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Microscopic theory of the Andreev gap
Tobias Micklitz1, Alexander Altland
1Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA.
Physical Review Letters
|October 2, 2009
Summary
We present a theory explaining the Andreev gap, where quantum fluctuations in chaotic cavities attached to superconductors eliminate low-energy states. This clarifies the hard gap phenomenon near the Fermi energy.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Mesoscopic physics
Background:
- The Andreev gap describes a phenomenon where the density of states (DOS) in normal chaotic cavities connected to superconductors exhibits a hard gap at the Fermi energy.
- Understanding this gap is crucial for applications in superconductivity and quantum electronics.
Purpose of the Study:
- To develop a microscopic theory for the Andreev gap phenomenon.
- To explain the role of quantum fluctuations in creating the hard gap.
- To compute the gap profile based on theoretical parameters.
Main Methods:
- Solving the quantum Eilenberger equation.
- Analyzing the regime where classical dwell time (tD) is much smaller than the Ehrenfest time (tE).
- Calculating the DOS and gap profile to leading order in the tD/tE parameter.
Main Results:
- Demonstrated that quantum fluctuations are responsible for eradicating the low-energy DOS.
- Derived the theoretical profile of the Andreev gap.
- Established a connection between the gap and the ratio of classical dwell time to Ehrenfest time.
Conclusions:
- The microscopic theory successfully explains the Andreev gap in normal chaotic cavities coupled to superconductors.
- Quantum fluctuations play a critical role in shaping the density of states near the Fermi energy.
- The findings provide a theoretical framework for understanding and potentially manipulating the Andreev gap.
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