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Electron Interactions in Mesoscopic Physics: Scanning Gate Microscopy and Interferometry at a Quantum Point Contact

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Electron Interactions in Mesoscopic Physics: Scanning Gate Microscopy and Interferometry at a Quantum Point Contact THÈSE Pour obtenir le grade de DOCTEUR DE L’UNIVERSITÉ DE GRENOBLE Spécialité : Physique de la matière condensé et du rayonnement Arrêté ministériel : 7 août 2006 Présentée par Boris BRUN Thèse dirigée par Marc SANQUER et codirigée par Hermann SELLIER préparée au sein l’Institut Néel, CNRS, Grenoble et de l’Ecole doctorale de physique de Grenoble Electron interactions in mesoscopic physics: scanning gate microscopy and interferometry at a quantum point contact Thèse soutenue publiquement le 17 Octobre 2014, devant le jury composé de : Patrice ROCHE CEA SPEC, Saclay, Rapporteur Francesco GIAZOTTO Scuola Normale Superiore, Pisa, Rapporteur Harold BARANGER Duke University, North Carolina, Examinateur Julia MEYER CEA INAC / UJF, Grenoble, Examinateur Dietmar WEINMANN CNRS IPCMS, Strasbourg, Examinateur Marc SANQUER CEA INAC, Grenoble, Directeur de thèse Hermann SELLIER CNRS NEEL / UJF, Grenoble, Co-Directeur de thèse - ii - Abstract In this thesis, we studied the effect of electron electron interactions in quantum point contacts (QPCs). Quantum point contacts are small quasi-one dimensional channels, designed on a high mobility two-dimensional electron gas (2DEG). A negative voltage applied on a pair of metallic split gates above the sample surface allows to open or close the QPC. As a QPC opens, more and more electronic modes are allowed to cross the QPC, and its conductance increases by discrete steps, separated by a conductance quan- tum 2e2/h. This can be understood from a single-particle picture in one-dimensional transport, as each transverse mode carries a conductance quantum. But from their first realization 25 years ago, quantum point contacts have shown devia- tions from this picture, attributed to electron electron interactions. The most well known are a shoulder below the first plateau, around 0.7 2e2/h, called the "0.7 anomaly", and a peak in the differential conductance that arises at× low temperature: the zero bias anomaly (ZBA). The tool we used to study these interaction effects is a scanning gate microscope (SGM). It consists by changing locally the device’s potential with the polarized tip of an atomic force microscope (AFM), and record the changes in conductance as a function of the tip position. By performing this technique at very low temperature, we showed that we can modulate the conductance anomalies of QPCs. We interpret our result as the signature of a small electrons crystal forming spontaneously at low density in the QPC due to the Coulomb repulsion: a Wigner crystal. We can modify the number of crystallized electrons by approaching the tip, and obtain signatures of the parity of the localized electrons num- ber in transport features. Depending on this parity, the Wigner crystal has a different spin state, and screening of this spin by the surrounding electrons through the so-called Kondo effect leads alternatively to a single peak or a split ZBA. This discovery brings a significant advance in this field, that has attracted research efforts of many important groups in the world over the past 15 years. We then performed interferometric measurements thanks to the scanning gate microscope by creating in-situ interferometers in the 2DEG. We obtained signatures of an additional phase shift accumulated by the electrons in the ZBA regime. We attribute this effect to the universal phase shift that electrons accumulate when crossing a Kondo singlet, rein- forcing that the debated origin of the ZBA lies in Kondo physics. Finally, we adapted the SGM technique to the study of thermoelectric transport in QPCs, and for the first time imaged interferences of electrons driven by a temperature difference. 1 - 2 - Résumé en français Au cours de cette thèse nous avons étudié les effets des interactions entre électrons dans les contacts ponctuels quantiques (QPCs). Les contacts ponctuels quantiques sont des pe- tits canaux quasi-unidimensionnels, définis à partir de gaz électroniques bidimensionnels de haute mobilité (2DEG). Une tension négative appliquée sur des grilles métalliques au dessus de la surface permet d’ouvrir ou fermer le QPC. Lorsqu’un QPC s’ouvre, de plus en plus de modes électroniques peuvent traverser le QPC, et sa conductance augmente par pas discrets, séparés par un quantum de conductance 2e2/h. On peut le comprendre par le transport unidimensionnel d’une seule particule, car chaque mode transverse contribue pour un quantum de conductance. Mais depuis leurs premières réalisations, les QPCs ont montré des déviations par rapport à ce modèle à une particule. Les plus connues sont un épaulement sous le premier plateau, autour de 0.7 2e2/h, appelé "l’anomalie 0.7", et un pic dans la conductance différentielle qui apparaît à× basse température: l’anomalie à zéro polarisation (ZBA). L’instrument que nous avons utilisé pour étudier ces effets d’interactions est un microscope à effet de grille local (SGM). Cette technique consiste à modifier localement le potentiel d’un dispositif à l’aide d’une pointe de microscope à force atomique (AFM) chargée néga- tivement, et enregistrer les modifications de la conductance en fonction de la position de la pointe. En utilisant cette technique à très basse température, nous avons montré que nous pouvons moduler les anomalies de conductance du QPC. Nous avons interprété nos résultats comme la signature d’un cristal d’électrons se formant spontanément à basse densité dans le QPC à cause de la répulsion Coulombienne: un cristal de Wigner. On peut modifier le nombre d’électrons cristallisés en approchant la pointe, et obtenir des signatures de la parité du nombre d’électrons localisés dans le transport électronique. En fonction de cette parité, le cristal de Wigner présente un état de spin différent, et l’écrantage de ce spin par les électrons de conduction au travers d’un mécanisme appelé effet Kondo donne une anomalie à zéro polarisation formant alternativement un simple pic ou un double pic. Cette découverte apporte une avancée significative à ce domaine, qui a concentré les efforts de plusieurs groupes importants ces 15 dernières années. Nous avons ensuite réalisé des mesures interférométriques à l’aide du microscope SGM, en créant in situ des interféromètres dans le gaz 2D. Nous avons obtenu les signatures d’un déphasage supplémentaire dans le régime de la ZBA. Nous attribuons cet effet au déphasage universel accumulé par les électrons à la traversée d’un singulet Kondo, ce qui renforce le fait que la ZBA trouve son origine dans les phénomènes Kondo. Enfin, nous avons adapté la technique SGM au transport thermoélectrique dans les QPCs, et avons imagé pour la première fois les interférences d’électrons se déplaçant sous l’effet d’une différence de température. 3 - 4 - Acknowledgments The time to acknowledge people who helped me all along this thesis comes at the very end, though I could never have achieved a tenth of this work without the help of numerous people. Of course I would first like to thank Hermann for having written and directed the scientific project, and chosen me as the PhD student in charge of this work. He always guided me with patience, spent time to follow my investigations and the experimental results, and encouraged me in creating new collaborations that proved to be essential in this work. Aside physics, I really enjoyed to spend time with him during these three years. Looking around, I understood that a passioning research subject is not the first require- ment for a satisfying thesis. It comes in second position, the first one being a friendly and understanding supervisor, and I enjoyed these three years particularly because Hermann definitely has these essential human skills. Marc has also been a wise director, helped me to follow the right directions, and suggested me essential collaborations. I also thank him for the time he spent to gather all the electronics spread in the C1 building each time I needed to measure devices in the LATEQS team. Fruitful collaborations have been the key for me to achieve this work. I first would like to acknowledge Vincent Bayot. If he had not invited me to visit Belgium, my thesis would have been completely different, and would probably not contain its principle re- sults. It is definitely in Louvain-La-Neuve that started the most fruitful and passioning collaboration. I have a special thanks for Benoit Hackens, and I apologize for having dried out his Helium fundings during my stays in his team! None of this would have been possible without the essential help of Frederico Martins. Thanks Fred for your contagious love of experimental physics, your determination, and all those good moments spent on the fridge sofa discussing about life till the end of the night to keep on measuring. It was a pleasure to work with Sebastien Faniel, and his fine knowledge of all the fridge’s whims! I also thank Damien Cabossart, and his promising work on graphene rings. Fi- nally I have a thought for the whole team, including Sadia and Jean-Michel, and I’m afraid to misspell Handra and Nhan’s names to thank them... See you soon, I’ll try to come back! I also thank many people from the near field team at Neel Institute, Aurelien for his every-day craziness, Guillaume for his calm enthusiasm, his Comsol simulations and a magic paraglide flight together, the irreplaceable Mr. Jean-Francois Motte, Serge for his great supervision of this team, and finally Jochen, Sven, Katrin, Joanna, Anna, Olivier, Arnaud, Pierre, Jean-Yves, Jean-Baptiste, Sayanti, Hervé, Benjamin for team lunches in a joyful mood! 5 On the other side of the border, in CEA, I also wish to thank many people, I hope not to forget too much of them! First in the LATEQS’ great experimentalists team, thanks to Benoit Voisin for his teach- ings in low-temperature nano-electronics and all those years spent at school together, but also away from the labs in everyday’s life.
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