We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent $z$ related to the energy and length scales $\Delta$ and $\xi$. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-critical dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid. We emphasize the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems. Finally we quote some recent inelastic neutron scattering experiments performed on heavy-fermions which lead to unusual scaling law in $\omega /T$ for the dynamical spin susceptibility revealing critical local modes beyond the itinerant magnetism scheme and mention new attempts to describe this local quantum critical point.

https://arxiv.org/pdf/cond-mat/0102119.pdf

Quantum Phase Transitions

Hydrogen - A sustainable energy carrier

A new thin film photochromic material: Oxygen-containing yttrium hydride

A key challenge for the development of active plasmonic nanodevices is the lack of materials with fully controllable plasmonic properties. In this work, we demonstrate that a plasmonic resonance in top-down nanofabricated yttrium antennas can be completely and reversibly turned on and off using hydrogen exposure. We fabricate arrays of yttrium nanorods and optically observe, in extinction spectra, the hydrogen-induced phase transition between the metallic yttrium dihydride and the insulating trihydride. Whereas the yttrium dihydride nanostructures exhibit a pronounced particle plasmon resonance, the transition to yttrium trihydride leads to a complete vanishing of the resonant behavior. The plasmonic resonance in the dihydride state can be tuned over a wide wavelength range by simply varying the size of the nanostructures. Furthermore, we develop an analytical diffusion model to explain the temporal behavior of the hydrogen loading and unloading trajectories observed in our experiments and gain informatio...

Yttrium Hydride Nanoantennas for Active Plasmonics

Apart from a reflecting and a transparent state, rare-earth-Mg alloys (RE-Mg) exhibit also a highly absorbing, black state during loading with hydrogen The occurrence of such a black state is due to the disproportionation into subwavelength size ${\mathrm{REH}}_{2+\ensuremath{\epsilon}}$ and Mg grains during the first hydrogen loading While the optical properties of ${\mathrm{REH}}_{x}$ change continuously with a further increase in hydrogen concentration x, Mg changes abruptly from a good reflector to a transparent insulator $({\mathrm{MgH}}_{2})$ Thin pure Mg films also show this black state when (un)loaded carefully at elevated temperatures By using the Bruggeman effective medium approximation in combination with the transfer matrix method it is shown that the coexistence of Mg and ${\mathrm{MgH}}_{2}$ grains is the cause of this high absorption Furthermore, we compare this phenomenon to the high absorption of light observed in metal-dielectric composites

/pdf/highly-absorbing-black-mg-and-rare-earth-mg-switchable-407n609aia.pdf

Highly absorbing black Mg and rare-earth-Mg switchable mirrors

Rare earth hydride films can be converted reversibly from metallic mirrors to insulating windows simply by changing the surrounding hydrogen gas pressure at room temperature. At low temperatures, in situ doping is not possible in this way as hydrogen cannot diffuse. However, our finding of persistent photoconductivity under ultraviolet illumination offers an attractive possibility to tune yttrium hydride through the T = 0 metal-insulator transition. Conductivity and Hall measurements are used to determine critical exponents. The unusually large value for the product of the static and dynamical critical exponents appears to signify the important role played by electron-electron interactions.

/pdf/light-induced-metal-insulator-transition-in-a-switchable-4se8n0243i.pdf

Light-induced metal-insulator transition in a switchable mirror.

The “switchable mirror” yttrium hydride is one of the few strongly correlated systems with a continuous Mott-Hubbard metal-insulator transition. We systematically map out the low temperature electrical transport from deep in the insulator to the quantum critical point using persistent photoconductivity as a drive parameter. Both activated hopping over a Coulomb gap and power-law quantum fluctuations must be included to describe the data. Collapse of the data onto a universal curve within a dynamical scaling framework (with corrections) requires zν=6.0±0.5, where ν and z are the static and dynamical critical exponents, respectively.

/pdf/quantum-fluctuations-and-the-closing-of-the-coulomb-gap-in-a-xnzas20fcg.pdf

Quantum fluctuations and the closing of the Coulomb gap in a correlated insulator.

A single yttrium hydride thin film is conveniently driven through the T = 0 metal-insulator transition by fine-tuning the charge :carrier density n via persistent photoconductivity at low temperature. Simultaneously, electrical conductivity and Hall measurements are performed for temperatures T down to 350 mK and magnetic fields up to 14 T. A scaling analysis is applied and critical exponents, resolved separately on the metallic and insulating sides of the critical region, are determined consistently. We introduce corrections to scaling to invoke collapse of the data onto a single master curve over an extended region of the (n, T) phase diagram.

Scaling at the Mott-Hubbard metal-insulator transition in yttrium hydride

A gas loading cell has been developed to load rare earth thin film samples with hydrogen at pressures up to 200 bars at room temperature. A miniature valve closes the gas inlet, after which the cell is suspended from the cold tail of a ^3He flow cryostat into the bore of a 16 T superconducting magnet. An ultraviolet stroboscope outside the cryostat illuminates the sample by way of an optical fiber to a window in the cell. Electrical feedthroughs permit photoconductivity and magnetotransport measurements over three decades in temperature. Extension to other materials, different gas atmospheres, and helium dilution refrigerator temperatures is straightforward.

/pdf/high-pressure-hydrogen-loading-cell-for-photoconductivity-4p933dma0n.pdf

A. F. Th. Hoekstra

Papers

Light-induced metal-insulator transition in a switchable mirror.

Quantum fluctuations and the closing of the Coulomb gap in a correlated insulator.

Scaling at the Mott-Hubbard metal-insulator transition in yttrium hydride

High pressure hydrogen loading cell for photoconductivity measurements down to the milliKelvin regime