Momentum-dependent power law measured in an interacting quantum wire beyond the Luttinger limit.

Power laws in physics have until now always been associated with a scale invariance originating from the absence of a length scale. Recently, an emergent invariance even in the presence of a length scale has been predicted by the newly-developed nonlinear-Luttinger-liquid theory for a one-dimensional (1D) quantum fluid at finite energy and momentum, at which the particle's wavelength provides the length scale. We present experimental evidence for this new type of power law in the spectral function of interacting electrons in a quantum wire using a transport-spectroscopy technique. The observed momentum dependence of the power law in the high-energy region matches the theoretical predictions, supporting not only the 1D theory of interacting particles beyond the linear regime but also the existence of a new type of universality that emerges at finite energy and momentum.

Nonlinear spectra of spinons and holons in short GaAs quantum wires.

One-dimensional electronic fluids are peculiar conducting systems, where the fundamental role of interactions leads to exotic, emergent phenomena, such as spin-charge (spinon-holon) separation. The distinct low-energy properties of these 1D metals are successfully described within the theory of linear Luttinger liquids, but the challenging task of describing their high-energy nonlinear properties has long remained elusive. Recently, novel theoretical approaches accounting for nonlinearity have been developed, yet the rich phenomenology that they predict remains barely explored experimentally. Here, we probe the nonlinear spectral characteristics of short GaAs quantum wires by tunnelling spectroscopy, using an advanced device consisting of 6000 wires. We find evidence for the existence of an inverted (spinon) shadow band in the main region of the particle sector, one of the central predictions of the new nonlinear theories. A (holon) band with reduced effective mass is clearly visible in the particle sector at high energies.

Dichotomy between the Hole and Electron Behavior in Multiband Superconductor FeSe Probed by Ultrahigh Magnetic Fields.

Magnetoresistivity ρ(xx) and Hall resistivity ρ(xy) in ultrahigh magnetic fields up to 88 T are measured down to 0.15 K to clarify the multiband electronic structure in high-quality single crystals of superconducting FeSe. At low temperatures and high fields we observe quantum oscillations in both resistivity and the Hall effect, confirming the multiband Fermi surface with small volumes. We propose a novel approach to identify from magnetotransport measurements the sign of the charge carriers corresponding to a particular cyclotron orbit in a compensated metal. The observed significant differences in the relative amplitudes of the quantum oscillations between the ρ(xx) and ρ(xy) components, together with the positive sign of the high-field ρ(xy), reveal that the largest pocket should correspond to the hole band. The low-field magnetotransport data in the normal state suggest that, in addition to one hole and one almost compensated electron band, the orthorhombic phase of FeSe exhibits an additional tiny electron pocket with a high mobility.

Hierarchy of modes in an interacting one-dimensional system.

Studying interacting fermions in one dimension at high energy, we find a hierarchy in the spectral weights of the excitations theoretically, and we observe evidence for second-level excitations experimentally. Diagonalizing a model of fermions (without spin), we show that levels of the hierarchy are separated by powers of R^{2}/L^{2}, where R is a length scale related to interactions and L is the system length. The first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalized single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power laws at the spectral edge. We measure momentum-resolved tunneling of electrons (fermions with spin) from or to a wire formed within a GaAs heterostructure, which shows parabolic dispersion of the first-level mode and well-resolved spin-charge separation at low energy with appreciable interaction strength. We find structure resembling the second-level excitations, which dies away quite rapidly at high momentum.

Probing spin-charge separation in a Tomonaga-Luttinger liquid.

In a one-dimensional (1D) system of interacting electrons, excitations of spin and charge travel at different speeds, according to the theory of a Tomonaga-Luttinger liquid (TLL) at low energies. However, the clear observation of this spin-charge separation is an ongoing challenge experimentally. We have fabricated an electrostatically gated 1D system in which we observe spin-charge separation and also the predicted power-law suppression of tunneling into the 1D system. The spin-charge separation persists even beyond the low-energy regime where the TLL approximation should hold. TLL effects should therefore also be important in similar, but shorter, electrostatically gated wires, where interaction effects are being studied extensively worldwide.

Breakdown of weak-field magnetotransport at a metallic quantum critical point.

We show how the collapse of an energy scale in a quantum critical metal can lead to physics beyond the weak-field limit usually used to compute transport quantities. For a density-wave transition we show that the presence of a finite magnetic field at the critical point leads to discontinuities in the transport coefficients as temperature tends to zero. The origin of these discontinuities lies in the breakdown of the weak-field Jones-Zener expansion which has previously been used to argue that magnetotransport coefficients are continuous at simple quantum critical points. The presence of potential scattering and magnetic breakdown rounds the discontinuities over a window determined by tauDelta < 1 where Delta is the order parameter and tau is the quasiparticle elastic lifetime.

Disorder-sensitive phase formation linked to metamagnetic quantum criticality.

Condensed systems of strongly interacting electrons are ideal for the study of quantum complexity. It has become possible to promote the formation of new quantum phases by explicitly tuning systems toward special low-temperature quantum critical points. So far, the clearest examples have been appearances of superconductivity near pressure-tuned antiferromagnetic quantum critical points. We present experimental evidence for the formation of a nonsuperconducting phase in the vicinity of a magnetic field-tuned quantum critical point in ultrapure crystals of the ruthenate metal Sr3Ru2O7, and we discuss the possibility that the observed phase is due to a spin-dependent symmetry-breaking Fermi surface distortion.

Ferromagnetic superconductivity driven by changing Fermi surface topology.

We introduce a simple but powerful zero temperature Stoner model to explain the unusual phase dia-gram of the ferromagnetic superconductor, UGe2. Triplet superconductivity is driven in the ferromagnetic phase by tuning the majority spin Fermi level through one of two peaks in the paramagnetic density of states (DOS). Each peak is associated with a metamagnetic jump in magnetization. The twin-peak DOS may be derived from a tight-binding, quasi-one-dimensional band structure, inspired by previous band-structure calculations.

Metamagnetic quantum criticality in metals.

We present a renormalization group treatment of metamagnetic quantum criticality in metals. We show that for clean systems the universality class is that of the overdamped, conserving (dynamical exponent z = 3) Ising type. We obtain detailed results for the field and temperature dependence of physical quantities including the differential susceptibility, resistivity, and specific heat. Our results are shown to be in quantitative agreement with data on Sr3Ru2O7 except very near to the critical point itself.

Sensitivity to disorder of the metallic state in the ruthenates.

We report the results of transport measurements on SrRuO3, Sr3Ru2O7, and CaRuO3. In SrRuO3 and Sr3Ru2O7, our findings are consistent with the predictions of Fermi liquid theory, in contrast to previous reports based on samples with much shorter mean free paths. In CaRuO3, however, a T1.5 power law is seen in the resistivity in the high purity samples studied here. Our work gives concrete evidence that even the metallic state of the ruthenates is highly sensitive to disorder.

Magnetic field-tuned quantum criticality in the metallic ruthenate Sr3Ru2O7.

The concept of quantum criticality is proving to be central to attempts to understand the physics of strongly correlated electrons. Here, we argue that observations on the itinerant metamagnet Sr3Ru2O7 represent good evidence for a new class of quantum critical point, arising when the critical end point terminating a line of first-order transitions is depressed toward zero temperature. This is of interest both in its own right and because of the convenience of having a quantum critical point for which the tuning parameter is the magnetic field. The relationship between the resultant critical fluctuations and novel behavior very near the critical field is discussed.

Metamagnetism and critical fluctuations in high quality single crystals of the bilayer ruthenate Sr3Ru2O7.

We report the results of low temperature transport, specific heat, and magnetization measurements on high quality single crystals of the bilayer perovskite Sr3Ru2O7, which is a close relative of the unconventional superconductor Sr2RuO4. Metamagnetism is observed, and transport and thermodynamic evidence for associated critical fluctuations is presented. These relatively unusual fluctuations might be pictured as variations in the Fermi surface topography itself.

The temporal properties of first- and second-order vision.

Vision is sensitive to first-order modulations of luminance and second-order modulations of image contrast. There is now a body of evidence that the two types of modulation are detected by separate mechanisms. Some previous experiments on motion detection have suggested that the second-order system is quite sluggish compared to the first-order system. Here we derive temporal properties of first- and second-order vision at threshold from studies of temporal integration and two-pulse summation. Three types of modulation were tested: luminance gratings alone, luminance modulations added to dynamic visual noise, and contrast modulations of dynamic noise. Data from the two-pulse summation experiment were used to derive impulse response functions for the three types of stimulus. These were then used to predict performance in the temporal integration experiment. Temporal frequency response functions were obtained as the Fourier transform of impulse responses derived from data averaged across two observers. The response to noise-free luminance gratings of 2 c/deg was bi-phasic and transient in the time domain, and bandpass in the frequency domain. The addition of dynamic noise caused the response to become mono-phasic, sustained and low-pass. The response to contrast modulated noise (second-order) was also mono-phasic, sustained and low-pass, with only a slightly longer integration time than in the first-order case. The ultimate roll-off at high frequencies was about the same as for the first-order case. We conclude that second-order vision may not be as sluggish as previously thought.

What does second-order vision see in an image?

The human visual system is sensitive to both first-order variations in luminance and second-order variations in local contrast and texture. Although there is some debate about the nature of second-order vision and its relationship to first-order processing, there is now a body of results showing that they are processed separately. However, the amount, and nature, of second-order structure present in the natural environment is unclear. This is an important question because, if natural scenes contain little second-order structure in addition to first-order signals, the notion of a separate second-order system would lack ecological validity. Two models of second-order vision were applied to a number of well-calibrated natural images. Both models consisted of a first stage of oriented spatial filters followed by a rectifying nonlinearity and then a second set of filters. The models differed in terms of the connectivity between first-stage and second-stage filters. Output images taken from the models indicate that natural images do contain useful second-order structure. Specifically, the models reveal variations in texture and features defined by such variations. Areas of high contrast (but not necessarily high luminance) are also highlighted by the models. Second-order structure--as revealed by the models--did not correlate with the first-order profile of the images, suggesting that the two types of image 'content' may be statistically independent.

Sensitivity to modulations of luminance and contrast in visual white noise: separate mechanisms with similar behaviour.

Human vision can detect spatiotemporal information conveyed by first-order modulations of luminance and by second-order, non-Fourier modulations of image contrast. Models for second-order motion have suggested two filtering stages separated by a rectifying nonlinearity. We explore here the encoding of stationary first-order and second-order gratings, and their interaction. Stimuli consisted of 2-D binary, broad-band, static, visual noise sinusoidally modulated in luminance (LM, first-order) or contrast (CM, second-order). Modulation thresholds were measured in a two-interval forced-choice staircase procedure. Sensitivity curves for LM and CM had similar shape as a function of spatial frequency, and as a function of the size of a circular Gaussian blob of modulation. Weak background gratings present in both intervals produced order-specific facilitation: LM background facilitated LM detection (the dipper function) and CM facilitated CM detection. LM did not facilitate CM, nor vice-versa, neither in-phase nor out-of-phase, and this is strong evidence that LM and CM are detected via separate mechanisms. This conclusion was further supported by an experiment on the detection of LM/CM mixtures. From a general mathematical model and a specific computer simulation we conclude that a single mechanism sensitive to both LM and CM cannot predict the pattern of results for mixtures, while a model containing separate pathways for LM and CM, followed by energy summation, does so successfully and is quantitatively consistent with the finding of order-specific facilitation.

Artificial neural networks simulating visual texture segmentation and target detection in line-element images.

Measurements were made of human observers' performance both in segmenting regions of line-elements and in detecting line-element targets in stimuli containing several orientations. Performance was modelled by four artificial neural networks constructed from processing units trained to mimic the gross functionality of certain loosely defined classes of cortical cells. Model 1 contained modules sensitive to absolute orientation only, and it provided a poor fit to the human-performance data. Model 2 contained modules sensitive to orientation contrast: the outputs of these modules could be suppressed with fields of uniformly oriented line-elements. Model 3 contained orientation-contrast-sensitive modules of a different type: their outputs could be suppressed with fields of randomly oriented line-elements. Models 2 and 3 both successfully processed line-element arrays with orientation heterogeneities, but these models still provided inadequate fits to the human-performance data. Model 4 contained both types of orientation-contrast-sensitive modules; this model was able to account for human performance in the segmentation and detection tasks, both qualitatively and quantitatively.