Temperature dependence of Fano line shapes in a weakly coupled single-electron transistor

Abstract

We report the temperature dependence of the zero-bias conductance of a single-electron transistor in the regime of weak coupling between the quantum dot and the leads. The Fano line shape, convoluted with thermal broadening, provides a good fit to the observed asymmetric Coulomb charging peaks. However, the width of the peaks increases more rapidly than expected from the thermal broadening of the Fermi distribution in a temperature range for which Fano interference is unaffected. The intrinsic width of the resonance extracted from the fits increases approximately quadratically with temperature. Above about 600 mK the asymmetry of the peaks decreases, suggesting that phase coherence necessary for Fano interference is reduced.PACS 73.23. Hk, 72.15.Qm, A single-electron transistor (SET) consists of a small, isolated conductor, coupled to metallic leads by tunnel junctions. The confinement quantizes the charge and energy of the isolated region, making it closely analogous to an atom 1,2 . For such structures the conductance, resulting from transmission of electrons from one lead to the other, consists of peaks as a function of gate voltage, one for each electron added to the artificial atom. The peaks occur when two charge states of the artificial atom are degenerate in energy, at which point resonant tunneling can occur at zero temperature. Between the peaks the conductance at low temperature is expected to be limited by virtual excitations of electrons on and off the artificial atom, a non-resonant process called co-tunneling 16 . Göres et al.3 have recently reported Fano line shapes in the conductance peaks for a small SET. This implies that there are two paths through the SET at each energy, one resonant and the other non-resonant, that interfere with each other. Göres et al. have examined the Fano interference for the case when the coupling to the leads is strong, and the non-resonant contribution to the conductance is then comparable in size to the resonant component. We here report the observation of Fano line shapes when the coupling is weak and the non-resonant conductance is small. We find that the Fano functional form, broadened by the Fermi-Dirac distribution function, provides a good fit to the line shape between 100 and 800 mK. With increasing temperature T the intrinsic width of the resonance increases, approximately quadratically with T . This increase is reminiscent of that expected from inelastic scattering, but it is more rapid and occurs at temperatures for which Fano interference is apparently unaffected. Above ∼ 600 mK the asymmetry of the peaks decreases more rapidly than predicted from thermal broadening alone, suggesting that phase coherence is destroyed with increasing T.The SETs we have studied are similar to the ones used by Goldhaber-Gordon et al . to study the Kondo effect 4,5 . The SET is created by imposing an external potential on a two-dimensional electron gas (2DEG) at the interface of a GaAs/AlAs heterostructure. Our 2DEG has a mobility of 91, 000 cm 2 /Vs and a density of 7.3 × 1...

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