Broken unitarity and phase measurements in Aharonov-Bohm interferometers

Aharonov-Bohm mesoscopic solid-state interferometers yield a conductance which contains a term $\cos(\phi+\beta)$, where $\phi$ relates to the magnetic flux. Experiments with a quantum dot on one of the interfering paths aim to relate $\beta$ to the dot's intrinsic Friedel transmission phase, $\alpha_1$. For closed systems, which conserve the electron current (unitarity), the Onsager relation requires that $\beta=0$. For open systems, we show that $\beta$ depends in general on the details of the broken unitarity. Although it gives information on the resonances of the dot, $\beta$ is generally not equal to $\alpha_1$. A direct relation between $\beta$ and $\alpha_1$ requires specific ways of opening the system, which are discussed.Comment: 4 pages, 3 figures(eps). Phys. Rev. Letters (in press

Channel Interference in a Quasi Ballistic Aharonov-Bohm Experiment

New experiments are presented on the transmission of electron waves through a 2DEG (2 dimensional electron gas) ring with a gate on top of one of the branches. Magnetoconductance oscillations are observed, and the phase of the Aharanov-Bohm signal alternates between 0 and pi as the gate voltage is scanned. A Fourier transform of the data reveals a dominant period in the voltage which corresponds to the energy spacing between successive transverse modes.A theoretical model including random phase shifts between successive modes reproduces the essential features of the experiment.Comment: 4 pages, 6 Postscript figures, TEX, submitted to Physical Review Letter

An Electronic Mach-Zehnder Interferometer

Double-slit electron interferometers, fabricated in high mobility two-dimensional electron gas (2DEG), proved to be very powerful tools in studying coherent wave-like phenomena in mesoscopic systems. However, they suffer from small fringe visibility due to the many channels in each slit and poor sensitivity to small currents due to their open geometry. Moreover, the interferometers do not function in a high magnetic field, namely, in the quantum Hall effect (QHE) regime, since it destroys the symmetry between left and right slits. Here, we report on the fabrication and operation of a novel, single channel, two-path electron interferometer that functions in a high magnetic field. It is the first electronic analog of the well-known optical Mach-Zehnder (MZ) interferometer. Based on single edge state and closed geometry transport in the QHE regime the interferometer is highly sensitive and exhibits very high visibility (62%). However, the interference pattern decays precipitously with increasing electron temperature or energy. While we do not understand the reason for the dephasing we show, via shot noise measurement, that it is not a decoherence process that results from inelastic scattering events.Comment: to appear in Natur

Transmission Phase Shift of a Quantum Dot with Kondo Correlations

We study the effects of Kondo correlations on the transmission phase shift of a quantum dot in an Aharonov-Bohm ring. We predict in detail how the development of a Kondo resonance should affect the dependence of the phase shift on transport voltage, gate voltage and temperature. This system should allow the first direct observation of the well-known scattering phase shift of pi/2 expected (but not directly measurable in bulk systems) at zero temperature for an electron scattering off a spin-1/2 impurity that is screened into a singlet.Comment: 4 pages Revtex, 4 figures, final published versio

Interference and zero-bias anomaly in tunneling between Luttinger-liquid wires

We present theoretical calculations and experimental measurements which reveal the Luttinger-liquid (LL) nature of elementary excitations in a system consisting of two quantum wires connected by a long narrow tunnel junction at the edge of a GaAs/AlGaAs bilayer heterostructure. The boundaries of the wires are important and lead to a characteristic interference pattern in measurements on short junctions. We show that the experimentally observed modulation of the conductance oscillation amplitude as a function of the voltage bias can be accounted for by spin-charge separation of the elementary excitations in the interacting wires. Furthermore, boundaries affect the LL exponents of the voltage and temperature dependence of the tunneling conductance at low energies. We show that the measured temperature dependence of the conductance zero-bias dip as well as the voltage modulation of the conductance oscillation pattern can be used to extract the electron interaction parameters in the wires.Comment: 17 pages, 12 figure

Spin-charge separation and localization in one-dimension

We report on measurements of quantum many-body modes in ballistic wires and their dependence on Coulomb interactions, obtained from tunneling between two parallel wires in a GaAs/AlGaAs heterostructure while varying electron density. We observe two spin modes and one charge mode of the coupled wires, and map the dispersion velocities of the modes down to a critical density, at which spontaneous localization is observed. Theoretical calculations of the charge velocity agree well with the data, although they also predict an additional charge mode that is not observed. The measured spin velocity is found to be smaller than theoretically predicted.Comment: There are minor textual differences between this version and the version that has been published in Science (follow the DOI link below to obtain it). In addition, here we have had to reduce figure quality to save space on the serve

Observation of Quantum Asymmetry in an Aharonov-Bohm Ring

We have investigated the Aharonov-Bohm effect in a one-dimensional GaAs/GaAlAs ring at low magnetic fields. The oscillatory magnetoconductance of these systems are for the first time systematically studied as a function of density. We observe phase-shifts of $\pi$ in the magnetoconductance oscillations, and halving of the fundamental $h/e$ period, as the density is varied. Theoretically we find agreement with the experiment, by introducing an asymmetry between the two arms of the ring.Comment: 4 pages RevTex including 3 figures, submitted to Phys. Rev.

Experimental Evidence for Resonant-Tunneling in a Luttinger-Liquid

We have measured the low temperature conductance of a one-dimensional island embedded in a single mode quantum wire. The quantum wire is fabricated using the cleaved edge overgrowth technique and the tunneling is through a single state of the island. Our results show that while the resonance line shape fits the derivative of the Fermi function the intrinsic line width decreases in a power law fashion as the temperature is reduced. This behavior agrees quantitatively with Furusaki's model for resonant tunneling in a Luttinger-liquid.Comment: 3 pages, 5 figures, corrected typo

Many Body Effects on Electron Tunneling through Quantum Dots in an Aharonov-Bohm Circuit

Tunneling conductance of an Aharonov-Bohm circuit including two quantum dots is calculated based on the general expression of the conductance in the linear response regime of the bias voltage. The calculation is performed in a wide temperature range by using numerical renormalization group method. Various types of AB oscillations appear depending on the temperature and the potential depth of the dots. Especially, AB oscillations have strong higher harmonics components as a function of the magnetic flux when the potential of the dots is deep. This is related to the crossover of the spin state due to the Kondo effect on quantum dots. When the temperature rises up, the amplitude of the AB oscillations becomes smaller reflecting the breaking of the coherency.Comment: 21 pages, 11 PostScript figures, LaTeX, uses jpsj.sty epsbox.st