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Published on: December 20, 2016
S-matrix formulation of mesoscopic systems and evanescent modes
Sheelan Sengupta Chowdhury1, P Singha Deo, A M Jayannavar
1Unit for Nanoscience and Technology, S N Bose National Centre for Basic Sciences, Salt Lake, Kolkata, India.
Summary
The Landauer-Buttiker formalism accurately describes linear transport in mesoscopic systems. Its extension to study persistent currents is valid for quasi-one-dimensional systems, though evanescent modes require reinterpretation.
Area of Science:
- Condensed matter physics
- Mesoscopic systems
- Quantum transport
Background:
- The Landauer-Buttiker formalism is a cornerstone for understanding linear transport in mesoscopic systems.
- Akkermans et al. extended this formalism to investigate thermodynamic properties like persistent currents.
- Previous verification of this extension was limited to simple one-dimensional systems.
Purpose of the Study:
- To assess the applicability of Akkermans et al.'s extended formalism to quasi-one-dimensional systems.
- To investigate the behavior of the formalism in systems with multiple conducting channels.
- To determine the conditions under which the extended formalism remains valid.
Main Methods:
- Theoretical analysis of the Landauer-Buttiker formalism.
- Extension of the formalism to quasi-one-dimensional systems with multiple channels.
- Examination of systems with both propagating and evanescent modes.
Main Results:
- The extended Landauer-Buttiker formalism remains valid for quasi-one-dimensional systems where all conducting modes are propagating.
- In systems with evanescent modes, the Akkermans et al. formula necessitates reinterpretation.
- The study confirms the formalism's utility but highlights limitations in specific scenarios.
Conclusions:
- The applicability of the extended Landauer-Buttiker formalism is confirmed for quasi-one-dimensional systems with propagating modes.
- Evanescent modes in multi-channel systems require a modified interpretation of the formalism.
- This research refines the understanding of thermodynamic transport in complex mesoscopic systems.
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