Imaging the electronic Wigner crystal in one dimension.

The quantum crystal of electrons, predicted more than 80 years ago by Eugene Wigner, remains one of the most elusive states of matter. In this study, we observed the one-dimensional Wigner crystal directly by imaging its charge density in real space. To image, with minimal invasiveness, the many-body electronic density of a carbon nanotube, we used another nanotube as a scanning-charge perturbation. The images we obtained of a few electrons confined in one dimension match the theoretical predictions for strongly interacting crystals. The quantum nature of the crystal emerges in the observed collective tunneling through a potential barrier. These experiments provide the direct evidence for the formation of small Wigner crystals and open the way for studying other fragile interacting states by imaging their many-body density in real space.

Universal Fermi liquid crossover and quantum criticality in a mesoscopic system.

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 behaviour 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. On detuning the exchange couplings we observe the Fermi liquid scale T*, at energies below which the spin is screened conventionally by the more strongly coupled channel. 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.

Measurement of quantum noise in a carbon nanotube quantum dot in the Kondo regime.

The current emission noise of a carbon nanotube quantum dot in the Kondo regime is measured at frequencies ν of the order or higher than the frequency associated with the Kondo effect k(B)T (K)/h, with TK the Kondo temperature. The carbon nanotube is coupled via an on-chip resonant circuit to a quantum noise detector, a superconductor-insulator-superconductor junction. We find for hν ≈ k(B)T(K) a Kondo effect related singularity at a voltage bias eV ≈ hν, and a strong reduction of this singularity for hν ≈ 3k(B)T(K), in good agreement with theory. Our experiment constitutes a new original tool for the investigation of the nonequilibrium dynamics of many-body phenomena in nanoscale devices.

Scaling theory of magnetoresistance and carrier localization in Ga1-xMnxAs.

We compare experimental resistivity data on Ga1-xMnxAs films with theoretical calculations using a scaling theory for strongly disordered ferromagnets. The characteristic features of the temperature dependent resistivity can be quantitatively understood through this approach as originating from the close vicinity of the metal-insulator transition. However, accounting for thermal fluctuations is crucial for a quantitative description of the magnetic field induced changes in resistance. While the noninteracting scaling theory is in reasonable agreement with the data, we find clear evidence for interaction effects at low temperatures.