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| Landauer–Büttiker | |
|---|---|
| Name | Landauer–Büttiker |
| Field | Condensed matter physics; Mesoscopic physics; Quantum transport |
| Introduced | 1957; 1986 |
| Related | Quantum Hall effect; Scattering theory; Anderson localization |
Landauer–Büttiker The Landauer–Büttiker framework unifies scattering-based approaches to electronic transport in mesoscopic conductors, connecting transmission probabilities to conductance through quantum scattering matrices. It builds on work by Rolf Landauer and advances by Markus Büttiker, integrating concepts from Claude Shannon-style information considerations, Maxwell's demon thought experiments, and experimental findings from Giulio F. Giuliani-era studies, influencing research at institutions such as IBM and Bell Labs.
The approach originates with Rolf Landauer's 1957 proposal linking conductance to transmission and was extended by Markus Büttiker in the 1980s to multi-terminal systems, drawing on formal scattering theory developed by John von Neumann, Lev Landau, and later formalizers like Hendrik Casimir. It sits alongside paradigms from Philip W. Anderson's localization theory and complements formulations by Niels Bohr-inspired quantum measurement discussions, impacting experiments at CERN-affiliated labs and university groups at Massachusetts Institute of Technology, University of Cambridge, and ETH Zurich.
The Landauer formula expresses two-terminal conductance via transmission eigenvalues derived from a scattering matrix, a construct rooted in work by Werner Heisenberg and refined using boundary-condition methods from Paul Dirac. It relates zero-temperature conductance to transmission probabilities between leads, echoing concepts used in Richard Feynman's path integral treatments and employing mathematical tools from Eugene Wigner's time-delay analyses and Hermann Weyl spectral theory. The formula influenced experimental designs at IBM Research, techniques used in NIST measurements, and theoretical treatments by groups associated with Stanford University and Tokyo University.
Büttiker generalized Landauer to multi-terminal conductors, introducing current–voltage relations reliant on transmission coefficients among reservoirs, adopting concepts from Ludwig Boltzmann's transport equations and operational ideas from John Bardeen. His formalism uses scattering matrices related to works by Michael Berry and symmetry classifications from Frederick J. Dyson, tying into studies of time-reversal symmetry by Eugene Wigner and experimental probes by teams at Bell Labs and IBM Zurich Research Laboratory.
Quantum conductance quantization in units of e^2/h emerges naturally from Landauer–Büttiker analysis, as seen in B. J. van Wees and D. A. Wharam experiments on quantum point contacts, connecting to the integer Quantum Hall effect discovered by Klaus von Klitzing and topological considerations by Thouless, David J.'s work. Mesoscopic phenomena such as universal conductance fluctuations and weak localization reference theories by Philip W. Anderson and G. Bergmann, and experimental validation occurred in setups at University of California, Berkeley and Weizmann Institute of Science.
Applications include interpretation of conductance in semiconductor heterostructures, single-molecule junctions investigated by groups at California Institute of Technology and University of Oxford, and carbon-based systems like graphene studied at University of Manchester and Columbia University. Experimental tests span shot-noise measurements by teams influenced by Yuli V. Nazarov and spin-dependent transport probed in collaborations associated with IBM and Hitachi, linking to devices developed at Hewlett-Packard Laboratories and spintronics research at Tohoku University.
Extensions incorporate interactions via non-equilibrium Green's functions developed by Leonard Kadanoff and Gabriel Baym, Floquet theory for time-periodic driving related to work by Shirley Jon and topological transport invoking F. D. M. Haldane. Generalizations address superconducting hybrids building on Brian D. Josephson's insights, thermoelectric transport connecting to Ilya Prigogine-inspired irreversible thermodynamics, and noise-related quantities using approaches from Claude Shannon and Harry Nyquist.
Derivations employ scattering matrix theory formalized by Eugene Wigner and Herman Feshbach, transfer-matrix methods used by P. W. Anderson, and random-matrix theory from Eugene Wigner and Freeman Dyson for statistical ensembles. Model systems include one-dimensional tight-binding chains (related to Felix Bloch's band theory), quantum dots treated via Giaever, Ivar-like tunneling paradigms, and microscopic derivations using Keldysh non-equilibrium Green's functions by Leonid Keldysh and diagrammatic techniques championed by Miguel A. Cazalilla's contemporaries.
Category:Quantum transport