Solvable regime of disorder and interactions in ballistic nanostructures: Consequences for Coulomb blockade

摘要: We provide a framework for analyzing the problem of interacting electrons in ballistic quantum dot with chaotic boundary conditions within an energy E T (the Thouless energy) Fermi energy. Within this window we show that interactions can be characterized by Landau Fermi-liquid parameters. When g, number (also dimensionless conductance when it has strong coupling to leads) dot, is large, find disordered solved saddle-point approximation which becomes exact as g → ∞ (as large-N theory). The infinite theory two phases function parameter u m channel angular momentum m: A weak-coupling phase where constant charging and exchange dominate low-energy physics, previous "universal Hamiltonian" treatments, strong-coupling same order Pomeranchuk transition clean systems (a spontaneous interaction-induced Fermi-surface distortion), but smeared pinned disorder. Thus, both disorder are crucial existence these phases. At finite critical point evolve into three regimes -1/g plane-weak- separated crossover lines from quantum-critical regime controlled point. In this, first part series, focus on consequences picture Coulomb Blockade experiments. employ analytical numerical methods predict statistics single-particle levels, peak spacings, heights, quasiparticle widths. regions, acquires width level spacing few Δ's due collective excitations. if odd, will (if isolated) orthogonal unitary ensemble exponentially small external flux or strongly coupled break time-reversal symmetry spontaneously. For any m, peak-spacing distribution broader than expected works even support at negative values, turn correlated heights. Ballistic/chaotic dots afford us unrivalled theoretical experimental control over simultaneous 1/g expansion our ability vary interaction much more readily bulk.