Coherent Probing of Excited Quantum Dot States in an Interferometer

Abstract

Measurements of elastic and inelastic cotunneling currents are presented on a two-terminal Aharonov-Bohm interferometer with a Coulomb blockaded quantum dot embedded in each arm. Coherent current contributions, even in magnetic field, are found in the nonlinear regime of inelastic cotunneling at finite bias voltage. The phase of the Aharonov-Bohm oscillations in the current exhibits phase jumps of π at the onsets of inelastic processes. We suggest that additional coherent elastic processes occur via the excited state. Our measurement technique allows the detection of such processes on a background of other inelastic current contributions and contains information about the excited state occupation probability and the inelastic relaxation rates.Quantum dots (QDs) in the Coulomb blockade regime show well understood conductance resonances at low bias voltage when the gate voltage is swept [1]. In interference experiments involving the Aharonov-Bohm (AB) effect a coherent current contribution was observed on such resonances [2]. At increased tunnel coupling, higher order cotunneling [3] leads to a finite conductance between these resonances. At low bias, elastic cotunneling occurs which is energy conserving. Elastic cotunneling has also been shown to have a coherent contribution [4]. At finite bias voltages, inelastic cotunneling is observed [5] in which the tunneling process excites the QD. Inelastic cotunneling was used for studying Zeeman-splitting [6] and the singlet-triplet gap [7].If the QD is embedded in an AB interferometer, inelastic processes are not expected to contribute to interference, because the resulting excited dot state allows which-path detection. Here we present the observation of coherent contributions to the current at and beyond the onset of inelastic cotunneling. We show that the corresponding AB oscillations exhibit a phase change of π at the bias voltage of the inelastic onset in most cases. An explanation of this finding requires the contribution of additional coherent elastic cotunneling processes through the involved excited state. The experiments therefore demonstrate the possibility of probing excited states and elastic cotunneling processes through them via the coherent current contribution in the nonlinear bias regime.The sample shown in Fig. 1(a) is based on a Ga[Al]As heterostructure with a two-dimensional electron gas (2DEG) 34 nm below the surface. It was fabricated by multiple-layer local oxidation with a scanning force microscope [8]: The 2DEG is depleted below the oxide lines written on the GaAs surface [bright lines in Fig. 1(a)] thus defining the ring-interferometer. A Ti film evaporated on top is cut by local oxidation [faint lines in Fig. 1(a)] into mutually isolated top gates.A QD is embedded in each arm of the resulting ABinterferometer as indicated by the dots in Fig. 1(a). Direct tunneling between the two dots is suppressed by applying a negative voltage between the 2DEG and the metallic top gate, in contrast to previous experiments [4]. In-plane gates pg1 and pg2 are ...

Green Function Techniques in the Treatment of Quantum Transport at the Molecular Scale

“…The traditional semiconductor nanoelectronics also remains in front of modern research, in particular due to recent experiments with small quantum dots, where cotunneling effects were observed [45,46,47], as well as new rectification effects in double quantum dots, interpreted as spin blockade [48,49,50,51]. Note, that semiconductor experiments are very well controlled at present time, so they play an important role as a benchmark for the theory.…”

The probe technique far from equilibrium: Magnetic field symmetries of nonlinear transport

“…In spatially symmetric systems odd conductance terms acquire even symmetry with respect to the magnetic field, as noted experimentally 33,35 , while even conductance terms, constructing R, are odd with respect to φ. The relation ∆I(φ) = R(φ) could be exploited in experimental studies: One could determine whether a quantum dot junction is L-R symmetric by testing this equality.…”

“…In AharonovBohm interferometers with conserved electron current this symmetry is displayed by the "phase rigidity" of the (linear) conductance oscillations with the magnetic field B, G 1 (B) = G 1 (−B) 27,28 . Beyond linear response, the phase symmetry of the conductance is not enforced, and several experiments 29,30,[32][33][34][35][36][37] have demonstrated its breakdown. Supporting theoretical works have elucidated the role of many-body interactions in the system [38][39][40][41][42] , typically approaching the problem by calculating the screening potential within the conductor in a self-consistent manner, a procedure often limited to low-order conduction terms 38,40,41 .…”

Sagnac interference in carbon nanotubes

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