Magnetic Field Symmetry and Phase Rigidity of the Nonlinear Conductance in a Ring

Leturcq, R.; Sánchez, David; Götz, G.; Ihn, Thomas; Ensslin, Klaus; Driscoll, D. C.; Gossard, A. C.

doi:10.1103/physrevlett.96.126801

Cited by 90 publications

(123 citation statements)

References 37 publications

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“…Also in this case AB oscillations are observed, but show a minimum at B = 0. We find either maxima or minima at B = 0, i.e., phase rigidity, for all investigated source-drain voltages (see below), in contrast to non Coulomb blockaded systems [11]. It is evident from the data that the participation of the inelastic cotunneling process does not hamper the occurrence of quantum interference.…”

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confidence: 66%

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Coherent Probing of Excited Quantum Dot States in an Interferometer

et al. 2007

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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 ...

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confidence: 66%

“…3(b) with changing V sd . The generalized Onsager symmetries imposed on the two-terminal measurement restrict the AB phase only at B = 0 and at low bias to be either zero or π [11]. The measurement shows that ϕ in our system is at B = 0 very close to 0 or π even in the nonlinear regime.…”

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confidence: 74%

Coherent Probing of Excited Quantum Dot States in an Interferometer

et al. 2007

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“…There has also been great interest in the nonlinear response of quantum ballistic constrictions, where the effects of quantum interference, spatial dispersion, and electron-electron interactions play crucial roles. [25][26][27][28][29][30][31][32][33][34][35][36][37] In this paper, we report a different type of nonlinearity of thermoelectric origin in a two-dimensional system of electrons. We have investigated the rectified ͑dc͒ voltage induced by microwave radiation applied locally to the boundary between two-dimensional electron systems with different electron densities n 1 and n 2 .…”

Section: Introductionmentioning

confidence: 79%

Scaling of thermoelectric voltage induced by microwave radiation at the boundary between two-dimensional electron systems

et al. 2008

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We report measurements of the rectification of microwave radiation ͑0.7-20 GHz͒ at the boundary between two-dimensional electron systems created by a narrow gap split gate on a silicon surface for different temperatures, electron densities, and microwave power. For frequencies above 4 GHz and different temperatures, the rectified voltage V dc as a function of microwave power P can be collapsed onto a single universal curve V dc * = f * ͑P * ͒ using two scaling parameters. The scaled voltage V dc * is a linear function of power P * for small power and proportional to ͑P * ͒ 1/2 at higher power. A theory is developed which attributes the observed voltage to the thermoelectric response associated with local heating by the microwave radiation of adjacent twodimensional electron systems with different densities n 1 and n 2 . Excellent quantitative agreement is obtained between theory and experiment.

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“…Spivak and Zuyzin [10] calculated this contribution for a mesoscopic diffusive system, whereas Andreev and Glazman [11] studied it for a semiclassical ballistic contact with an asymmetric obstacle. This contribution was observed in several experiments [12][13][14][15]. A qualitative relation between the magnetic field asymmetric current ∆I and the voltage derivative of the noise ∆S was established in a pioneering experiment for an Aharonov-Bohm interferometer [16].…”

Section: T [∂∆S/∂vmentioning

confidence: 90%

Magnetic-Field-Induced Non-Gaussian Fluctuations in Macroscopic Equilibrium Systems

et al. 2010

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We calculate the magnetic-field dependent nonlinear conductance and noise in a two-dimensional macroscopic inhomogeneous system. If the system does not possess a specific symmetry, the magnetic field induces a nonzero third cumulant of the current even at equilibrium. This cumulant is related to the first and second voltage derivatives of the spectral density and average current in the same way as for mesoscopic quantum-coherent systems, but these quantities may be much larger. The system provides a robust test of a non-equilibrium fluctuation relation. PACS numbers: 73.21.Hb, 73.50.Lw It is commonly believed that equilibrium fluctuations in macroscopic systems are Gaussian [1]. If their correlation length l c is much smaller than all the dimensions of the sample L, this is a direct consequence of the central limit theorem, which says that the sum of a large number of random variables will have approximately normal distribution. This is why higher cumulants of current are usually calculated and measured for mesoscopic systems, whose size is smaller than l c . Typically, l c is the inelastic scattering length and if L < l c , the conductor behaves as a single quantum scatterer. In a macroscopic system, higher cumulants are usually much smaller than the second one. However some fluctuations do not exponentially decay with distance and therefore do not have a definite correlation length. For example, fluctuations of charge density in two-dimensional conductors are screened according to a power law. If they are nonlinearly coupled to the current, this may result in a non-Gaussian noise even in an equilibrium macroscopic system. Below we propose a model of such noise. Moreover, the nonzero equilibrium third cumulant of current in it obeys the fluctuation relations recently derived for mesoscopic systems. Recent studies [5][6][7] showed that the fluctuation relations hold even in a magnetic field that breaks the microscopic reversibility. In particular, they link the contribution to the mean current proportional to magnetic field and quadratic in voltage ∆I ∝ V 2 H to a noise contribution proportional to the temperature, magnetic field, and voltage ∆S ∝ T HV , and to the third cumulant of equilibrium current fluctuations C 0 . Consequently, this cumulant is an odd function of the magnetic field. However the relations obtained in 3T [∂∆S/∂V − T ∂2 ∆I/∂V 2 ], whereas Saito and Utsumi [6] obtained a stronger condition C 0 = 2T ∂∆S/∂V = 6T 2 ∂ 2 ∆I/∂V 2 valid for a more restricted class of systems. The weaker condition permits magnetic field asymmetric conductance and noise even if the third cumulant of the equilibrium noise vanishes.The nonlinear contributions to the average current ∆I ∝ V 2 H were calculated for a number of mesoscopic systems. Sanchez and Polianski and one of the authors [8, 9] investigated a quantum Hall bar with an antidot and a chaotic cavity connected to quantum point contacts. Spivak and Zuyzin [10] calculated this contribution for a mesoscopic diffusive system, whereas Andreev and Glazman [11]...

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Magnetic Field Symmetry and Phase Rigidity of the Nonlinear Conductance in a Ring

Cited by 90 publications

References 37 publications

Coherent Probing of Excited Quantum Dot States in an Interferometer

Coherent Probing of Excited Quantum Dot States in an Interferometer

Scaling of thermoelectric voltage induced by microwave radiation at the boundary between two-dimensional electron systems

Magnetic-Field-Induced Non-Gaussian Fluctuations in Macroscopic Equilibrium Systems

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