Bulk charge density modulations, recently observed in high critical-temperature $\left(T_{\mathrm{c}}\right)$ cuprate superconductors, coexist with the so-called pseudogap and compete with superconductivity. However, its direct observation has been limited to a narrow doping region in the underdoped regime. Using energy-resolved resonant x-ray scattering we have found evidence for such bulk charge modulations, or soft collective charge modes (soft CCMs), in optimally doped ${\mathrm{Bi}}_{1.5}{\mathrm{Pb}}_{0.6}{\mathrm{Sr}}_{1.54}{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Pb-Bi2212) around the summit of the superconducting dome with momentum transfer $q_{\parallel }\sim 0.28$ reciprocal lattice units (r.l.u.) along the Cu-O bond direction. The signal is stronger at $T\simeq T_{\mathrm{c}}$ than at lower temperatures, thereby confirming a competition between soft CCMs and superconductivity. These results demonstrate that soft CCMs are not constrained to the underdoped regime, suggesting that soft CCMs appear across a large part of the phase diagram of cuprates and are intimately entangled with high-$T_{\mathrm{c}}$ superconductivity.

There are three basic processes that determine hopping transport: (a) hopping between normally empty sites (i.e., having exponentially small occupation numbers at equilibrium), (b) hopping between normally occupied sites, and (c) transitions between normally occupied and unoccupied sites. In conventional theories all these processes are considered Markovian and the correlations of occupation numbers of different sites are believed to be small (i.e., not exponential in temperature). We show that, contrary to this belief, memory effects suppress the processes of type (c) and manifest themselves in a subleading exponential temperature dependence of the variable-range hopping conductivity. This temperature dependence originates from the property that sites of type (a) and (b) form two independent resistor networks that are weakly coupled to each other by processes of type (c). This leads to a two-color percolation problem which we solve in the critical region.

The residual resistivity of metals at the absolute zero of temperature is usually understood in terms of electrons scattering from random impurities. This mechanism, however, does not take into account dynamical many-body effects, which cannot be described in terms of a static electron-impurity potential. Here we show that dynamical corrections to the resistivity, already known to play a role in nanoscale conductors, are of quantitative importance in the calculation of the residual resistivity of simple metals, and lead to a significantly improved agreement between theory and experiment in the case of impurities embedded in an Al host. Our calculations are based on a recently proposed form of the time-dependent many-body exchange-correlation potential, which is derived from the time-dependent current density functional theory. Surprisingly, we find that the largest correction to the residual resistivity arises from the real part of the exchange-correlation kernel of time-dependent current density functional theory, rather than from its imaginary part. This unexpected result is shown to be consistent with recent theories of the dynamical corrections to the resistivity of nanoscale conductors.

We study the superconductivity pairing symmetry in ${\mathrm{Sr}}_2$${\mathrm{RuO}}_4$ in the limit of small interaction by extending a renormalization group calculation developed by Raghu et al. [Phys. Rev. B 81, 224505 (2010)] to include spin-orbit coupling and multiband effects. We show these effects to be crucial to discriminate between the possible order parameters. In contrast to previous results and without the necessity of fine-tuning, we obtain pseudospin-triplet gaps of the same order of magnitude on the two-dimensional $\gamma$ band and the quasi-one-dimensional $\alpha$ and $\beta$ bands. The ratio of the gap amplitude on the different bands varies continuously with the interaction parameter. The favored pairing symmetry is shown to be chiral when $\gamma$ is slightly dominant and helical when $\alpha$ and $\beta$ are slightly dominant.

Multiple, consecutive high-temperature transitions in NaI involving dynamical order and/or localization in the energy-momentum spectrum but not in the average crystal structure are revealed by lattice dynamics, x-ray lattice spacing, and heat-capacity measurements. Distinctive energy-momentum patterns and lattice distortions indicate dynamical structures forming within randomly stacked planes, rather than the isolated point-defect-like intrinsic localized modes predicted. Transition entropies are accounted for by vibrational entropy changes, and the transition enthalpies are explained by the strain energy of forming stacking-fault-like planar distortions deduced from x-ray-diffraction peak shifts. The vibrational entropy of the dynamical structures stabilizes surrounding elastic distortions.

We report the quasiparticle band gap, excitons, and highly anisotropic optical responses of few-layer black phosphorous (phosphorene). It is shown that these materials exhibit unique many-electron effects; the electronic structures are dispersive essentially along one dimension, leading to particularly enhanced self-energy corrections and excitonic effects. Additionally, within a wide energy range, including infrared light and part of visible light, few-layer black phosphorous absorbs light polarized along the structures' armchair direction and is transparent to light polarized along the zigzag direction, making them potentially viable linear polarizers for applications. Finally, the number of phosphorene layers included in the stack controls the material's band gap, optical absorption spectrum, and anisotropic polarization energy window across a wide range.

Shallow donors in silicon are favorable candidates for the implementation of solid-state quantum computer architectures because of the promising combination of atomiclike coherence properties and scalability from the semiconductor manufacturing industry. Quantum processing schemes require (among other things) controlled information transfer for readout. Here we demonstrate controlled electron tunneling at 10 K from P to Sb impurities and vice versa with the assistance of resonant terahertz photons.

We introduce a minimal spin model for describing the magnetic properties of ${\mathrm{CuCrO}}_2$. Our Monte Carlo simulations of this model reveal a rich magnetic-field-induced phase diagram, which explains the measured field dependence of the electric polarization. The sequence of phase transitions between different multiferroic states arises from a subtle interplay between spatial and spin anisotropy, magnetic frustration, and thermal fluctuations. Our calculations are compared to new measurements up to 92 T.

The pressure effect on the frustrated magnetic system $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_2$ exhibiting multiferroic behavior has been studied by means of time-of-flight single crystal neutron diffraction combined with a hybrid-anvil-type pressure cell. The nonpolar collinear magnetic ground state (CM1 phase) with propagation vector $\mathit{k}=(0,\frac{1}{2},\frac{1}{2})$ turns into a proper screw magnetic ordering with incommensurate modulation $\mathit{k}=(0,q,\frac{1}{2};q\simeq 0.4)$ and a polar ${21}^{\prime }$ magnetic point group (ICM2 phase), between 3 and 4 GPa. This spin structure is similar to the ferroelectric phase induced by magnetic field or chemical doping under ambient pressure. Above, 4 GPa, a magnetic phase (ICM3) appears, with an incommensurate propagation vector that is unique for the $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_2$ system, $\mathit{k}=(q_a,q_b,q_c;q_a\simeq 0,q_b\simeq 0.34,q_c\simeq 0.43)$. This propagation vector at the general point results in triclinic magnetic symmetry which implies an admixture of both cycloidal and proper screw spin configurations. The ICM3 phase is stable in a narrow pressure range, and above 6 GPa, the spin-density collinear structure (ICM1 phase), similar to the first ordered state at ambient pressure, takes place. Comparing the degree of lattice distortions among the magnetic phases observed at ambient pressure, we discuss the origin of the pressure-induced magnetic phase transitions in $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_2$.

We consider a model for a one-dimensional quantum wire with Rashba spin-orbit coupling and repulsive interactions, proximity coupled to a conventional $s$-wave superconductor. Using a combination of Hartree-Fock and density matrix renormalization group calculations, we show that for sufficiently strong interactions in the wire, a time-reversal-invariant topological superconducting phase can be stabilized in the absence of an external magnetic field. This phase supports two zero-energy Majorana bound states at each end, which are protected by time-reversal symmetry. The mechanism for the formation of this phase is a reversal of the sign of the effective pair potential in the wire, due to the repulsive interactions. We calculate the differential conductance into the wire and its dependence on an applied magnetic field using the scattering-matrix formalism. The behavior of the zero-bias anomaly as a function of the field direction can serve as a distinct experimental signature of the topological phase.

We have synthesized single crystals of ${\mathrm{Na}}_2$(${\mathrm{Ir}}_{1-x}$${\mathrm{Ti}}_x$)${\mathrm{O}}_3$ and polycrystals of ${\mathrm{Li}}_2$(${\mathrm{Ir}}_{1-x}$${\mathrm{Ti}}_x$)${\mathrm{O}}_3$ and studied the effect of magnetic depletion on the magnetic properties by measurements of the magnetic susceptibility, specific heat, and magnetocaloric effect at temperatures down to 0.1 K. In both systems, the nonmagnetic substitution rapidly changes the magnetically ordered ground state into a spin glass, indicating strong frustration. While for the Li system the Weiss temperature ${\Theta }_{\mathrm{W}}$ remains unchanged up to $x=0.55$, a strong decrease $|{\Theta }_{\mathrm{W}}|$ is found for the Na system. This suggests that only for the former system magnetic exchange beyond nearest neighbors is dominating. This is also corroborated by the observation of a smeared quantum phase transition in ${\mathrm{Li}}_2$(${\mathrm{Ir}}_{1-x}$${\mathrm{Ti}}_x$)${\mathrm{O}}_3$ near $x=0.5$, i.e., much beyond the site percolation threshold of the honeycomb lattice.

We present a microscopic theory for ultrafast control of solids with high-intensity terahertz frequency optical pulses. When resonant with selected infrared-active vibrations, these pulses transiently modify the crystal structure and lead to new collective electronic properties. The theory predicts the dynamical path taken by the crystal lattice using first-principles calculations of the energy surface and classical equations of motion, as well as symmetry considerations. Two classes of dynamics are identified. In the perturbative regime, displacements along the normal mode coordinate of symmetry-preserving Raman active modes can be achieved by cubic anharmonicities. This explains the light-induced insulator-to-metal transition reported experimentally in manganites. We predict a regime in which ultrafast instabilities that break crystal symmetry can be induced. This nonperturbative effect involves a quartic anharmonic coupling and occurs above a critical threshold, below which the nonlinear dynamics of the driven mode displays softening and dynamical stabilization.

We report the direct observation in real space of the charge density wave (CDW) phase transition in pristine $2H$-${\text{NbSe}}_2$ using atomic-resolution scanning tunneling microscopy. We find that static CDW order is established in nanoscale regions in the vicinity of defects at temperatures that are several times the bulk transition temperature $T_{\mathrm{CDW}}$. On lowering the temperature, the correlation length of these patches increases steadily until CDW order is established in all of space, demonstrating the crucial role played by defects in the physics of the transition region. The nanoscale CDW order has an energy- and temperature-independent wavelength. Spectroscopic imaging measurements of the real-space phase of the CDW provide indirect evidence that an energy gap in ${\text{NbSe}}_2$ occurs at 0.7 eV below the Fermi energy in the CDW phase, suggesting that strong electron-lattice interactions, and not Fermi surface physics, are the dominant cause for CDW formation in ${\text{NbSe}}_2$.

We have investigated, experimentally and theoretically, the series (${\mathrm{Na}}_{1-x}$${\mathrm{Li}}_x$)${}_2$${\mathrm{IrO}}_3$. Contrary to what has been believed so far, only for $x\le 0.25$ does the system form uniform solid solutions where Li preferentially goes to the ${\mathrm{Ir}}_2$Na planes, as observed in our density functional theory calculations and consistent with x-ray diffraction analysis. For larger Li content, as evidenced by powder x-ray diffraction, scanning electron microscopy, and density functional theory calculations, the system shows a miscibility gap and a phase separation into an ordered ${\mathrm{Na}}_3$${\mathrm{LiIr}}_2$${\mathrm{O}}_6$ phase with alternating ${\mathrm{Na}}_3$ and ${\mathrm{LiIr}}_2$${\mathrm{O}}_6$ planes, and a Li-rich phase close to pure ${\mathrm{Li}}_2$${\mathrm{IrO}}_3$. For $x\le 0.25$ we observe (1) an increase of $c/a$ with Li doping up to $x=0.25$, despite the fact that $c/a$ in pure ${\mathrm{Li}}_2$${\mathrm{IrO}}_3$ is smaller than in ${\mathrm{Na}}_2$${\mathrm{IrO}}_3$, and (2) a gradual reduction of the antiferromagnetic ordering temperature $T_N$ and ordered moment. In view of our results showing clear evidence for phase separation for $0.25\le x\le 0.6$, more detailed studies are needed to confirm the presence or absence of phase separation at the higher doping $x\sim 0.7$, where a continuum quantum phase transition has been proposed previously.

By placing the biased tip of an atomic force microscope at a specific position above a semiconductor surface we can locally shape the potential landscape. Inducing a local repulsive potential in a two-dimensional electron gas near a quantum point contact, one obtains a potential minimum which exhibits a remarkable behavior in transport experiments at high magnetic fields and low temperatures. In such an experiment, we observe distinct and reproducible oscillations in the measured conductance as a function of magnetic field, voltages, and tip position. They follow a systematic behavior consistent with a resonant tunneling mechanism. From the periodicity in the magnetic field we can find the characteristic width of this minimum to be of the order of 100 nm. Surprisingly, this value remains almost the same for different values of the bulk filling factors, although the tip position has to be adjusted by distances of the order of one micron.

We report the structure and the elementary physical properties of ${\mathrm{Ca}}_3{\mathrm{Ir}}_4{\mathrm{Ge}}_4$. This compound crystallizes in the cubic, noncentrosymmetric ${\mathrm{Na}}_3{\mathrm{Pt}}_4{\mathrm{Ge}}_4$ structure type with the space group $I\overline{4}3m$ and the unit cell dimension $a=7.56895\left(4\right)$ Å. We find that ${\mathrm{Ca}}_3{\mathrm{Ir}}_4{\mathrm{Ge}}_4$ is a superconductor with a critical temperature of $T_c\approx 1.8$ K. The bulk character of the superconducting state is evidenced by the occurrence of a well developed discontinuity in the specific heat at $T_c$ with $\Delta C/T_c\approx 38$ mJ mol${}^{-1}$ K${}^{-2}$. Well above $T_c$, the compound is a weakly paramagnetic metal with Fermi liquid behavior. The low-temperature specific-heat and resistivity measurements reveal a Kadowaki-Woods ratio comparable to that of heavy fermion materials. Furthermore, the magnetization measurements show a Stoner enhancement factor of 0.57. These findings are indicators for significant electron-electron correlation in this compound.

A charge fluctuator which is electrostatically coupled to a conducting channel may fully dephase quantum transport through the latter. Here, we address the case where a quantum dot, playing the role of a charge fluctuator, is tunnel coupled to an additional channel. In the case where the latter may support fractional charge, distinct differences from the integer case arise: Abrupt phase lapses of the transmission through the conducting channel occur (which may or may not be equal to $\pi$). This is accompanied by a cusplike suppression of the interferometer's visibility, yet no full dephasing. We interpret our findings in terms of the entanglement between the fluctuator and the conducting channels.

The Meissner effect has been directly demonstrated by depth-resolved muon spin rotation measurements in high-quality thin films of the $T^{\prime }$-structured cuprate, $T^{\prime }$-${\mathrm{La}}_{1.9}$${\mathrm{Y}}_{0.1}$${\mathrm{CuO}}_4$, to confirm bulk superconductivity ($T_c\simeq 21$ K) in its undoped state. The gradual expelling of an external magnetic field is observed over a depth range of $\sim$100 nm in films with a thickness of 275(15) nm, from which the penetration depth is deduced to be 466(22) nm. Based on this result, we argue that the true ground state of the “parent” compound of the $n$-type cuprates is not a Mott insulator but a strongly correlated metal with colossal sensitivity to apical oxygen impurities.

Transverse-field muon-spin rotation ($\mu$SR) experiments were performed on a single crystal sample of the noncentrosymmetric system MnSi. The observed angular dependence of the muon precession frequencies matches perfectly the one of the Mn-dipolar fields acting on the muons stopping at a 4$a$ position of the crystallographic structure. The data provide a precise determination of the magnetic dipolar tensor. In addition, we have calculated the shape of the field distribution expected below the magnetic transition temperature $T_C$ at the 4$a$ muon site when no external magnetic field is applied. We show that this field distribution is consistent with the one reported by zero-field $\mu$SR studies. Finally, we present ab initio calculations based on the density-functional theory which confirm the position of the muon stopping site inferred from transverse field $\mu$SR. In view of the presented evidence we conclude that the $\mu$SR response of MnSi can be perfectly and fully understood without invoking a hypothetical magnetic polaron state.

Using a method called momentum polarization, we study the quasiparticle topological spin and the edge-state chiral central charge of non-Abelian topological ordered states described by Gutzwiller-projected wave functions. Our results verify that the fractional Chern insulator state obtained by Gutzwiller projection of two partons in bands of Chern number 2 is described by SU(2)${}_2$ Chern-Simons theory coupled to fermions, rather than the pure $\text{SU}{\left(2\right)}_2$ Chern-Simons theory. In addition, by introducing an adiabatic deformation between one Chern-number-2 band and two Chern-number-1 bands, we show that the topological order in the Gutzwiller-projected state does not always agree with the expectation of topological field theory. Even if the parton mean-field state is adiabatically deformed, the Gutzwiller projection can introduce a topological phase transition between Abelian and non-Abelian topologically ordered states. Our approach applies to more general topologically ordered states described by Gutzwiller-projected wave functions.