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In the quantum anomalous Hall effect, quantized Hall resistance and vanishing longitudinal resistivity are predicted to result from the presence of dissipationless, chiral edge states and an insulating 2D bulk, without requiring an external magnetic field. Here, we explore the potential of this effect in magnetic topological insulator thin films for metrological applications. Using a cryogenic current comparator system, we measure quantization of the Hall resistance to within one part per million and longitudinal resistivity under 10 m$\Omega$ per square at zero magnetic field. Increasing the current density past a critical value leads to a breakdown of the quantized, low-dissipation state, which we attribute to electron heating in bulk current flow. We further investigate the pre-breakdown regime by measuring transport dependence on temperature, current, and geometry, and find evidence for bulk dissipation, including thermal activation and possible variable-range hopping., Comment: 9 pages, 4 figures, with 7 pages of supplementary information

The recent prediction, and subsequent discovery, of the quantum anomalous Hall (QAH) effect in thin films of the three-dimensional ferromagnetic topological insulator (MTI) (Cr$_y$Bi$_x$Sb$_{1-x-y}$)$_2$Te$_3$ has opened new possibilities for chiral-edge-state-based devices in zero external magnetic field. Like the $\nu=1$ quantum Hall system, the QAH system is predicted to have a single chiral edge mode circulating along the boundary of the film. Backscattering of the chiral edge mode should be suppressed, as recently verified by the observation of well-quantized Hall resistivities $\rho_{yx} = \pm h/e^2$, along with longitudinal resistivities as low as a few ohms. Dissipationless 1D conduction is also expected along magnetic domain walls. Here, we intentionally create a magnetic domain wall in a MTI and study electrical transport along the domain wall. We present the first observation of chiral transport along domain walls, in agreement with theoretical predictions. We present further evidence that two modes equilibrate and co-propagate along the length of the domain wall., Comment: 5 pages, 3 figures, with 8 pages of supplementary information

Incorporating ferromagnetic dopants, such as chromium or vanadium, into thin films of the three-dimensional (3D) topological insulator (TI) (Bi,Sb)2Te3 has recently led to the realisation of the quantum anomalous Hall effect (QAHE), a unique phase of quantum matter. These materials are of great interest, since they may support electrical currents that flow without resistance via edge channels, even at zero magnetic field. To date, the QAHE has been investigated using low-frequency transport measurements. However, transport requires contacting the sample and results can be difficult to interpret due to the presence of parallel conductive paths, via either the bulk or surface, or because additional non-chiral edge channels may exist. Here, we move beyond transport measurements by probing the microwave response of a magnetised disk of Cr-(Bi,Sb)2Te3. We identify features associated with chiral edge magnetoplasmons (EMPs), a signature that robust edge-channels are indeed intrinsic to this material system. Our results provide a measure of the velocity of edge excitations without contacting the sample, and pave the way for a new, on-chip circuit element of practical importance: the TI, zero-field microwave circulator.

We study the electronic transport across an electrostatically-gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without applied magnetic field. We control carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the 2D gap, magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus which reflect the equilibration between 1D chiral modes across the junction. As carrier density approaches zero in the central region and at moderate fields, we observe oscillations in resistance that we attribute to Fabry-Perot interference in the helical states, enabled by the broken time reversal symmetry. At higher fields, those oscillations disappear, in agreement with the expected absence of helical states when band inversion is lifted., Comment: 5 pages, 4 figures, supp. mat

In Coulomb drag, a current flowing in one conductor can induce a voltage across an adjacent conductor via the Coulomb interaction. The mechanisms yielding drag effects are not always understood, even though drag effects are sufficiently general to be seen in many low-dimensional systems. In this Letter, we observe Coulomb drag in a Coulomb-coupled double quantum dot (CC-DQD) and, through both experimental and theoretical arguments, identify cotunneling as essential to obtaining a correct qualitative understanding of the drag behavior., Comment: Main text: 5 pages, 5 figures; SM: 11 pages, 5 figures, 1 table

We report measurements of the polar Kerr effect, proportional to the out-of-plane component of the magnetization, in thin films of the magnetically doped topological insulator $(\text{Cr}_{0.12}\text{Bi}_{0.26}\text{Sb}_{0.62})_2\text{Te}_3$. Measurements of the complex Kerr angle, $\Theta_K$, were performed as a function of photon energy in the range $0.8\text{ eV}<\hbar\omega<3.0\text{ eV}$. We observed a peak in the real part of $\Theta_K(\omega)$ and zero crossing in the imaginary part that we attribute to resonant interaction with a spin-orbit avoided crossing located $\approx$ 1.6 eV above the Fermi energy. The resonant enhancement allows measurement of the temperature and magnetic field dependence of $\Theta_K$ in the ultrathin film limit, $d\geq2$ quintuple layers. We find a sharp transition to zero remanent magnetization at 6 K for $d<8$~QL, consistent with theories of the dependence of impurity spin interactions on film thickness and their location relative to topological insulator surfaces., Comment: 6 pages, 5 figures

Quantum critical systems derive their finite temperature properties from the influence of a zero temperature quantum phase transition. The paradigm is essential for understanding unconventional high-Tc superconductors and the non-Fermi liquid properties of heavy fermion compounds. However, the microscopic origins of quantum phase transitions in complex materials are often debated. Here we demonstrate experimentally, with support from numerical renormalization group calculations, a universal crossover from quantum critical non-Fermi liquid behavior to distinct Fermi liquid ground states in a highly controllable quantum dot device. Our device realizes the non-Fermi liquid two-channel Kondo state, based on a spin-1/2 impurity exchange-coupled equally to two independent electronic reservoirs. Arbitrarily small detuning of the exchange couplings results in conventional screening of the spin by the more strongly coupled channel for energies below a Fermi liquid scale T*. We extract a quadratic dependence of T* on gate voltage close to criticality and validate an asymptotically exact description of the universal crossover between strongly correlated non-Fermi liquid and Fermi liquid states., Comment: Text and supplementary information. Text: 14 pages, 3 figures. Supplementary information: 11 pages, 6 figures

We report a nearly ideal quantum anomalous Hall effect in a three-dimensional topological insulator thin film with ferromagnetic doping. Near zero applied magnetic field we measure exact quantization in Hall resistance to within a part per 10,000 and longitudinal resistivity under 1 ohm per square, with chiral edge transport explicitly confirmed by non-local measurements. Deviations from this behavior are found to be caused by thermally-activated carriers, which can be eliminated by taking advantage of an unexpected magnetocaloric effect., Comment: 5 pages, 4 figures, with 9 pages of supplementary information

The electronic properties of graphene are described by a Dirac Hamiltonian with a fourfold symmetry of spin and valley. This symmetry may yield novel fractional quantum Hall (FQH) states at high magnetic field depending on the relative strength of symmetry breaking interactions. However, observing such states in transport remains challenging in graphene, as they are easily destroyed by disorder. In this work, we observe in the first two Landau levels (v<6) the composite-fermion sequences of FQH states at p/(2p+1) between each integer filling factor. In particular, odd numerator fractions appear between v=1 and v=2, suggesting a broken valley symmetry, consistent with our observation of a gap at charge neutrality and zero field. Contrary to our expectations, the evolution of gaps in a parallel magnetic field suggests that states in the first Landau level are not spin-polarized even up to very large out of plane fields.

This review article describes theoretical and experimental advances in using quantum dots as a system for studying impurity quantum phase transitions and the non-Fermi liquid behavior at the quantum critical point., Comment: 33 pages and 6 figures

We report on transport measurements of dual-gated, single-layer graphene devices in the quantum Hall regime, allowing for independent control of the filling factors in adjoining regions. Progress in device quality allows us to study scattering between edge states when the four-fold degeneracy of the Landau level is lifted by electron correlations, causing edge states to be spin and/or valley polarized. In this new regime, we observe a dramatic departure from the equilibration seen in more disordered devices: edge states with opposite spins propagate without mixing. As a result, the degree of equilibration inferred from transport can reveal the spin polarization of the ground state at each filling factor. In particular, the first Landau level is shown to be spin-polarized at half-filling, providing an independent confirmation of a conclusion of Ref.[1]. The conductance in the bipolar regime is strongly suppressed, indicating that co-propagating edge states, even with the same spin, do not equilibrate along PN interfaces. We attribute this behavior to the formation of an insulating nu=0 stripe at the PN interface.

Central to condensed matter physics are quantum impurity models, which describe how a local degree of freedom interacts with a continuum. Surprisingly, these models are often universal in that they can quantitatively describe many outwardly unrelated physical systems. Here we develop a double quantum dot-based experimental realization of the SU(4) Kondo model, which describes the maximally symmetric screening of a local four-fold degeneracy. As demonstrated through transport measurements and detailed numerical renormalization group calculations, our device affords exquisite control over orbital and spin physics. Because the two quantum dots are coupled only capacitively, we can achieve orbital state- or "pseudospin"-resolved bias spectroscopy, providing intimate access to the interplay of spin and orbital Kondo effects. This cannot be achieved in the few other systems realizing the SU(4) Kondo state., Comment: Text and supplementary information. Text: 17 pages, 4 figures. Supplementary information: 24 pages, 9 figures

We report measurements of the electron dephasing time extracted from the weak localization (WL) correction to the average conductance in an open AlGaAs/GaAs quantum dot from 1 K to 13 mK. In agreement with theoretical predictions but in contrast with previous measurements in quantum dots, the extracted dephasing time does not saturate at the lowest temperatures. We find that the dephasing time follows an inverse linear power law with temperature. We determine that the extraction of the dephasing time from WL is applicable down to our lowest temperatures, but extraction from finite magnetic field conductance fluctuations is complicated by charging effects below 13 mK., Comment: 5 pages, 3 figures, supplementary information available by request (igrau@stanford.edu)

The fate of the low-temperature conductance at the charge-neutrality (Dirac) point in a single sheet of graphene is investigated down to 20 mK. As the temperature is lowered, the peak resistivity diverges with a power-law behavior and becomes as high as several Megohms per square at the lowest temperature, in contrast with the commonly observed saturation of the conductivity. As a perpendicular magnetic field is applied, our device remains insulating and directly transitions to the broken-valley-symmetry, nu=0 quantum Hall state, indicating that the insulating behavior we observe at zero magnetic field is a result of broken valley symmetry. Finally we discuss the possible origins of this effect.

We report measurements of the Kondo effect in a double quantum dot (DQD), where the orbital states act as pseudospin states whose degeneracy contributes to Kondo screening. Standard transport spectroscopy as a function of the bias voltage on both dots shows a zero-bias peak in conductance, analogous to that observed for spin Kondo in single dots. Breaking the orbital degeneracy splits the Kondo resonance in the tunneling density of states above and below the Fermi energy of the leads, with the resonances having different pseudospin character. Using pseudospin-resolved spectroscopy, we demonstrate the pseudospin character by observing a Kondo peak at only one sign of the bias voltage. We show that even when the pseudospin states have very different tunnel rates to the leads, a Kondo temperature can be consistently defined for the DQD system., Comment: Text and supplementary information. Text: 4 pages, 5 figures. Supplementary information: 4 pages, 4 figures

We report on transport properties of Josephson junctions in hybrid superconducting-topological insulator devices, which show two striking departures from the common Josephson junction behavior: a characteristic energy that scales inversely with the width of the junction, and a low characteristic magnetic field for suppressing supercurrent. To explain these effects, we propose a phenomenological model which expands on the existing theory for topological insulator Josephson junctions.

We report on the fabrication and measurement of a graphene tunnel junction using hexagonal-boron nitride as a tunnel barrier between graphene and a metal gate. The tunneling behavior into graphene is altered by the interactions with phonons and the presence of disorder. We extract prop- erties of graphene and observe multiple phonon-enhanced tunneling thresholds. Finally, differences in the measured properties of two devices are used to shed light on mutually-contrasting previous results of scanning tunneling microscopy in graphene.

We report low-temperature, high-field magnetotransport measurements of SrTiO3 gated by an ionic gel electrolyte. A saturating resistance upturn and negative magnetoresistance that signal the emergence of the Kondo effect appear for higher applied gate voltages. This observation, enabled by the wide tunability of the ionic gel-applied electric field, promotes the interpretation of the electric field-effect induced 2D electron system in SrTiO3 as an admixture of magnetic Ti3+ ions, i.e. localized and unpaired electrons, and delocalized electrons that partially fill the Ti 3d conduction band., Comment: Minor changes and Supp Info added

Using scanning gate microscopy (SGM), we probe the scattering between a beam of electrons and a two-dimensional electron gas (2DEG) as a function of the beam's injection energy, and distance from the injection point. At low injection energies, we find electrons in the beam scatter by small-angles, as has been previously observed. At high injection energies, we find a surprising result: placing the SGM tip where it back-scatters electrons increases the differential conductance through the system. This effect is explained by a non-equilibrium distribution of electrons in a localized region of 2DEG near the injection point. Our data indicate that the spatial extent of this highly non-equilibrium distribution is within ~1 micrometer of the injection point. We approximate the non-equilibrium region as having an effective temperature that depends linearly upon injection energy., Comment: 8 pages, 6 figures

We report the observation of Coulomb blockade in a quantum dot contacted by two quantum point contacts each with a single fully-transmitting mode, a system previously thought to be well described without invoking Coulomb interactions. At temperatures below 50 mK we observe a periodic oscillation in the conductance of the dot with gate voltage that corresponds to a residual quantization of charge. From the temperature and magnetic field dependence, we infer the oscillations are Mesoscopic Coulomb Blockade, a type of Coulomb blockade caused by electron interference in an otherwise open system., Comment: Text and supplementary information. Text: 4 pages, 4 figures. Supplementary information: 4 pages, 4 figures

GaAs-based two-dimensional electron gases (2DEGs) show a wealth of remarkable electronic states, and serve as the basis for fast transistors, research on electrons in nanostructures, and prototypes of quantum-computing schemes. All these uses depend on the extremely low levels of disorder in GaAs 2DEGs, with low-temperature mean free paths ranging from microns to hundreds of microns. Here we study how disorder affects the spatial structure of electron transport by imaging electron flow in three different GaAs/AlGaAs 2DEGs, whose mobilities range over an order of magnitude. As expected, electrons flow along narrow branches that we find remain straight over a distance roughly proportional to the mean free path. We also observe two unanticipated phenomena in high-mobility samples. In our highest-mobility sample we observe an almost complete absence of sharp impurity or defect scattering, indicated by the complete suppression of quantum coherent interference fringes. Also, branched flow through the chaotic potential of a high-mobility sample remains stable to significant changes to the initial conditions of injected electrons., Comment: 22 pages, 4 figures, 1 table

We show an electron interferometer between a quantum point contact (QPC) and a scanning gate microscope (SGM) tip in a two-dimensional electron gas. The QPC and SGM tip act as reflective barriers of a lossy cavity; the conductance through the system thus varies as a function of the distance between the QPC and SGM tip. We characterize how temperature, electron wavelength, cavity length, and reflectivity of the QPC barrier affect the interferometer. We report checkerboard interference patterns near the QPC and, when injecting electrons above or below the Fermi energy, effects of dephasing., Comment: Text and supplementary information. Text: 4 pages, 4 figures. Supplementary information: 5 pages, 2 figures

Understanding the flow of spins in magnetic layered structures has enabled an increase in data storage density in hard drives over the past decade of more than two orders of magnitude1. Following this remarkable success, the field of 'spintronics' or spin-based electronics is moving beyond effects based on local spin polarisation and is turning its attention to spin-orbit interaction (SOI) effects, which hold promise for the production, detection and manipulation of spin currents, allowing coherent transmission of information within a device. While SOI-induced spin transport effects have been observed in two- and three-dimensional samples, these have been subtle and elusive, often detected only indirectly in electrical transport or else with more sophisticated techniques. Here we present the first observation of a predicted 'spin-orbit gap' in a one-dimensional sample, where counter-propagating spins, constituting a spin current, are accompanied by a clear signal in the easily-measured linear conductance of the system., Comment: 10 pages, 5 figures, supplementary information

Potential steps naturally develop in graphene near metallic contacts. We investigate the influence of these steps on the transport in graphene Field Effect Transistors. We give simple expressions to estimate the voltage-dependent contribution of the contacts to the total resistance and noise in the diffusive and ballistic regimes., Comment: 6 pages, 4 figures; Figs 3 and 4 completed and appendix added

Transport through potential barriers in graphene is investigated using a set of metallic gates capacitively coupled to graphene to modulate the potential landscape. When a gate-induced potential step is steep enough, disorder becomes less important and the resistance across the step is in quantitative agreement with predictions of Klein tunneling of Dirac fermions up to a small correction. We also perform magnetoresistance measurements at low magnetic fields and compare them to recent predictions., Comment: Major changes made: 1) Taking into account properly the contribution of the resistance of monopolar junctions to the odd part of the resistance. To better present the results we use a fitting parameter for the amplitude of screening in graphene. 2) Wrong data for the diffusive model in figures 3, 9 and 10 was plotted in former version. 3) Figure 5 moved to EPAPS

We perform electrical transport measurements in graphene with several sample geometries. In particular, we design ``invasive'' probes crossing the whole graphene sheet as well as ``external'' probes connected through graphene side arms. The four-probe conductance measured between external probes varies linearly with charge density and is symmetric between electron and hole types of carriers. In contrast measurements with invasive probes give a strong electron-hole asymmetry and a sub-linear conductance as a function of density. By comparing various geometries and types of contact metal, we show that these two observations are due to transport properties of the metal/graphene interface. The asymmetry originates from the pinning of the charge density below the metal, which thereby forms a p-n or p-p junction depending on the polarity of the carriers in the bulk graphene sheet. Our results also explain part of the sub-linearity observed in conductance as a function of density in a large number of experiments on graphene, which has generally been attributed to short-range scattering only., Comment: 4 pages, 5 figures, Supplementary information will come soon

Recent advances in the fabrication of microelectromechanical systems (MEMS) and their evolution into nanoelectromechanical systems (NEMS) have allowed researchers to measure extremely small forces, masses, and displacements. In particular, researchers have developed position transducers with resolution approaching the uncertainty limit set by quantum mechanics. The achievement of such resolution has implications not only for the detection of quantum behavior in mechanical systems, but also for a variety of other precision experiments including the bounding of deviations from Newtonian gravity at short distances and the measurement of single spins. Here we demonstrate the use of a quantum point contact (QPC) as a sensitive displacement detector capable of sensing the low-temperature thermal motion of a nearby micromechanical cantilever. Advantages of this approach include versatility due to its off-board design, compatibility with nanoscale oscillators, and, with further development, the potential to achieve quantum limited displacement detection., Comment: 5 pages, 5 figures

Scaling laws and universality play an important role in our understanding of critical phenomena and the Kondo effect. Here we present measurements of non-equilibrium transport through a single-channel Kondo quantum dot at low temperature and bias. We find that the low-energy Kondo conductance is consistent with universality between temperature and bias and characterized by a quadratic scaling exponent, as expected for the spin-1/2 Kondo effect. The non-equilibrium Kondo transport measurements are well-described by a universal scaling function with two scaling parameters., Comment: v2: improved introduction and theory-experiment comparsion

In a single-walled carbon nanotube, we observe the spin-1/2 Kondo effect. The energy of spin-resolved Kondo peaks is proportional to magnetic field at high fields, contrary to recent reports. At lower fields, the energy falls below this linear dependence, in qualitative agreement with theoretical expectations. For even electron occupancy, we observe a spin-1 Kondo effect due to the degeneracy of the triplet ground states. Tuning gate voltage within the same Coulomb diamond drives a transition to a singlet ground state. We also independently tune the energy difference between singlet and triplet states with a magnetic field. The Zeeman splitting thus measured confirms the value of the g-factor measured from the spin-1/2 Kondo feature., Comment: 10 pp., 5 fig. cond-mat/0606258 was split into two papers to clarify their separate stories. cond-mat/0606258v2 treats the effect of C60 intercalation on transport in nanotubes. 0704.3641 is on Kondo physics in a nanotube in B-field. We now note: the splitting of Kondo resonances with B-field is sub-linear at low field, in qualitative agreement with theories

The peculiar nature of electron scattering in graphene is among many exciting theoretical predictions for the physical properties of this material. To investigate electron scattering properties in a graphene plane, we have created a gate-tunable potential barrier within a single-layer graphene sheet. We report measurements of electrical transport across this structure as the tunable barrier potential is swept through a range of heights. When the barrier is sufficiently strong to form a bipolar junctions (npn or pnp) within the graphene sheet, the resistance across the barrier sharply increases. We compare these results to predictions for both diffusive and ballistic transport, as the barrier rises on a length scale comparable to the mean free path. Finally, we show how a magnetic field modifies transport across the barrier., Comment: 5 pages, 5 figures

A dilute concentration of magnetic impurities can dramatically affect the transport properties of an otherwise pure metal. This phenomenon, known as the Kondo effect, originates from the interactions of individual magnetic impurities with the conduction electrons. Nearly a decade ago, the Kondo effect was observed in a new system, in which the magnetic moment stems from a single unpaired spin in a lithographically defined quantum dot, or artificial atom. The discovery of the Kondo effect in artificial atoms spurred a revival in the study of Kondo physics, due in part to the unprecedented control of relevant parameters in these systems. In this review we discuss the physics, origins, and phenomenology of the Kondo effect in the context of recent quantum dot experiments., Comment: 50 pages, 18 figures, contribution to the Handbook of Magnetism and Advanced Magnetic Materials, Vol. 5, Wiley

Some of the most intriguing problems in solid state physics arise when the motion of one electron dramatically affects the motion of surrounding electrons. Traditionally, such highly-correlated electron systems have been studied mainly in materials with complex transition metal chemistry. Over the past decade, researchers have learned to confine one or a few electrons within a nanoscale semiconductor "artificial atom", and to understand and control this simple system in exquisite detail. In this Article, we combine such individually well-understood components to create a novel highly-correlated electron system within a nano-engineered semiconductor structure. We tune the system in situ through a quantum phase transition between two distinct states, one familiar and one subtly new. The boundary between these states is a quantum critical point: the exotic and previously elusive two-channel Kondo state, in which electrons in two reservoirs are entangled through their interaction with a single localized spin., Comment: 8 pages including 5 figures. Supplementary information will appear separately as cond-mat/0610723

This document provides detailed descriptions of data acquisition and data analysis in support of the accompanying Article, cond-mat/0610721: Observation of the two-channel Kondo effect. Some of the most intriguing problems in solid state physics arise when the motion of one electron dramatically affects the motion of surrounding electrons. Traditionally, such highly-correlated electron systems have been studied mainly in materials with complex transition metal chemistry. Over the past decade, researchers have learned to confine one or a few electrons within a nanoscale semiconductor "artificial atom", and to understand and control this simple system in exquisite detail. In the accompanying Article, we combine such individually well-understood components to create a novel highly-correlated electron system within a nano-engineered semiconductor structure. We tune the system in situ through a quantum phase transition between two distinct states, one familiar and one subtly new. The boundary between these states is a quantum critical point: the exotic and previously elusive two-channel Kondo state, in which electrons in two reservoirs are entangled through their interaction with a single localized spin., Comment: 14 pages including 6 figures. Supplementary information for cond-mat/0610721

We measure the conductance of carbon nanotube peapods from room temperature down to 250mK. Our devices show both metallic and semiconducting behavior at room temperature. At the lowest temperatures, we observe single electron effects. Our results suggest that the encapsulated C$_{60}$ molecules do not introduce substantial backscattering for electrons near the Fermi level. This is remarkable given that previous tunneling spectroscopy measurements show that encapsulated C$_{60}$ strongly modifies the electronic structure of a nanotube away from the Fermi level., Comment: 9 pages, 4 figures. This is one of two manuscripts replacing the one orginally submitted as arXiv:cond-mat/0606258. The other one is arXiv:0704.3641 [cond-mat]

We study the transport properties of a quantum dot (QD) with highly resistive gate electrodes, and show that the QD displays a quantum phase transition analogous to the famous dissipative phase transition first identified by S. Chakravarty [Phys. Rev. Lett. {\bf 49}, 681 (1982)]; for a review see [A. J. Leggett {\em et al.}, Rev. Mod. Phys. {\bf 59}, 1 (1987)]. At temperature T=0, the charge on the central island of a conventional QD changes smoothly as a function of gate voltage, due to quantum fluctuations. However, for sufficiently large gate resistance charge fluctuations on the island can freeze out even at the degeneracy point, causing the charge on the island to change in sharp steps as a function of gate voltage. For $R_g

We measure the low-field Hall resistivity of a magnetically-doped two-dimensional electron gas as a function of temperature and electrically-gated carrier density. Comparing these results with the carrier density extracted from Shubnikov-de Haas oscillations reveals an excess Hall resistivity that increases with decreasing temperature. This excess Hall resistivity qualitatively tracks the paramagnetic polarization of the sample, in analogy to the ferromagnetic anomalous Hall effect. The data are consistent with skew-scattering of carriers by disorder near the crossover to localization.

Conductance fluctuations in GaAs quantum dots with spin-orbit and Zeeman coupling are investigated experimentally and compared to a random matrix theory formulation that defines a number of regimes of spin symmetry depending on experimental parameters. Accounting for orbital coupling of the in-plane magnetic field, which can break time-reversal symmetry, yields excellent overall agreement between experiment and theory., Comment: related papers available at http://marcuslab.harvard.edu

We measure the spin splitting in a magnetic field $B$ of localized states in single-electron transistors using a new method, inelastic spin-flip cotunneling. Because it involves only internal excitations, this technique gives the most precise value of the Zeeman energy $\Delta = \ZeemanE$. In the same devices we also measure the splitting with $B$ of the Kondo peak in differential conductance. The Kondo splitting appears only above a threshold field as predicted by theory. However, the magnitude of the Kondo splitting at high fields exceeds $2 \ZeemanE$ in disagreement with theory., Comment: Replaced with version published in Phys. Rev. Lett

We report sharp peaks in the differential conductance of a single-electron transistor (SET) at low temperature, for gate voltages at which charge fluctuations are suppressed. For odd numbers of electrons we observe the expected Kondo peak at zero bias. For even numbers of electrons we generally observe Kondo-like features corresponding to excited states. For the latter, the excitation energy often decreases with gate voltage until a new zero-bias Kondo peak results. We ascribe this behavior to a singlet-triplet transition in zero magnetic field driven by the change of shape of the potential that confines the electrons in the SET., Comment: 4 p., 4 fig., 5 new ref. Rewrote 1st paragr. on p. 4. Revised author list. More detailed fit results on page 3. A plotting error in the horizontal axis of Fig. 1b and 3 was corrected, and so were the numbers in the text read from those fig. Fig. 4 was modified with a better temperature calibration (changes are a few percent). The inset of this fig. was removed as it is unnecessary here. Added remarks in the conclusion. Typos are corrected

In situ control of spin-orbit coupling in coherent transport using a clean GaAs/AlGaAs 2DEG is realized, leading to a gate-tunable crossover from weak localization to antilocalization. The necessary theory of 2D magnetotransport in the presence of spin-orbit coupling beyond the diffusive approximation is developed and used to analyze experimental data. With this theory the Rashba contribution and linear and cubic Dresselhaus contributions to spin-orbit coupling are separately estimated, allowing the angular dependence of spin-orbit precession to be extracted at various gate voltages., Comment: related papers at http://marcuslab.harvard.edu

Besides the usual conductance plateaus at multiples of 2e2/h, quantum point contacts typically show an extra plateau at ~ 0.7(2e2/h), believed to arise from electron-electron interactions that prohibit the two spin channels from being simultaneously occupied. We present evidence that the disappearance of the 0.7 structure at very low temperature signals the formation of a Kondo-like correlated spin state. Evidence includes a zero-bias conductance peak that splits in a parallel field, scaling of conductance to a modified Kondo form, and consistency between peak width and the Kondo temperature.

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 with increasing temperature., Comment: 6 pages, 4 figures. New references have been added to support the analysis

We have observed asymmetric Fano resonances in the conductance of a single electron transistor resulting from interference between a resonant and a nonresonant path through the system. The resonant component shows all the features typical of quantum dots, but the origin of the non-resonant path is unclear. A unique feature of this experimental system, compared to others that show Fano line shapes, is that changing the voltages on various gates allows one to alter the interference between the two paths., Comment: 8 pages, 6 figures. Submitted to PRB

We demonstrate that the conductance through a single-electron transistor at low temperature is in quantitative agreement with predictions of the equilibrium Anderson model. When an unpaired electron is localized within the transistor, the Kondo effect is observed. Tuning the unpaired electron's energy toward the Fermi level in nearby leads produces a cross-over between the Kondo and mixed-valence regimes of the Anderson model., Comment: 3 pages plus one 2 page postscript file of 5 figures. Submitted to PRL

The question of how localized electrons interact with delocalized electrons is central to many problems at the forefront of solid state physics. The simplest example is the Kondo phenomenon, which occurs when an impurity atom with an unpaired electron is placed in a metal, and the energy of the unpaired electron is far below the Fermi energy. At low temperatures a spin singlet state is formed between the unpaired localized electron and delocalized electrons at the Fermi energy. The confined droplet of electrons interacting with the leads of a single electron transistor (SET) is closely analogous to an impurity atom interacting with the delocalized electrons in a metal. (Meir, Wingreen and Lee, 1993) We report here measurements on a new generation of SETs that display all the aspects of the Kondo phenomenon: the spin singlet forms and causes an enhancement of the zero-bias conductance when the number of electrons on the artificial atom is odd but not when it is even. The singlet is altered by applying a voltage or magnetic field or by increasing the temperature, all in ways that agree with predictions. (Wingreen and Meir 1994), Comment: 10 pages of LaTeX plus 5 separate ps/eps figures. Submitted to Nature

The temperature dependence of conductance resonances is used to measure the evolution with the magnetic field of the average level spacing $\Delta\epsilon$ of a droplet containing $\sim 30$ electrons created by lateral confinement of a two-dimensional electron gas in GaAs. $\Delta\epsilon$ becomes very small ($< 30\mu$eV) near two critical magnetic fields at which the symmetry of the droplet changes and these decreases of $\Delta\epsilon$ are predicted by Hartree-Fock (HF) for charge excitations. Between the two critical fields, however, the largest measured $\Delta\epsilon= 100\mu$eV is an order of magnitude smaller than predicted by HF but comparable to the Zeeman splitting at this field, which suggests that the spin degrees of freedom are important. PACS: 73.20.Dx, 73.20.Mf, Comment: 11 pages of text in RevTeX, 4 figures in Postscript (files in the form of uuencoded compressed tar file)