We propose a nonperturbative renormalization-group (NPRG) approach to fermion systems in the two-particle-irreducible (2PI) effective action formalism, based on an exact RG equation for the Luttinger-Ward functional. This approach enables us to describe phases with spontaneously broken symmetries while satisfying the Mermin-Wagner theorem. We show that it is possible to choose the Hartree-Fock random phase approximation theory as initial condition of the RG flow and argue that the 2PI-NPRG is not restricted to the weak-coupling limit. An expansion of the Luttinger-Ward functional about the minimum of the 2PI effective action including only the two-particle 2PI vertex leads to nontrivial RG equations where interactions between fermions and collective excitations naturally emerge.

The fluorescence of single colloidal thick-shell CdSe/CdS nanocrystals (NCs), at cryogenic temperature (4 K) and room temperature (RT), is studied using the intensity autocorrelation function (ACF) and lifetime measurements. The radiative and Auger decay rates corresponding to the desexcitation of the charged biexcitonic state are determined through an original method of photon postselection. Especially, the charged biexciton quantum yield increases from about 15% at RT to 60% at 4 K. The high inhibition of Auger recombination already observed for the trion state of CdSe/CdS NCs at low temperature is also demonstrated for the charged biexcitonic state. At 4 K, the ACF is equal to 1 for time scales ranging from 50 ns to 200 ms. In contrast with RT operation, the intensity of the trion emission is then perfectly stable and no blinking is observed. All the results highlight the strong confinement of the charge carriers in the CdSe core.

The envelope function method is applied to hole and exciton states in wurtzite and zinc-blende structure cylindrical nanowires using the axial Kohn-Luttinger Hamiltonian including a crystal-field splitting for the wurtzite case. The quantized states are found to be mixtures of heavy- and light-hole band derived states. Explicit expressions for the mixing coefficients and the conditions giving the quantized energy states are derived. These are then applied to obtain the relative intensity of light emitted polarized parallel and perpendicular to the nanowire for the lowest-energy excitons. Slightly different expressions are obtained in the weak quantization and strong quantization limits. In the latter case, an overlap integral of the hole and electron envelope function is involved, while in the former case only an integral over the hole envelope function is required. An expression for the degree of polarization of the spectrally integrated photoluminescence as a function of temperature is obtained by summing over the excitons within the integration range. The degree of polarization as a function of temperature is explored numerically as a function of nanowire radius and crystal-field splitting for GaAs and GaN nanowires. Examples of complete reversal of the polarization are illustrated.

Based on first-principles calculations, we demonstrate that Co-decorated silicene can host a quantum anomalous Hall state. The exchange field induced by the Co atoms combined with the strong spin-orbit coupling of the silicene opens a nontrivial band gap at the $K$ point. As compared to other transition metals, Co-decorated silicene is unique in this respect, since usually hybridization and spin-polarization induced in the silicene suppress a quantum anomalous Hall state.

We study the effect of electrostatic disorder on the conductivity of a three-dimensional antiferromagnetic insulator (a stack of quantum anomalous Hall layers with staggered magnetization). The phase diagram contains regions where the increase of disorder first causes the appearance of surface conduction (via a topological phase transition), followed by the appearance of bulk conduction (via a metal-insulator transition). The conducting surface states are stabilized by an effective time-reversal symmetry that is broken locally by the disorder but restored on long length scales. A simple self-consistent Born approximation reliably locates the boundaries of this so-called “statistical” topological phase.

We identify $dd$ excitations in the quasi-one-dimensional compound Ca${}_2$Y${}_2$Cu${}_5$O${}_{10}$ using resonant inelastic x-ray scattering. By tuning across the Cu $L_3$ edge, we observe abrupt shifts in the $dd$-peak positions as a function of incident photon energy. This observation demonstrates orbital-specific coupling of the high-energy excited states of the system to the low-energy degrees of freedom. A Franck-Condon treatment of electron-lattice coupling, consistent with other measurements in this compound, reproduces these shifts, explains the Gaussian line shapes, and highlights charge-orbital-lattice renormalization in the high-energy $d$ manifold.

The correlated motion of a positron surrounded by electrons is a fundamental many-body problem. We approach this by modeling the momentum density of annihilating electron-positron pairs using the framework of reduced density matrices, natural orbitals, and natural geminals (electron-positron pair wave functions) of the quantum theory of many-particle systems. We find that an expression based on the natural geminals provides an exact, unique, and compact expression for the momentum density. The natural geminals can be used to define and to determine enhancement factors for enhancement models going beyond the independent-particle model for a better understanding of the results of positron annihilation experiments.

Here we present a systematic study of the dynamics of a single quantum emitter near a flat metal-dielectric interface. We identify the key elements that determine the onset of reversibility in these systems by using a formalism suited for absorbing media and through an exact integration of the dynamics. Moreover, when the quantum emitter separation from the surface is small, we are able to describe the dynamics within a pseudomode description that yields analytical understanding and allows more powerful calculations.

At the spin transition point of $\nu =2/3$ quantum Hall states, nuclear spins in a two-dimensional electron gas are polarized by an electric current. Using GaAs/AlGaAs double-quantum-well samples, we first observed the spatial diffusion of nuclear spin polarization between the two layers when the nuclear spin polarization is current induced in one layer. By numerical simulation, we estimated the diffusion constant of the nuclear spin polarization to be $15\pm 7{\mathrm{nm}}^2/\mathrm{s}$.

We present the expression for the quasiparticle vertex function ${\Gamma }^{\omega }(K_F,P_F)$ (proportional to the Landau interaction function) in a 2D Fermi liquid (FL) near an instability towards antiferromagnetism. This function is relevant in many ways in the context of metallic quantum criticality. Previous studies have found that near a quantum critical point, the system enters into a regime in which the fermionic self-energy is large near hot spots on the Fermi surface [points on the Fermi surface connected by the antiferromagnetic ordering vector $q_{\pi }=(\pi ,\pi )$] and has much stronger dependence on frequency than on momentum. We show that in this regime, which we termed a critical FL, the conventional random-phase-approximation- (RPA) type approach breaks down, and to properly calculate the vertex function one has to sum up an infinite series of terms which were explicitly excluded in the conventional treatment. Besides, we show that, to properly describe the spin component of ${\Gamma }^{\omega }(K_F,P_F)$ even in an ordinary FL, one has to add Aslamazov-Larkin (AL) terms to the RPA vertex. We show that the total ${\Gamma }^{\omega }(K_F,P_F)$ is larger in a critical FL than in an ordinary FL, roughly by an extra power of magnetic correlation length $\xi$, which diverges at the quantum critical point. However, the enhancement of ${\Gamma }^{\omega }(K_F,P_F)$ is highly nonuniform: It holds only when, for one of the two momentum variables, the distance from a hot spot along the Fermi surface is much larger than for the other one. This fact renders our case different from quantum criticality at small momentum, where the enhancement of ${\Gamma }^{\omega }(K_F,P_F)$ was found to be homogeneous. We show that the charge and spin components of the total vertex function satisfy the universal relations following from the Ward identities related to the conservation of the particle number and the total spin. We show that in a critical FL, the Ward identity involves ${\Gamma }^{\omega }(K_F,P_F)$ taken between particles on the FS. We find that the charge and spin components of ${\Gamma }^{\omega }(K_F,P_F)$ are identical to leading order in the magnetic correlation length. We use our results for ${\Gamma }^{\omega }(K_F,P_F)$ and for the quasiparticle residue to derive the Landau parameters $F_c^{l=0}=F_s^{l=0}$, the density of states, and the uniform ($q=0$) charge and spin susceptibilities ${\chi }_c^{l=0}={\chi }_s^{l=0}$. We show that the density of states $N_F$ diverges as $log\xi$; however, $F_{c,s}^{l=0}$ also diverge as $log\xi$, such that the total ${\chi }_{c,s}^{(l=0)}\propto N_F/(1+F_c^{l=0})$ remain finite at $\xi =\infty$. We show that at weak coupling these susceptibilities are parametrically smaller than for free fermions.

The phonons at the zone center are calculated for the layered material $V_2{\mathrm{O}}_5$ using density functional perturbation theory and are compared with experimental infrared and Raman spectra from literature. We find that significantly better agreement is obtained when the pseudopotential treats vanadium semicore states $3s$ and $3p$ as bands. Remaining discrepancies are shown to be related to the local density approximation overestimate of the bond-stretch mode frequencies. The vibrational mode patterns are studied and presented in detail. The same method is then applied to well-separated monolayers. We find significant changes in some phonon frequencies. In particular, the highest-frequency vanadium vanadyl-oxygen stretch modes show a blue-shift of order 6%–8%. The origin of this blue-shift is analyzed in terms of the force-constant changes between bulk and monolayer and is found to arise from a delicate balance of short- and long-range dipolar force components. The latter are affected by the changes in dielectric constants and in the Born-effective charges. The red-shifts of some of the low-frequency modes are found also to be related to a reduction in force constants within the layer, rather than the removal of interlayer bonds. In this case, it is primarily motions along the $x$ direction that are affected. The static and high-frequency dielectric constants are both found to be reduced in the monolayer.

We study the angular and energy dependence of surface and bulk plasmon losses accompanying deep core excitations in simple metals. Here full multiple scatterings of photoelectrons are taken into account before and after the plasmon losses within the quantum Landau formula, which can describe overall features of the photoemission bands. For example, multiple plasmon loss features can be calculated by use of the formula. Two simple metals, Al and Na, are studied here. The depth profiles of the plasmon losses are strongly influenced by the elastic scatterings. The model assuming single elastic scatterings overestimates the losses from deep emitters due to the forward focusing effects, whereas the model accounting for full multiple scatterings gives a much rapidly decaying function of the depth due to the defocusing effects and rich structures due to the photoelectron diffraction. The single elastic scattering approximation gives a poor result both for the depth profiles and for the loss spectra. The present multiple scattering calculations successfully explain the azimuthal dependence of the loss spectra, which reflect the local geometry around the emitters.

The spin of a single electron in a suspended carbon nanotube can be read out by using its coupling to the nanomechanical motion of the nanotube. To show this, we consider a single electron confined within a quantum dot formed by the suspended carbon nanotube. The spin-orbit interaction induces a coupling between the spin and one of the bending modes of the suspended part of the nanotube. We calculate the response of the system to pulsed external driving of the mechanical motion using a Jaynes-Cummings model. To account for resonator damping, we solve a quantum master equation, with parameters comparable to those used in recent experiments, and show how information about the spin state of the system can be acquired by measuring the mechanical motion of the nanotube. The latter can be detected by observing the current through a nearby charge sensor.

We investigate the adsorption of a single tetracyanoethylene (TCNE) molecule on the silver (001) surface. Adsorption structures, electronic properties, and scanning tunneling microscopy (STM) images are calculated within density-functional theory. Adsorption occurs most favorably in on-top configuration, with the C=C double bond directly above a silver atom and the four N atoms bound to four neighboring Ag atoms. The lowest unoccupied molecular orbital of TCNE becomes occupied due to electron transfer from the substrate. This state dominates the electronic spectrum and the STM image at moderately negative bias. We discuss and employ a spatial extrapolation technique for the calculation of STM and scanning tunneling spectroscopy (STS) images. Our calculated images are in good agreement with experimental data.

A theory based in the semiclassical eikonal approximation is developed to describe energy transfer in the collision of an atomic projectile with a surface which is either ordered or disordered. This theory is extended from the quantum mechanical regime to the classical regime of complete quantum decoherence via the Bohr correspondence principle of large numbers of excited quanta. In the quantum mechanical regime, the theory reproduces the well-known eikonal approximation for elastic collisions, provides a simple and useful expression for single-phonon inelastic scattering, and leads to further expressions for multiple-phonon transfers. In the classical limit, the theory produces an expression that includes the effects of surface corrugation in addition to the excitations of large numbers of phonons. This theory shows that a simple measurement of the most probable intensity of energy-resolved scattering spectra taken as a function of surface temperature, with all other experimentally controllable parameters held fixed, can be used to extract the surface corrugation amplitude. Comparisons with data for Ar scattering from the molten metals Ga and In show good agreement with the measured energy-resolved spectra, the in-plane angular distributions, the out-of-plane angular distributions, and produces values for the corrugation amplitudes that range from 10% to 30% of the average interparticle spacing.

We present a combined experimental and theoretical study of the spin-$\frac{1}{2}$ compound CuP${}_2$O${}_6$ that features a network of two-dimensional (2D) antiferromagnetic (AFM) square planes, interconnected via one-dimensional (1D) AFM spin chains. Magnetic susceptibility, high-field magnetization, and electron spin resonance (ESR) data, as well as microscopic density-functional band-structure calculations and subsequent quantum Monte Carlo simulations, show that the coupling $J_{2\mathrm{D}}\simeq 40$ K in the layers is an order of magnitude larger than $J_{1\mathrm{D}}\simeq 3$ K in the chains. Below $T_N\simeq 8$ K, CuP${}_2$O${}_6$ develops long-range order, as evidenced by a weak net moment on the 2D planes induced by anisotropic magnetic interactions of Dzyaloshinsky-Moriya type. A striking feature of this 3D ordering transition is that the 1D moments grow significantly slower than the ones on the 2D units, which is evidenced by the persistent paramagnetic ESR signal below $T_N$. Compared to typical quasi-2D magnets, the ordering temperature of CuP${}_2$O${}_6$ $T_N/J_{2\mathrm{D}}\simeq 0.2$ is unusually low, showing that weakly coupled spins sandwiched between 2D magnetic units effectively decouple these units and impede the long-range ordering.

Patterned nanostructures on the order of 200 nm $\times$ 200 nm of the itinerant ferromagnet ${\mathrm{SrRuO}}_3$ give rise to superparamagnetic behavior below the Curie temperature ($\sim 150\mathrm{K}$) down to a sample-dependent blocking temperature. We monitor the superparamagnetic fluctuations of an individual volume and demonstrate that the field dependence of the time-averaged magnetization is well described by the Langevin equation. On the other hand, the rate of the fluctuations suggests that the volume in which the magnetization fluctuates is smaller by more than an order of magnitude. We suggest that switching via nucleation followed by propagation gives rise to Langevin behavior of the total volume, whereas the switching rate is determined by a much smaller nucleation volume.

We report the results of a zero-field muon-spin relaxation (ZF-$\mu$SR) study of superconducting Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ ($0.5\le x\le 0.9$) in search of weak spontaneous internal magnetic fields associated with proposed time-reversal-symmetry-breaking mixed pairing states. The measurements were performed on polycrystalline samples, which do not exhibit the mesoscopic phase separation previously observed in single crystals of Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$. No evidence of spontaneous internal magnetic fields is found in any of the samples at temperatures down to $T\sim 0.02$ K.

Coupling of the charge carriers in the high-temperature superconducting oxides to bosonic modes has been widely reported using a variety of experimental probes. These include angular resolved photoemission (ARPES), scanning tunneling spectroscopy, Raman scattering, and infrared optical spectroscopy. The energy scale investigated has been mostly limited to a relatively small range up to 300 meV or so. Although some ARPES experiments report boson structure up to 800 meV in the dressed electron dispersion curves, the data are not analyzed to recover the spectral density of the fluctuation spectrum. We have extended to higher energies up to 2.2 eV the usual maximum entropy technique used to invert optical data so as to obtain an electron-boson spectral density. This has required that we include in our inversions, the calculated (local-density approximation) particle-hole symmetrized energy-dependent electronic density of states. Our analysis reveals that significant spectral weight remains in the fluctuation spectra up to 2.2 eV in the Bi-2212 family and 1.2 eV in Bi-2201 for all doping levels considered.

We study the thermal transport properties of FeSb${}_2$, a promising thermoelectric material for cooling applications at cryogenic temperatures. A first-principles formalism based on density functional theory and ab initio lattice dynamics is applied. We calculate the electronic structure, the phonon dispersion relation, the bulk thermal expansion coefficient, and the thermal conductivity of FeSb${}_2$ and compare them with other calculations and experiments. Our calculation is found insufficient to fully explain the temperature dependence of the lattice thermal conductivity of FeSb${}_2$, suggesting new scattering mechanisms in this strongly correlated system. The mean free path distribution of different phonon modes is also calculated, which may provide valuable guidance in designing nanostructures for reducing the thermal conductivity of FeSb${}_2$ and improving the thermoelectric figure of merit zT.