Observing the Transition from classical to Landauer resistivity dipoles
An electric current consists of electrons flowing through a conductor. Along the way, the electrons may encounter material defects, such as tiny holes, which force the electrons to move around the defects and increase the conductor's electrical resistance. Researchers at Forschungszentrum Jülich now revealed how the resistance resulting from such defects changes systematically as the defects become smaller. To do so, they used a scanning tunneling microscope to examine individual holes in an extremely thin layer of bismuth.
Around larger holes, electrons collide multiple times while moving around them. This is similar to people pushing past each other while walking around a barrier in a crowd. In this scenario, called “diffusive” transport, the smaller the hole is, the smaller its resistance will be. However, something different happens around holes that are very small, only a few nanometers wide. Most electrons can travel past them without colliding. However, electrons that hit the barrier head-on are reflected and bounce back. In this "ballistic" scenario, resistance does not decrease as the hole size decreases further. Instead, it reaches a finite minimum value called Landauer resistivity, named after physicist Rolf Landauer, who predicted this effect more than 60 years ago.
The researchers have now systematically revealed the transition between the two scenarios, finding that it takes place at hole sizes of about five nanometers. Using Landauer’s theory, the researchers were able to estimate the Fermi wave vector, which provides information about the momentum of conduction electrons that is usually difficult to access. Overall, this study is the first to examine how electron flow changes systematically from diffusive to ballistic movement around very small material defects. Understanding this behavior is important for designing future electronic devices that are only a few nanometers in size.
S. Kovalchuk, D. Kämpfer, J. K. Hofmann, T. Balashov, V. Cherepanov, B. Voigtländer, I. Morawski, F. S. Tautz, and F. Lüpke "Imaging the transition from diffusive to Landauer resistivity dipoles" Phys. Rev. B 114, 165411 (2026)
Contact
Dr. Felix Lüpke
Group leader at Peter Grünberg Institute (PGI-3)