Quantum Tunneling from Giaever Junctions to Scanning Tunneling Microscopy
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Keywords
quantum tunneling, scanning tunneling microscopy, Giaever junctions, Bardeen–Giaever current theory
Abstract
Quantum tunneling allows electrons to pass through a classically forbidden region. This effect can help us to research the electronic structure of materials. This paper examines how Giaever tunneling works and how to measure the energy gap and DOS. It then shows how these theories work in STM. This paper discusses the rectangular barrier model, the Bardeen–Giaever current theory, the Fermi occupation, and the superconducting DOS. It connects these theories to the Tersoff–Hamann STM model under particular assumptions. This paper derives how Giaever's tunneling current is determined by the DOS, the occupation window, and the tunneling matrix element. The transmission coefficient obeys T∝e^(-2κa) and STM extended the theory into local density of states (LDOS). Giaever spectroscopy measures an area-averaged superconducting DOS, whereas STM measures spatially resolved LDOS; each model is valid only under its stated assumptions.
References
- [1] C. J. Chen, Introduction to Scanning Tunneling Microscopy, 2nd ed. (Oxford University Press, Oxford, 2008).
- [2] I. Giaever, “Energy Gap in Superconductors Measured by Electron Tunneling,” Physical Review Letters 5, 147-148 (1960). https://doi.org/10.1103/PhysRevLett.5.147
- [3] I. Giaever, “Electron Tunneling Between Two Superconductors,” Physical Review Letters 5, 464-466 (1960). https://doi.org/10.1103/PhysRevLett.5.464
- [4] J. Bardeen, “Tunnelling from a Many-Particle Point of View,” Physical Review Letters 6, 57-59 (1961). https://doi.org/10.1103/PhysRevLett.6.57
- [5] W. A. Harrison, “Tunneling from an Independent-Particle Point of View,” Physical Review 123, 85-89 (1961). https://doi.org/10.1103/PhysRev.123.85
- [6] J. G. Simmons, “Generalized Formula for the Electric Tunnel Effect between Similar Electrodes Separated by a Thin Insulating Film,” Journal of Applied Physics 34, 1793-1803 (1963). https://doi.org/10.1063/1.1702682
- [7] Z. Ahmed, “Tunneling through a One-Dimensional Potential Barrier,” Physical Review A 47, 4761-4767 (1993). https://doi.org/10.1103/PhysRevA.47.4761
- [8] J. Tersoff and D. R. Hamann, “Theory of the Scanning Tunneling Microscope,” Physical Review B 31, 805-813 (1985). https://doi.org/10.1103/PhysRevB.31.805
- [9] M. S. J. Marshall and M. R. Castell, “Scanning Tunnelling Microscopy of Epitaxial Nanostructures,” Chemical Society Reviews 43, 2226-2239 (2014). https://doi.org/10.1039/c3cs60458f
- [10] C. Bracher, M. Riza, and M. Kleber, “Propagator Theory of Scanning Tunneling Microscopy,” Physical Review B 56, 7704-7715 (1997). https://doi.org/10.1103/PhysRevB.56.7704
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