Department of Condensed Matter Physics, Universidad Autónoma de Madrid (UAM), Spain.
«Visualizing superconductors through scanning tunneling microscopy«
This course provides an in-depth introduction to contemporary condensed matter physics through the lens of a powerful experimental technique: scanning tunneling microscopy and spectroscopy (STM/STS). By focusing on atomic-scale tunneling measurements, the lectures bridge fundamental concepts with forefront research topics, illustrating how electronic phenomena in complex materials can be directly visualized and quantitatively analyzed. Attention is given to superconductivity in its conventional and unconventional manifestations, low-dimensional electronic systems, and the interplay between electronic correlations, magnetism, and superconducting order.
The first part of the course introduces tunneling spectroscopy as a probe spanning macroscopic and atomic length scales. Beginning with the basic concept of electron tunneling, the lecture explains how the tunneling process grants access to the electronic density of states and highlights the essential differences between macroscopic junctions and atomic-scale tunneling contacts [1]. The discussion then turns to the experimental foundations of STM, including cryogenic positioning mechanisms, piezoelectric control, and measurement techniques that enable sub-angstrom spatial resolution and meV energy resolution [2]. Techniques bridging different length scales and the angle between the surface and the applied magnetic field will be discussed. The superconducting density of states is examined across different materials [1]. The lecture further introduces quasiparticle interference to extract information about band structure and scattering processes. Overall, we will try to establish a relationship between macroscopic physical properties and the local electronic density of states.
The second lecture addresses low-dimensional and surface-related phenomena, highlighting the surface both as a window into bulk properties and as a physical system with its own emergent behavior. Topics include the electronic structure of surfaces and its relationship to the bulk, with particular emphasis on two-dimensional superconductivity and reduced dimensionality effects. The lecture explores strongly correlated electron systems under STM, focusing on heavy fermion materials and introducing the concept of cotunneling in strongly interacting regimes. Charge density waves and superconducting pair density modulations are discussed as examples of spatially ordered electronic states revealed by real-space techniques. Lateral quantization, quantum corrals, and confined electronic states are presented as paradigms of quantum coherence at the nanoscale [3]. The lecture concludes with quantized states in magnetic semiconductors and semimetals, illustrating how magnetism, topology, and correlations can be probed at the atomic scale. The overarching goal is to develop a nuanced understanding of how surface-sensitive measurements reflect both bulk physics and genuinely low-dimensional phenomena.
The third lecture focuses on vortex physics and phase coherence in superconductors, connecting local spectroscopy to collective behavior. The electronic structure of Abrikosov vortex cores is examined through Andreev bound states, with an introduction to Majorana phenomenology in superconducting systems. Vortex lattices in both conventional and unconventional superconductors are discussed, including their symmetry, disorder, and field-driven melting transitions [1,4,5]. Dynamical aspects such as vortex motion and pinning are addressed, as well as the impact of disorder on superconducting properties [6]. The lecture further introduces the Josephson effect at the atomic scale, presenting scanning Josephson spectroscopy as a local probe of superconducting phase coherence [7]. Complementary spectroscopic techniques, including Andreev and phonon spectroscopies, are discussed to illustrate the richness of tunneling-based measurements. Through these examples, the lecture demonstrates how isolated vortex cores and vortex lattices act as sensitive probes of superconducting symmetries, interactions, and emergent phases.
Altogether, the course combines experimental methodology with conceptual insight, showing how scanning tunneling microscopy enables direct visualization of electronic phenomena in complex quantum materials. By integrating instrumentation, theory, and modern research examples, the lectures aim to provide students with a unified understanding of superconductivity and correlated electron systems from the atomic scale upward.
References
- Imaging superconducting vortex cores and lattices with a scanning tunneling microscope. H Suderow et al, Superconductor Science and Technololgy 27, 063001 (2014).
- Compact very low temperature scanning tunneling microscope with mechanically driven horizontal linear positioning stage. H. Suderow et al, Review of Scientific Instruments 82, 033711 (2011).
- Quantum-well states at the surface of a heavy-fermion superconductor. E. Herrera et al, Nature 616, 465 (2003).
- Direct observation of melting in a two-dimensional superconducting vortex lattice. I. Guillamón et al, Nature Physics 5, 651 (2009).
- Enhancement of long-range correlations in a 2D vortex lattice by an incommensurate 1D disorder potential, Nature Physics 10, 851 (2014).
- Gapless Superconductivity From Extremely Dilute Magnetic Disorder in 2H-NbSe2-xSx, J.A. Moreno, Advanced Materials, e19118 (2026).
- The feedback driven atomic scale Josephson microscope. S.D. Escribano et al, Nature Communications 16, 5843 (2025).