We review studies of the electromagnetic response of various classes of correlated electron materials including transition metal oxides, organic and molecular conductors, intermetallic compounds with $d$- and $f$-electrons as well as magnetic semiconductors. Optical inquiry into correlations in all these diverse systems is enabled by experimental access to the fundamental characteristics of an ensemble of electrons including their self-energy and kinetic energy. Steady-state spectroscopy carried out over a broad range of frequencies from microwaves to UV light and fast optics time-resolved techniques provide complimentary prospectives on correlations. Because the theoretical understanding of strong correlations is still evolving, the review is focused on the analysis of the universal trends that are emerging out of a large body of experimental data augmented where possible with insights from numerical studies.

/pdf/electrodynamics-of-correlated-electron-materials-2qg1x9aaaz.pdf

Electrodynamics of correlated electron materials

High-temperature superconductivity in copper oxides arises when a parent insulator compound is 'doped' by adding or removing valence electrons, usually by inserting atoms into the lattice structure. This would be better achieved by tuning the carrier density using the electric field effect, as it removes ambiguity about whether the electronic properties change because of alterations in the crystal structure or in the electronic structure. Such tuning is difficult to achieve because it requires perfect, ultrathin films and a huge local field. Bollinger et al. report the synthesis of one-cell-thick epitaxial films of La2xSrxCuO4, and the use of the films to make double-layer transistors. The transistors have very large fields, and by changing the surface carrier density, the critical temperature can be shifted by up to 30 K. The resistance varies as predicted for a two-dimensional superconductor–insulator transition. High-temperature superconductivity in copper oxides arises when a parent insulator compound is doped beyond some critical concentration; what exactly happens at this superconductor–insulator transition is a key open question1. The cleanest approach is to tune the carrier density using the electric field effect2,3,4,5,6,7; for example, it was learned in this way5 that weak electron localization transforms superconducting SrTiO3 into a Fermi-glass insulator. But in the copper oxides this has been a long-standing technical challenge3, because perfect ultrathin films and huge local fields (>109 V m−1) are needed. Recently, such fields have been obtained using electrolytes or ionic liquids in the electric double-layer transistor configuration8,9,10. Here we report synthesis of epitaxial films of La2− xSr x CuO4 that are one unit cell thick, and fabrication of double-layer transistors. Very large fields and induced changes in surface carrier density enable shifts in the critical temperature by up to 30 K. Hundreds of resistance versus temperature and carrier density curves were recorded and shown to collapse onto a single function, as predicted for a two-dimensional superconductor–insulator transition11,12,13,14. The observed critical resistance is precisely the quantum resistance for pairs, RQ = h/(2e)2 = 6.45 kΩ, suggestive of a phase transition driven by quantum phase fluctuations, and Cooper pair (de)localization.

Superconductor-insulator transition in La2 - xSrxCuO4 at the pair quantum resistance.

We review the resonating valence bond (RVB) theory of high-temperature superconductivity using Gutzwiller projected wave functions that incorporate strong correlations. After a general overview of the phenomenon of high-temperature superconductivity, we discuss Anderson's RVB picture and its implementation by renormalized mean-field theory (RMFT) and variational Monte Carlo (VMC) techniques. We review RMFT and VMC results with an emphasis on recent developments in extending VMC and RMFT techniques to excited states. We compare results obtained from these methods with angle-resolved photoemission spectroscopy (ARPES) and scanning tunnelling microscopy (STM). We conclude by summarizing recent successes of this approach and discuss open problems that need to be solved for a consistent and complete description of high-temperature superconductivity using Gutzwiller projected wave functions.

/pdf/gutzwiller-rvb-theory-of-high-temperature-superconductivity-4mwiieo9hw.pdf

Gutzwiller–RVB theory of high-temperature superconductivity: Results from renormalized mean-field theory and variational Monte Carlo calculations

In the underdoped high temperature superconductors, instead of a complete Fermi surface above Tc, only disconnected Fermi arcs appear, separated by regions that still exhibit an energy gap. We show that in this pseudogap phase, the energy-momentum relation of electronic excitations near EF behaves like the dispersion of a normal metal on the Fermi arcs, but like that of a superconductor in the gapped regions. We argue that this dichotomy in the dispersion is difficult to reconcile with a competing order parameter, but is consistent with pairing without condensation.

/pdf/evidence-for-pairing-above-the-transition-temperature-of-29g6lkvqjx.pdf

Evidence for pairing above the transition temperature of cuprate superconductors from the electronic dispersion in the pseudogap phase.

This is a short review of the theoretical work on the two-dimensional Hubbard model performed in Sherbrooke in the last few years. It is written on the occasion of the twentieth anniversary of the discovery of high-temperature superconductivity. We discuss several approaches, how they were benchmarked and how they agree sufficiently with each other that we can trust that the results are accurate solutions of the Hubbard model. Then comparisons are made with experiment. We show that the Hubbard model does exhibit d-wave superconductivity and antiferromagnetism essentially where they are observed for both hole- and electron-doped cuprates. We also show that the pseudogap phenomenon comes out of these calculations. In the case of electron-doped high temperature superconductors, comparisons with angle-resolved photoemission experiments are nearly quantitative. The value of the pseudogap temperature observed for these compounds in recent photoemission experiments had been predicted by theory before it was obse...

Pseudogap and high-temperature superconductivity from weak to strong coupling. Towards a quantitative theory (Review Article)

The superfluid density ${\ensuremath{\rho}}_{s}(T)\ensuremath{\equiv}1/{\ensuremath{\lambda}}^{2}(T)$ has been measured at 2.64 GHz in highly underdoped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+y}$, at 37 dopings with ${T}_{c}$ between 3 and 17 K. Within limits set by the transition width $\ensuremath{\Delta}{T}_{c}\ensuremath{\approx}0.4\text{ }\text{ }\mathrm{K}$, ${\ensuremath{\rho}}_{s}(T)$ shows no evidence of critical fluctuations as $T\ensuremath{\rightarrow}{T}_{c}$, with a mean-field-like transition and no indication of vortex unbinding. Instead, we propose that ${\ensuremath{\rho}}_{s}$ displays the behavior expected for a quantum phase transition in the ($3+1$)-dimensional $XY$ universality class, with ${\ensuremath{\rho}}_{s0}\ensuremath{\propto}(p\ensuremath{-}{p}_{c})$, ${T}_{c}\ensuremath{\propto}(p\ensuremath{-}{p}_{c}{)}^{1/2}$, and ${\ensuremath{\rho}}_{s}(T)\ensuremath{\propto}({T}_{c}\ensuremath{-}T{)}^{1}$ as $T\ensuremath{\rightarrow}{T}_{c}$.

Superfluid Density in a Highly Underdoped YBa 2 Cu 3 O 6 + y Superconductor

The two most prominent states of matter in the phase diagram of the high temperature superconductors are the Mott insulator and d‐wave superconductor. Important clues for connecting the two states can be obtained by studying how the fundamental excitations evolve with doping. Using a breakthrough in the preparation of high purity YBa2Cu3O6+x crystals, we can tune into a regime of the underdoped cuprate phase diagram in which the transition temperature can be varied continuously between Tc = 25 K and zero, without changing cation disorder. A combination of microwave spectroscopy and measurements of the lower critical field Hc1 has been used to map out the temperature‐dependent superfluid density as a function of doping, with surprising results. The superfluid density becomes anomalously small in this doping range but shows no sign of a Kosterlitz‐Thouless transition. In addition, the temperature slope of the superfluid density is roughly proportional to Tc, suggesting a strong doping dependence of the char...

In‐Plane Superfluid Density of Highly Underdoped YBa2Cu3O6+x

MXenes’ tunable properties make them excellent candidates for many applications in future nanoelectronics. In this work, we explore the suitability of Sc[Formula: see text]CX (X=N[Formula: see text], ON, O[Formula: see text]) MXenes to act as the active anode materials in Na-ion based batteries (NIBs) by means of ab initio simulations. After analyzing the structural and elastic properties of all the possible models to evaluate the energetically favorable N and O functionalization sites, our calculations show that both Sc[Formula: see text]CON and Sc[Formula: see text]CN[Formula: see text] present a clear metallic character, making them potential candidates as anode materials. The investigation of the most relevant features for anode performance, such as the adsorption and diffusion of Na atoms, the intrinsic capacity, the open circuit voltage, and the storage capacity, shows that both systems are serious alternatives to the most common 2D materials currently employed in alkali metal batteries. In particular, Sc[Formula: see text]CN[Formula: see text] presents better diffusion behavior thanks to the absence of Na clustering on its surface, with optimal diffusion barriers comparable to other 2D materials, such as MoN[Formula: see text], while the values of diffusion barriers for Sc[Formula: see text]CON are at least three times smaller than those found for other anode candidates. Similarly, while the capacity of Sc[Formula: see text]CON is close to the one reported for 2D Sc[Formula: see text]C, Sc[Formula: see text]CN[Formula: see text] possesses a power density more than twice higher than the ones of 2D materials, such as Sc[Formula: see text]C, graphite, and MoS[Formula: see text]. Our results, thus, confirm the urge for further experimental exploration of the MXene Sc[Formula: see text]CX (X=N[Formula: see text], ON, O[Formula: see text]) family as anode material in NIBs.

/pdf/sc2cx-x-n2-on-o2-mxenes-as-a-promising-anode-material-a-3spa1crl.pdf

Sc2CX (X=N2, ON, O2) MXenes as a promising anode material: A first-principles study

The already intriguing electronic and optical properties of the MXene Sc2C family can be further tuned through a wide range of possible functionalizations. Here, by means of density functional theory, we show that the 36 possible elements of the Janus MXT (M: Sc2C, X: O, F, OH, T: C, N, S) family, built by considering the four possible structural models (i) FCC, (ii) HCP, (iii) FCC + HCP, and (iv) HCP + FCC, are all potentially stable. The analysis of their mechanical properties shows the excellent mechanical flexibility of functionalized MXenes (f-MXenes) under large strain, making them more suitable for applications where stress could be an issue. Interestingly, while Sc2C presents a metallic character, Sc2COS, Sc2CFN and Sc2COHN are found to be semiconductors with bandgaps of 2.5 eV (indirect), 1.67 eV (indirect) and 1.1 eV (direct), respectively, which presents promising applications for nano- and optoelectronics. Moreover, Sc2CFC presents a ferromagnetic ground state with the 2 × 2 × 1 supercell magnetic moment of 3.99 μB, while the ground state of Sc2COHC might be antiferromagnetic with a magnetic moment of 3.98 μB, depending on the environment. Remarkably, the band structures of Sc2CFC and Sc2COHC present a half-metallic character with an HSE06 fundamental band gap of 0.60 eV and 0.48 eV, respectively. Our results confirm the extraordinary potential of the Janus MXT (M: Sc2C, X: O, F, OH, T: C, N, S) family for novel applications in 2D nano-,opto- and spintronics.

Exploring a novel class of Janus MXenes by first principles calculations: structural, electronic and magnetic properties of Sc2CXT, X = O, F, OH; T = C, S, N.

The superfluid density rho_s(T) = 1/lambda^2(T) has been measured at 2.64 GHz in highly underdoped YBCO, at 37 dopings with T_c between 3 K and 17 K. Within limits set by the transition width Delta T_c ~ 0.4 K, rho_s(T) shows no evidence of critical fluctuations as T goes to T_c, with a mean-field-like transition and no indication of vortex unbinding. Instead, we propose that rho_s displays the behaviour expected for a quantum phase transition in the (3 + 1)-dimensional XY universality class, with rho_s0 ~ (p - p_c), T_c ~ (p - p_c)^1/2 and rho_s(T) ~ (T_c - T)^1 as T goes to T_c.

Superfluid density reveals a quantum critical point between d-wave superconductivity and a Mott insulator

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