Scanning probe microscopy techniques like STM and AFM let us peek into the tiny world of superconductors. These tools give us a close-up view of how electrons behave and how the material's surface looks at the atomic level.

Magnetic imaging takes things a step further by showing us how magnetic fields move through superconductors. This helps us understand vortex dynamics and pinning, which are key to how superconductors work in real-world applications.

Scanning Tunneling Microscopy for Superconductors

Principles and Operation of STM

• Scanning tunneling microscopy (STM) is a powerful technique for studying the local electronic structure and topography of superconductors at the atomic scale
• STM operates by bringing an atomically sharp conducting tip close to the sample surface and applying a bias voltage between the tip and the sample
• The tunneling current between the tip and the sample is exponentially sensitive to the tip-sample distance, allowing for high-resolution imaging of the surface topography
• STM can probe the local density of states (LDOS) of superconductors by measuring the differential conductance (dI/dV) as a function of the applied bias voltage
  • The dI/dV spectra provide information about the superconducting energy gap, quasiparticle excitations, and other electronic features

Applications of STM in Studying Superconductors

• STM can detect spatial variations in the superconducting properties, such as the presence of impurities, defects, or inhomogeneities in the superconducting order parameter
• Applications of STM in studying superconductors include:
  • Mapping the superconducting energy gap and its spatial distribution (NbSe2, Bi2Sr2CaCu2O8+δ)
  • Investigating the effect of impurities and defects on the local superconducting properties (Fe-based superconductors, MgB2)
  • Studying the interplay between superconductivity and other electronic phenomena, such as charge density waves or magnetic ordering (NbSe2, CeCoIn5)
• STM can also be combined with other techniques, such as scanning tunneling spectroscopy (STS) or quasiparticle interference (QPI) imaging, to gain deeper insights into the electronic structure and pairing mechanism of superconductors

STM Imaging of Superconducting Properties

Interpretation of STM Topographic Images

• STM images provide a direct visualization of the surface topography and the local electronic structure of superconductors
• In constant-current mode, the STM tip maintains a constant tunneling current while scanning across the sample surface, resulting in a topographic image that reflects the surface morphology
• The topographic images can reveal surface features such as atomic lattice, steps, defects, or adsorbates that may influence the superconducting properties (Nb, NbN thin films)
• Spatial variations in the surface morphology can be correlated with changes in the local superconducting properties, such as the critical temperature or the energy gap

Analysis of STM Spectroscopic Data

• In spectroscopic mode, the STM tip is held at a fixed position, and the differential conductance (dI/dV) is measured as a function of the applied bias voltage, providing information about the local density of states (LDOS)
• The superconducting energy gap appears as a suppression of the differential conductance near zero bias voltage in the dI/dV spectra
  • The width of the gap corresponds to twice the superconducting order parameter (2Δ)
  • Spatial variations in the gap size can indicate inhomogeneities in the superconducting properties (Bi2Sr2CaCu2O8+δ, FeSe)
• Quasiparticle excitations, such as Andreev bound states or Caroli-de Gennes-Matricon states, can be observed as sharp peaks or oscillations in the dI/dV spectra within the superconducting gap (Pb, Nb)
• Impurities or defects in the superconductor can appear as local variations in the STM topography or as distinct features in the dI/dV spectra, such as bound states or resonances (Fe-based superconductors, CuxBi2Se3)

Atomic Force Microscopy of Superconductors

Principles and Operation of AFM

• Atomic force microscopy (AFM) is a scanning probe technique that measures the force interactions between a sharp tip and the sample surface to obtain high-resolution topographic images and mechanical properties
• AFM operates by scanning a cantilever with a sharp tip over the sample surface and measuring the deflection of the cantilever due to the tip-sample forces
  • The deflection is typically detected using a laser beam reflected from the back of the cantilever onto a position-sensitive photodetector
• AFM can be operated in various modes, including contact mode, non-contact mode, and tapping mode, depending on the nature of the tip-sample interactions and the desired information

Applications of AFM in Characterizing Superconductors

• In the context of superconductors, AFM can be used to study the surface morphology, roughness, and mechanical properties of superconducting films or crystals
• AFM can detect surface features such as grain boundaries, steps, or domains that may influence the superconducting properties (YBCO thin films, MgB2)
• By combining AFM with other techniques, such as scanning tunneling spectroscopy (STS) or magnetic force microscopy (MFM), it is possible to correlate the surface morphology with the local electronic or magnetic properties of superconductors
• Applications of AFM in characterizing superconductors include:
  • Investigating the growth mechanism and surface quality of superconducting thin films (NbN, FeSe)
  • Studying the effect of surface roughness or defects on the superconducting properties (YBCO, Nb)
  • Probing the mechanical properties, such as elasticity or adhesion, of superconducting materials (Nb3Sn, BSCCO)

Magnetic Imaging of Vortex Dynamics

Magnetic Imaging Techniques for Superconductors

• Magnetic imaging techniques, such as magnetic force microscopy (MFM) or scanning SQUID microscopy (SSM), provide valuable insights into the magnetic properties and vortex dynamics in superconductors
• MFM measures the magnetic force gradient between a magnetized tip and the sample surface, allowing for the visualization of the local magnetic field distribution
  • In superconductors, MFM can image the magnetic field penetration at the sample edges, domain walls, or vortices (Nb, YBCO)
  • The magnetic contrast in MFM images depends on the strength and orientation of the local magnetic fields
• SSM uses a superconducting quantum interference device (SQUID) as a sensitive magnetic field sensor to map the local magnetic field distribution with high spatial resolution
  • SSM can detect the presence of individual magnetic vortices and their arrangement in superconductors (NbSe2, Bi2Sr2CaCu2O8+δ)
  • The vortex configuration can provide information about the pinning landscape, critical current density, and vortex dynamics

Analysis of Magnetic Imaging Data

• Analyzing the magnetic imaging data requires understanding the relationship between the superconducting properties and the observed magnetic field distribution
  • The vortex density and arrangement can be related to the applied magnetic field, temperature, and pinning strength in the superconductor
  • The motion of vortices under the influence of current or temperature gradients can be studied by time-resolved magnetic imaging
• Magnetic imaging can be used to investigate various phenomena in superconductors, such as:
  • Vortex lattice melting and phase transitions (Bi2Sr2CaCu2O8+δ, MgB2)
  • Vortex pinning and depinning mechanisms (YBCO, FeSe)
  • Current-induced vortex dynamics and flux flow (Nb, NbSe2)
  • Interaction between vortices and structural defects or inhomogeneities (Fe-based superconductors, CuxBi2Se3)
• Quantitative analysis of the magnetic imaging data, such as vortex counting, spatial correlation functions, or flux profile fitting, can provide valuable information about the superconducting properties and vortex behavior