Semiclassical transport in nearly symmetric quantum dots I: symmetry-breaking in the dot

Abstract

We apply the semiclassical theory of transport to quantum dots with exact and approximate spatial symmetries; left-right mirror symmetry, up-down mirror symmetry, inversion symmetry or four-fold symmetry. In this work - the first of a pair of articles - we consider (a) perfectly symmetric dots and (b) nearly symmetric dots in which the symmetry is broken by the dot's internal dynamics. The second article addresses symmetry-breaking by displacement of the leads. Using semiclassics, we identify the origin of the symmetry-induced interference effects that contribute to weak-localization corrections and universal conductance fluctuations. For perfect spatial symmetry, we recover results previously found using the random-matrix theory conjecture. We then go on to show how the results are affected by asymmetries in the dot, magnetic fields and decoherence. In particular, the symmetry-asymmetry crossover is found to be described by a universal dependence on an asymmetry parameter ${\gamma }_{asym}$. However, the form of this parameter is very different depending on how the dot is deformed away from spatial symmetry. Symmetry-induced interference effects are completely destroyed when the dot's boundary is globally deformed by less than an electron wavelength. In contrast, these effects are only reduced by a finite amount when a part of the dot's boundary smaller than a lead-width is deformed an arbitrarily large distance.

(18pages - 9figs) This is the first of a pair of articles (v3 minor improvements to text)

References in corpus (18)

• Semiclassical Foundation of Universality in Quantum Chaos
• Periodic-Orbit Theory of Universality in Quantum Chaos
• Periodic-Orbit Theory of Level Correlations
• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Semiclassical Theory of Chaotic Conductors
• Semiclassical Approach to Chaotic Quantum Transport
• Induced Violation of Time-Reversal Invariance in the Regime of Weakly Overlapping Resonances
• Quantum-to-classical correspondence in open chaotic systems
• Dynamical model for the quantum-to-classical crossover of shot noise
• Quantum Andreev map: A paradigm of quantum chaos in superconductivity
• Suppression of weak-localization (and enhancement of noise) by tunnelling in semiclassical chaotic transport
• Symmetry causes a huge conductance peak in double quantum dots
• Dephasing in quantum chaotic transport: a semiclassical approach
• Interplay of Ehrenfest time and dephasing time in ballistic conductors
• Semiclassical transport in nearly symmetric quantum dots II: symmetry-breaking due to asymmetric leads
• Staggered repulsion of transmission eigenvalues in symmetric open mesoscopic systems
• Dephasing in the semiclassical limit is system-dependent
• Universal parametric correlations in the classical limit of quantum transport

Cited by in corpus (9)

• Quantum noise and self-sustained radiation of PT-symmetric systems
• Semiclassical approach to discrete symmetries in quantum chaos
• Semiclassical transport in nearly symmetric quantum dots II: symmetry-breaking due to asymmetric leads
• Effect of potential fluctuations on shot noise suppression in mesoscopic cavities
• Classical origin of conductance oscillations in an integrable cavity
• Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry
• Experimental evidence of enhanced broadband transmission in disordered systems with mirror symmetry
• Disappearance of Quantum Chaos in Coupled Chaotic Quantum Dots
• Correlations between spectra with different symmetry: any chance to be observed?