Transport moments and Andreev billiards with tunnel barriers
arXiv:1210.7948 · doi:10.1088/1751-8113/46/5/055101
Abstract
Open chaotic systems are expected to possess universal transport statistics and recently there have been many advances in understanding and obtaining expressions for their transport moments. However when tunnel barriers are added, which represents the situation in more general experimental physical systems much less is known about the behaviour of the moments. By incorporating tunnel barriers in the recursive semiclassical diagrammatic approach we obtain the moment generating function of the transmission eigenvalues at leading and subleading order. For reflection quantities quantum mechanical tunneling phases play an essential role and we introduce new structures to deal with them. This allows us to obtain the moment generating function of the reflection eigenvalues and the Wigner delay times at leading order. Our semiclassical results are in complementary regimes to the leading order results derived from random matrix theory expanding the range of theoretically known moments. As a further application we derive to leading order the density of states of Andreev billiards coupled to a superconductor through tunnel barriers.
Final refereed version. 25 pages, 7 figures. Corrected a reference
References in corpus (19)
- Semiclassical Foundation of Universality in Quantum Chaos
- Periodic-Orbit Theory of Universality in Quantum Chaos
- Periodic-Orbit Theory of Level Correlations
- Semiclassical Theory of Chaotic Conductors
- Semiclassical Approach to Chaotic Quantum Transport
- Systematic approach to statistics of conductance and shot-noise in chaotic cavities
- Nonlinear statistics of quantum transport in chaotic cavities
- Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry
- Andreev billiards
- Suppression of weak-localization (and enhancement of noise) by tunnelling in semiclassical chaotic transport
- Moments of the transmission eigenvalues, proper delay times and random matrix theory II
- Integrable theory of quantum transport in chaotic cavities
- Full counting statistics of chaotic cavities from classical action correlations
- Universality in chaotic quantum transport: The concordance between random matrix and semiclassical theories
- Towards a semiclassical justification of the `effective random matrix theory' for transport through ballistic chaotic quantum dots
- Statistics of reflection eigenvalues in chaotic cavities with non-ideal leads
- Statistics of thermal to shot noise crossover in chaotic cavities
- Conductance fluctuations in chaotic systems with tunnel barriers
- Semiclassical approach to universality in quantum chaotic transport
Cited by in corpus (12)
- Semiclassical roots of universality in many-body quantum chaos
- Efficient semiclassical approach for time delays
- Combinatorial theory of the semiclassical evaluation of transport moments I: Equivalence with the random matrix approach
- Anti-correlation for Conductance Fluctuations in Chaotic Quantum Dots
- Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions
- Multifractal Magnetoconductance Fluctuations in Mesoscopic Systems
- Semiclassical treatment of quantum chaotic transport with a tunnel barrier
- Time delay statistics for finite number of channels in all symmetry classes
- Semiclassical approach to matrix energy correlations and time delay in chaotic systems
- Exponentially small quantum correction to conductance
- Quantum transport in chaotic cavities with tunnel barriers
- Electronic transport in three-terminal chaotic systems with a tunnel barrier