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Laura Rincón García Laura Rincón García Thesis Supervisor: Prof. Nicolás Agraït de la Puente Departamento de Física de la Materia Condensada Universidad Autónoma de Madrid Cover: Sc3N@C80 molecular junctions in a thermal gradient (red to blue) which generates a thermoelectric response. The direction of the thermoelectric current (depicted in light blue) depends on the orientation of the molecule. Image by E. Sahagún (www.scixel.es) Thesis presented by Laura Rincón García for the degree of Doctor in Physics by Universidad Autónoma de Madrid Thesis Supervisor Prof. Nicolás Agraït de la Puente Department of Condensed Matter Physics, Faculty of Sciences Madrid, November 2019 Memoria presentada por Laura Rincón García para optar al grado de Doctora en Ciencias Físicas por la Universidad Autónoma de Madrid Dirigida por Prof. Nicolás Agraït de la Puente Departamento de Física de la Materia Condensada, Facultad de Ciencias Madrid, Noviembre 2019 A los míos. “What I want to talk about is the problem of manipulating and controlling things on a small scale. [..] Now, you might say, “Who should do this and why should they do it?” Well, I pointed out a few of the economic applications, but I know that the reason that you would do it might be just for fun. But have some fun!” Richard P. Feynman, “There's Plenty of Room at the Bottom”, December 29th 1959. Acknowledgements Esta tesis no habría sido posible sin la contribución en mayor o menor medida de todas las personas que han formado parte de mi vida a lo largo de este tiempo. Han sido cinco años de aprendizaje y duro trabajo, llenos de colaboraciones científicas y proyectos formativos, pero también de grandes momentos personales. En caso de olvidar mencionar a alguien en estas páginas, vaya por delante mi más profundo agradecimiento a todas ellas. Mi más sincera gratitud a mi director de tesis, Nicolás Agraït, por darme la oportunidad de llevar a cabo esta tesis y por compartir conmigo su visión de la física y su pasión por los experimentos y la programación. Mi trabajo en su grupo comenzó como estudiante de grado con la preparación de un vídeo de divulgación científica y no podía sospechar entonces todo lo que aprendería después. La autonomía en el laboratorio, la asistencia a conferencias, las colaboraciones con otros grupos, las publicaciones realizadas... Todo ello ha sido posible gracias a su buen hacer científico y su generosidad, siempre con nuevas ideas, viendo el lado positivo y con Matlab al alcance de la mano. Realmente he disfrutado trabajando contigo. En lo referente a posibilitar la realización de esta tesis, gracias igualmente al Ministerio de Educación, Cultura y Deporte por la ayuda no. FPU014/03368 con la que ha financiado la mayor parte de este trabajo y al apoyo financiero de la Universidad Autónoma de Madrid en los inicios de mi doctorado a través de una Ayuda para la realización del plan de investigación. I would also like to thank Prof. Pramod Reddy and all his group at University of Michigan for welcoming me during my six-month stay in Ann Arbor, and in especial Dakotah Thompson for his great explanations about the near field radiative heat transfer setup and his mentoring in the clean room, where Spanish lessons made waiting times shorter. My stay with you was a very enriching experience. Special thanks go to all the people I have collaborated with along these years in different scientific projects. To Prof. Colin J. Lambert and his group, in particular, for the theoretical calculations performed and the exciting meetings trying to understand the origin of bi- thermoelectricity. To the different groups of chemical synthesis we have worked with for sharing with us their molecules and their patience with the times of experiments. By extension, thank you to all the people involved in MOLESCO and QuIET European projects. I have experienced with you the feeling of a scientific community working together towards a common goal and it is wonderful, in addition to have had the opportunity to travel all around Europe, to visit different facilities and to learn about different working approaches. Volviendo al lugar en el que he desarrollado la tesis, me gustaría agradecer a los profesores del Departamento de Física de la Materia Condensada su contribución en mi formación científica. Gracias en especial a Gabino Rubio-Bollinger por sus lecciones en el laboratorio, a José Gabriel Rodrigo por su inestimable ayuda en la preparación de las clases de Técnicas Experimentales II, a Miguel Ángel Ramos por su interés por la docencia, a Sebastián Vieira por su confianza y a Hermann Suderow por la oportunidad de organizar las jornadas del INC de 2017 y por llevarlas a cabo cada año; han sido un valioso punto de referencia. Gracias de manera muy especial a los estudiantes de doctorado que formaban parte del grupo de Nicolás cuando me incorporé: Charalambos (Chara), Siya (coffee time?), Aday y Jorge. Todos xi ellos son ya doctores y siendo mi referencia más cercana en el laboratorio, su proceso de aprendizaje ha inspirado sin duda el mío. Mi más profunda gratitud a Chara, por todo lo que aprendí con él de STM, moléculas y termoelectricidad y sobre todo por el equipo fantástico que heredé y que me ha permitido desarrollar la mayor parte del trabajo de esta tesis. Gracias igualmente a otros miembros del grupo: a David (que ya es casi doctor también), a Simon, a Alex, y, de manera particular, a Teresa y a Ed, con los que colaboro en los proyectos de oligoinos y porfirinas y cuya ayuda ha sido esencial para llegar a los resultados y conclusiones que presento. A las nuevas incorporaciones al grupo (Juan, Rubén, Juanjo), el relevo, gracias por vuestro espíritu de trabajo y os deseo todo lo mejor en la aventura de la investigación. Quisiera agradecer también el granito de arena aportado por otros estudiantes de doctorado o investigadores del departamento, del laboratorio de bajas temperaturas en particular (Pepe, Edwin, Antón, Isabel, Víctor, Fran, Roberto, Tomás, y por extensión Isidoro, Juanpe, Antonio), de los técnicos del departamento (Andrés, Chema, Rafa, Sara, José María, Santiago, Nacho) (vuestra aportación a esta tesis es realmente esencial) y al resto de personal del departamento (Elsa, Luisa, Ana, Macarena). A lo largo de estos años he sentido el departamento como mi segunda casa gracias a todos vosotros, a lo que también han contribuido los miembros de la cafetería de Ciencias. Y hablando de la cafetería de Ciencias, gracias al grupo de comida formado a lo largo de estos años para compartir desayunos, comidas, meriendas y cenas, en la facultad y fuera de ella. María, Laura, Elena, David, Álex, Sergio, Iris, Gus, Juanfran, Aitor, Alicia. Gracias también por los viajes y actividades varias, por las risas y el estrés compartidos. Habéis sido un verdadero punto de apoyo a lo largo de estos años, avanzando juntos en la iniciación al mundo de la investigación. Otro punto de apoyo esencial han sido mis chiquitas bonitas, Araceli, Estefanía y María. Gracias por tantas y tantas cenas a lo largo de estos años, las vacaciones y los momentos increíbles que hemos compartido. Cualquier plan con vosotras es siempre inmejorable y me recarga las pilas; somos la prueba de que letras y ciencias pueden hacer buenas migas. A mi círculo más cercano le debo sin duda el haber conseguido llegar hasta aquí. Gracias a mis padres, Vicenta y Juan Carlos, por su apoyo y su fe en mí; han estado ahí desde el principio y sé que siempre puedo contar con ellos. Ah, y todo en orden, papá, creo que no se ha escapado ninguna molécula del experimento. Gracias a mi hermano, Richi, por su cariño incondicional aunque sea en la distancia; hemos crecido y aprendido juntos y siempre estaremos unidos por ello. Y gracias a Mariano por su apoyo y su paciencia, por el tiempo de cálculo en su torre y las promociones locas, por creer en mí y compartir el camino conmigo; soy mejor física y mejor persona desde que te conozco. Por último, y no por ello menos importante, gracias igualmente al resto de mi familia; os llevo siempre conmigo y todos habéis contribuido a lo que soy. Esta tesis no habría sido posible sin todos vosotros. ¡Muchas gracias! xii Table of Contents Abstract ................................................................................................................... 1 Resumen .................................................................................................................. 5 1. Motivation and theoretical background ................................................................ 9 1.1 Molecular electronics ...................................................................................................... 9 1.2 Electrical transport: from macroscopic to nanoscopic systems .................................... 11 1.2.1 Landauer formula for coherent transport through a nanojunction ...................... 12 1.2.2 Quantum tunnelling .............................................................................................. 14 1.2.3 Scattering formalism – multichannel Landauer formula ...................................... 17 1.3 Thermoelectric effect: from macroscopic to nanoscopic systems ................................ 19 1.3.1 Macroscopic scale ................................................................................................. 19 1.3.2 Nanoscopic scale – Landauer formalism ............................................................... 22 1.4 Electrical conductance and thermopower of molecular junctions ............................... 25 1.4.1 Transmission function of molecular junctions -
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