detector remains operating even in adverse conditions like under the influence of magnetic fields of several Teslas or while RF pulses in the MHz regime are applied to the QD. These findings are in particular relevant for experiments addressing spin states or relaxation processes in graphene QDs. Special emphasis lies on the influence of the detector on the transport properties of the probed QD. The effects of back action and counter flow are measured and discussed. The relaxation dynamics of excited states of graphene QDs is investigated. Finite-bias spectroscopy measurements unveil the excited state spectrum of the device. Long and narrow constrictions are used as tunneling barriers which allow driving the overall tunneling rate to a few MHz. In such a regime rectangular RF pulse schemes are applied to an in-plane gate to probe the relaxation dynamics of excited state to ground state transitions. Measurements of the current averaged over a large number of pulse cycles yield an estimate of a lower bound for charge relaxation times on the order of 60 to 100 ns which is roughly a factor of 5 to 10 larger than what has been reported in III/V quantum dots. The experimental results are compared to a basic model regarding electron-phonon coupling as the dominant relaxation mechanism. A bilayer graphene double quantum dot device is characterized. The capacitive interdot coupling can be tuned systematically by a local gate. The electronic excited state spectrum features a single-particle level spacing independent on the number of charge carriers on the QDs which is in contrast to single-layer graphene. In in-plane magnetic fields a level splitting of the order of Zeeman splittings is observed. ii Zusammenfassung Graphen-Quantenbauelemente wie Einzelelektronentransistoren und Quantenpunk- te sind seit sechs Jahren ein lebendiges Forschungsgebiet von steigendem Interesse. Graphen-Quantenpunkte werden als ein interessantes System zur Implementierung von Spin-Quantenbits angesehen. Im Vergleich zu den verbreiteten auf GaAs basie- renden Bauelementen besteht der Vorteil in einer kleineren Hyperfein- und Spin- Bahn-Wechselwirkung, was vorteilhafte Spin-Koh¨arenzzeiten verspricht. W¨ahrend die Pr¨aparation, Manipulation und das Auslesen einzelner Spins in GaAs Quanten- punkten bereits gezeigt wurden, steht die Forschung an Graphen-Quantenpunkten noch am Anfang. Effekte wie Coulomb-Blockade, Elektron-Loch-Ubergang¨ und Spin-Zust¨ande wurden bereits untersucht. Diese Arbeit zeigt Tieftemperatur-Transportexperimente an ein- und zweilagi- gen Graphen-Quantenpunkten mit dem Fokus auf der Analyse von Anregungsspek- tren und der Untersuchung der Relaxationsdynamik von angeregten Zust¨anden. Ladungssensoren basierend auf Graphen-Streifen werden charakterisiert und als wichtiges Instrument eingesetzt um Ladungsuberg¨ ¨ange in einem benachbarten Quantenpunkt nachzuweisen. Alle Proben sind basierend auf dem Konzept der breiten-modulierten Nano- strukturen hergestellt. Wird Graphen in Streifen mit einer Breite auf Nanometers- kala geschnitten ¨offnet sich effektiv eine Bandlucke.¨ Das bietet eine M¨oglichkeit die Einschr¨ankungen zu umgehen, die darauf beruhen, dass ausgedehntes Graphen keine Bandlucke¨ besitzt. Es werden kleine Inseln (typische Durchmesser zwischen 50 und 120 nm) hergestellt, die mit den Kontakten uber¨ schmale Streifen (Brei- te zwischen 30 und 50 nm) verbunden sind. Dadurch entstehen Quantenpunkte verbunden mit gate-steuerbaren Tunnelbarrieren. Ladungsdetektoren basierend auf Graphen-Nanostreifen gekoppelt an Quanten- iii punkte werden charakterisiert. Sie erlauben Ladungsvorg¨ange des Quantenpunkts aufzul¨osen, selbst wenn der direkte Strom durch den Quantenpunkt unterhalb des Rauschniveaus liegt. Weiterhin k¨onnen angeregte Zust¨ande des Quantenpunkts mit dieser Technik nachgewiesen werden. Der Detektor funktioniert auch noch unter ungunstigen¨ Bedingungen, wie dem Einfluss eines mehrere Tesla starken Magnet- fels oder wenn Hochfrequenz-Pulse im MHz-Bereich an den Quantenpunkt angelegt werden. Diese Ergebnisse sind besonders fur¨ Experimente an Spin-Zust¨anden oder zur Untersuchung von Relaxationsprozessen interessant. Ein weiterer Schwerpunkt liegt auf dem Einfluss des Detektors auf die Transporteigenschaften des Quanten- punkts. Die Relaxationsdynamik von angeregten Zust¨anden in Graphen-Quantenpunkten wird untersucht. Bias-Spektroskopie-Messungen l¨osen das Spektrum der angereg- ten Zust¨ande auf. Lange und schmale Zuleitungen zum Quantenpunkt erm¨oglichen, die Tunnelrate bis zu wenigen MHz zu reduzieren. In einem solchen Bereich wer- den Sequenzen aus Rechteckpulsen an ein Gate angelegt um damit die Relaxation von angeregten Zust¨anden zum Grundzustand zu untersuchen. Messungen des uber¨ mehrere Pulszyklen gemittelten Stroms erlauben eine untere Absch¨atzung der Ladungsrelaxationszeit in der Gr¨oßenordnung von 60 bis 100 ns, was etwa 5 bis 10 mal gr¨oßer ist als was fur¨ III/V-Quantenpunkte berichtet wurde. Die ex- perimentellen Ergebnisse werden mit einem vereinfachten Modell verglichen, das Elektron-Kopplung als den wesentlichen Relaxationsmechanismus annimmt. Ein Doppel-Quantenpunkt aus zweilagigem Graphen wird charakterisiert. Die kapazitive Kopplung zwischen beiden Quantenpunkten kann systematisch durch Gates gesteuert werden. Das elektronische Anregungsspektrum weist Einteilchen- Energieabst¨ande auf, die (im Gegensatz zu einlagigem Graphen) unabh¨angig von der Anzahl der Ladungstr¨ager auf dem Quantenpunkt sind. Ein paralleles Ma- gnetfeld fuhrt¨ zu einem Aufspalten der Energieniveaus
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