Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

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Low-Temperature Conduction of a Quantum Dot 113 It is clear from (50) that the fluctuations of the conductance are of the order of the conductance itself, despite naive expectations that the large number of the contributing states results in self-averaging. The reason is that one has to add amplitudes, rather than probabilities, in order to compute the conductance. Because the fluctuations of the conductance are large, its distribution function is not Gaussian. Given the statistics (48) of the amplitudes, it is not quite surprising that the distribution of Gel normalized to its average coincides with Porter-Thomas distribution (23). This result was obtained first in [41] by a different (and more general) method. Finally, it is interesting to compare the elastic co-tunneling contribution to the conductance fluctuations with that of inelastic co-tunneling [41], δG2 in ∼ G2 δE in T with Gin given by (40). Even though the inelastic co-tunneling is the main conduction mechanism at T � Tel, see (47), elastic co-tunneling continues to dominate the fluctuations as long as T � Tel(EC/δE) 1/6 . 5 Kondo Regime in Transport through a Quantum Dot In the above discussion of the elastic co-tunneling we made a tacit assumption that all single-particle levels in the dot are either empty or doubly occupied. This, however, is not the case when the dot has a non-zero spin in the ground state. A dot with odd number of electrons, for example, would necessarily have a half-integer spin S. In the most important case of S =1/2 the top-most occupied single-particle level is filled by a single electron and is spin-degenerate. This opens a possibility of a co-tunneling process in which a transfer of an electron between the leads is accompanied by a flip of electron’s spin with simultaneous flip of the spin on the dot, see Fig. 3(c). The amplitude of such a process, calculated in the fourth order in tunneling matrix elements, diverges logarithmically when the energy ω of an incoming electron approaches 0. Since ω ∼ T , the logarithmic singularity in the transmission amplitude translates into a dramatic enhancement of the conductance G across the dot at low temperatures: G may reach values as high as the quantum limit 2e 2 /h [42, 43]. This conductance enhancement is not really a surprise. Indeed, in the spin-flip co-tunneling process a quantum dot with odd N behaves as S =1/2 magnetic impurity embedded into a tunneling barrier separating two massive conductors [44]. It is known [45] since mid-60’s that the presence of such impurities leads to zero-bias anomalies in tunneling conductance [46], which are adequately explained [47, 48] in the context of the Kondo effect [5].
114 M. Pustilnik and L.I. Glazman 5.1 Effective Low-Energy Hamiltonian At energies well below the threshold ∆ ∼ δE for intradot excitations the transitions within the (2S + 1)-fold degenerate ground state manifold of a dot can be conveniently described by a spin operator S. The form of the effective Hamiltonian describing the interaction of the dot with conduction electrons in the leads is then dictated by SU(2) symmetry 4 , Heff = � αks ξ k c † αks c αks � + Jαα ′(sα ′ α · S) (51) � with sαα ′ = kk ′ ss ′ c† αks (σss ′/2) cα ′ k ′ s ′. The sum over k in (51) is restricted to |ξk|
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Lecture Notes in Physics Editorial
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W. Dieter Heiss (Ed.) Quantum Dots:
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Preface Nanoscale physics, nowadays
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Contents A Guide for the Reader ...
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A Guide for the Reader Quantum dots
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The Renormalization Group Approach
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RG for Interacting Fermions 5 where
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where � is a shorthand: � ≡ 3
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RG for Interacting Fermions 9 These
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RG for Interacting Fermions 11 is i
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RG for Interacting Fermions 13 the
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RG for Interacting Fermions 15 this
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RG for Interacting Fermions 17 equa
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� p � dθp = g 2π RG for Inter
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RG for Interacting Fermions 21 the
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References RG for Interacting Fermi
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Semiconductor Few-Electron Quantum
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1.2 Implementations Semiconductor F
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GaAs n-AlGaAs AlGaAs GaAs Semicondu
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ε1 ε0 e Semiconductor Few-Electro
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250 Ω twisted pair 20 MΩ powder
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10 5 0 -5 Semiconductor Few-Electro
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G ( e / h) 2 2 1 0 Semiconductor Fe
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V R (V) V R (V) Semiconductor Few-E
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V L (V) -1.084 -1.082 -1.080 -1.078
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164 C.W.J. Beenakker As described i
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166 C.W.J. Beenakker 0.30 � Egap
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168 C.W.J. Beenakker The τE-depend
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Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

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