Cooperative Ce and Yb valence fluctuations have recently been proposed as the mechanism responsible for stabilizing correlated electron phenomena in Ce${}_{1-x}$Yb${}_x$CoIn${}_5$ over an unexpectedly large range of concentrations. In order to better understand the origins and character of this stability, we have measured the effect of applied pressure on relevant energy scales such as the superconducting critical ($T_c$) and Kondo-lattice coherence ($T^{*}$) temperatures of Ce${}_{1-x}{R}_x$CoIn${}_5$ with $R=\text{Yb}$, Y, and Gd. Electrical resistivity measurements were performed under applied pressure on samples doped with intermediate-valent Yb and stable-valent Gd and Y, and the responses of $T_c$ and $T^{*}$ to increased pressure in these systems are compared. The character of $T_c\left(P\right)$ and $T^{*}\left(P\right)$ in Ce${}_{1-x}{R}_x$CoIn${}_5$ depends only on their respective ambient-pressure values $T_c\left(0\right)$ and $T^{*}\left(0\right)$, independent of the electronic configuration of $R$ or concentration $x$. The consequences of this result are discussed within the context of possible cooperative valence fluctuations in Ce${}_{1-x}$Yb${}_x$CoIn${}_5$.

We consider possible exotic ground states of quantum spin ice as realized in rare earth pyrochlores. Prior work [Savary and Balents, Phys. Rev. Lett. 108, 037202 (2012).] introduced a gauge mean-field theory (gMFT) to treat spin or pseudospin Hamiltonians for such systems, reformulated as a problem of bosonic spinons coupled to a $U\left(1\right)$ gauge field. We extend gMFT to treat the most general nearest-neighbor exchange Hamiltonian, which contains a further exchange interaction. This term leads to interactions between spinons and requires a significant extension of gMFT, which we provide. As an application, we focus especially on the non-Kramers materials Pr${}_{2}T{M}_2$O${}_7$ ($TM=$ Sn, Zr, Hf, and Ir), for which the additional term is especially important, but for which an Ising-planar exchange coupling discussed previously is forbidden by time-reversal symmetry. In this case, when the planar $\mathit{XY}$ exchange is unfrustrated, we perform a full analysis and find three quantum ground states: a $U\left(1\right)$ quantum spin liquid (QSL), an antiferroquadrupolar ordered state and a noncoplanar ferroquadrupolar ordered one. We also consider the case of frustrated $\mathit{XY}$ exchange, and find that it favors a $\pi$-flux QSL, with an emergent line degeneracy of low-energy spinon excitations. This feature greatly enhances the stability of the QSL with respect to classical ordering.

The effect of a small substitution of Mn with Al in TbMnO${}_3$ has been studied. We report results of heat capacity, magnetization, and dielectric constant studies in TbMn${}_{1-x}$Al${}_x$O${}_3$ compounds ($x$ ≤ 0.1). Al has the same valence as substituted Mn but is nonmagnetic and its small size gives rise to microstructural strain which affects the multiferroic properties of the parent compound. Long-range antiferromagnetic ordering is observed in all compounds but the transition temperature decreases as the Al content increases. TbMn${}_{0.95}$Al${}_{0.05}$O${}_3$ exhibits a ferroelectric phase transition which is absent in TbMn${}_{0.9}$Al${}_{0.1}$O${}_3$. The dielectric constant of the latter compound reveals a relaxor behavior suggesting the presence of nanosize polar domains for this compound. A neutron diffraction study on a single crystal of TbMn${}_{0.9}$Al${}_{0.1}$O${}_3$ reveals that Mn shows a sinusoidal incommensurate ordering down to low temperature. Tb moments exhibit an incommensurate short-range ordering but the application of a magnetic field leads to metamagnetic transitions. In particular, a field parallel to the $b$ axis induces a commensurate long-range ordering of Tb of type $C_x$$F_y$. The magnetic field also affects the magnetic structure of Mn${}^{3+}$ moments at low temperature which develop an incommensurate cycloid ordering in the $ab$ plane. This result suggests that dilution of a magnetic multiferroic with a small nonmagnetic atom might yield materials with a relaxor to ferroelectric transition driven by a magnetic field.

We construct a two-dimensional (2D) quantum spin model that realizes an Ising paramagnet with gapless edge modes protected by Ising symmetry. This model provides an example of a “symmetry-protected topological phase.” We describe a simple physical construction that distinguishes this system from a conventional paramagnet: We couple the system to a ${\mathbb{Z}}_2$ gauge field and then show that the $\pi$-flux excitations have different braiding statistics from that of a usual paramagnet. In addition, we show that these braiding statistics directly imply the existence of protected edge modes. Finally, we analyze a particular microscopic model for the edge and derive a field theoretic description of the low energy excitations. We believe that the braiding statistics approach outlined in this paper can be generalized to a large class of symmetry-protected topological phases.

We study resonating valence bond (RVB) states in the projected entangled pair states (PEPS) formalism. Based on symmetries in the PEPS description, we establish relations between the toric code state, the orthogonal dimer state, and the $\mathrm{SU}\left(2\right)$ singlet RVB state on the kagome lattice: We prove the equivalence of toric code and dimer state, and devise an interpolation between the dimer state and the RVB state. This interpolation corresponds to a continuous path in Hamiltonian space, proving that the RVB state is the fourfold degenerate ground state of a local Hamiltonian on the (finite) kagome lattice. We investigate this interpolation using numerical PEPS methods, studying the decay of correlation functions, the change of overlap, and the entanglement spectrum, none of which exhibits signs of a phase transition.

We report first-principles calculations for a ferroelectric organic crystal of phenazine and chloranilic acid molecules. Weak intermolecular interactions are properly treated by using a second version of the van der Waals density functional known as vdW-DF2 [K. Lee et al., Phys. Rev. B 82, 081101 (2010)]. Lattice constants, total energies, spontaneous electric polarizations, phonon modes and frequencies, and the energy barrier of proton transfer are calculated and compared with PBE and experiments whenever possible. We show that the donation of one proton from a chloranilic acid molecule to a neighboring phenazine molecule is energetically favorable. This proton transfer is the key structural change that breaks the centrosymmetry and leads to the ferroelectric structure. However, there is no unstable phonon associated with the proton transfer, and an energy barrier of 8 meV is found between the paraelectric and ferroelectric states.

The low-temperature elementary spin excitations in the AFM molecular wheel Fe${}_{18}$ were studied experimentally by inelastic neutron scattering and theoretically by modern numerical methods, such as dynamical density matrix renormalization group or quantum Monte Carlo techniques, and analytical spin-wave theory calculations. Fe${}_{18}$ involves eighteen spin-5/2 Fe${}^{\mathrm{III}}$ ions with a Hilbert space dimension of $\sim$${10}^{14}$, constituting a physical system that is situated in a region between microscopic and macroscopic. The combined experimental and theoretical approach allowed us to characterize and discuss the magnetic properties of Fe${}_{18}$ in great detail. It is demonstrated that physical concepts such as the rotational-band or $L\mathit{\text{and}}E$-band concepts developed for smaller rings are still applicable. In particular, the higher-lying low-temperature elementary spin excitations in Fe${}_{18}$ or AFM wheels, in general, are of discrete antiferromagnetic spin-wave character.

Native defects in pnictogen chalcogenides are currently a great barrier toward the realization of the exotic properties of this class of topological insulators. Previous first-principles results of low-energy defects in Bi${}_2$Te${}_3$ and Sb${}_2$Te${}_3$ are in qualitative agreement with experiments. However, for Bi${}_2$Se${}_3$ the calculated low-energy defects are antisites, opposed to the Se vacancy ($V_{\mathrm{Se}}$) as observed experimentally. We find that the inclusion of spin-orbit interaction drastically shifts the band-edge energies of the bulk states with respect to defect transition energies. It turns the Bi antisite (Bi${}_{\mathrm{Se}}$) from an acceptor to a donor and makes $V_{\mathrm{Se}}$ more stable than Bi${}_{\mathrm{Se}}$. This brings the calculated results for native defects in pnictogen chalcogenides into agreement with experiments.

We propose and demonstrate a new method to probe local spin polarization in semiconductor microdevices at low and zero magnetic fields. By connecting a single-lead quantum dot to a semiconductor microdevice and monitoring electron tunneling into singlet and triplet states in the dot, we can detect the local spin polarization formed in the target device. We confirm the validity of this detection scheme utilizing spin-split quantum Hall edge states. We also observe nonzero local spin polarization at the device edge in low magnetic fields, which is not detectable with conventional macroscopic probes.

The “spin-ice” state found in the rare-earth pyrochlore magnets Ho${}_2$Ti${}_2$O${}_7$ and Dy${}_2$Ti${}_2$O${}_7$ offers a beautiful realization of classical magnetostatics, complete with magnetic monopole excitations. It has been suggested that in “quantum spin-ice” materials, quantum-mechanical tunneling between different ice configurations, could convert the magnetostatics of spin ice into a quantum spin liquid that realizes a fully dynamical, lattice analogue of quantum electromagnetism. Here, we explore how such a state might manifest itself in experiment, within the minimal microscopic model of a such a quantum spin ice. We develop a lattice field theory for this model, and use this to make explicit predictions for the dynamical structure factor that would be observed in neutron scattering experiments on a quantum spin ice. We find that “pinch points,” which are the signal feature of a classical spin ice, fade away as a quantum ice is cooled to its zero-temperature ground state. We also make explicit predictions for the ghostly, linearly dispersing magnetic excitations which are the “photons” of this emergent electromagnetism. The predictions of this field theory are shown to be in quantitative agreement with quantum Monte Carlo simulations at zero temperature.

We map out the possible ordered states in bilayer graphene at the neutrality point by extending the previous renormalization group treatment of many-body instabilities to finite temperature, trigonal warping and externally applied perpendicular electric field. We were able to analytically determine all outcomes of the RG flow equations for the nine four-fermion coupling constants. While the full phase diagram exhibits a rich structure, we confirm that when forward scattering dominates, the only ordering tendency with divergent susceptibility at finite temperature is the nematic. At finite temperature, this result is stable with respect to small back and layer imbalance scattering; further increasing their strength leads to the layer antiferromagnet. We also determine conditions for other ordered states to appear and compare our results to the special cases of attractive and repulsive Hubbard models where exact results are available.

In a cubic topological insulator (TI), there is a band inversion whereby the $s$-like ${\Gamma }_{6\mathrm{c}}$ conduction band is below the $p$-like ${\Gamma }_{7\mathrm{v}}+{\Gamma }_{8\mathrm{v}}$ valence bands by the “inversion energy” ${\Delta }_i<0$. In TIs based on the zinc-blende structure such as HgTe, the Fermi energy intersects the degenerate ${\Gamma }_{8\mathrm{v}}$ state so the insulating gap E${}_g$ between occupied and unoccupied bands vanishes. To achieve an insulating gap E${}_g>0$ critical for TI applications, one often needs to resort to structural manipulations such as structural symmetry lowering (e.g., Bi${}_2$Se${}_3$), strain, or quantum confinement. However, these methods have thus far opened an insulating gap of only $<$0.1 eV. Here we point out that there is an electronic rather than structural way to affect an insulating gap in a TI: if one can invert the spin-orbit levels and place ${\Gamma }_{8\mathrm{v}}$ below ${\Gamma }_{7\mathrm{v}}$ (“negative spin-orbit splitting”), one can realize band inversion (${\Delta }_i<0$) with a large insulating gap (E${}_g$ up to 0.5 eV). We outline design principles to create negative spin-orbit splitting: hybridization of $d$ orbitals into $p$-like states. This general principle is illustrated in the “filled tetrahedral structures” (FTS) demonstrating via GW and density functional theory (DFT) calculations E${}_g>0$ with ${\Delta }_i<0$, albeit in a metastable form of FTS.

Engineering devices with a large electrical response to magnetic field is of fundamental importance for a range of applications such as magnetic field sensing and magnetic read heads. We show that a colossal nonsaturating linear magnetoresistance (NLMR) arises in two-dimensional electron systems hosted in a GaAs/AlGaAs heterostructure in the strongly insulating regime. When operated at high source-drain bias, the magnetoresistance of our devices increases almost linearly with magnetic field, reaching nearly 10 000$\%$ at 8 T, thus surpassing many known nonmagnetic materials that exhibit giant NLMR. The temperature dependence and mobility analysis indicate that the NLMR has a purely classical origin, driven by nanoscale inhomogeneities. A large NLMR combined with small device dimensions makes these systems an attractive candidate for on-chip magnetic field sensing.

We study, theoretically and experimentally, disorder-induced resonances in randomly layered samples and develop an algorithm for the detection and characterization of the effective cavities that give rise to these resonances. This algorithm enables us to find the eigenfrequencies and to pinpoint the locations of the resonant cavities that appear in individual realizations of random samples for arbitrary distributions of the widths and refractive indices of the layers. Each cavity is formed in a region whose size is a few localization lengths. Its eigenfrequency is independent of the location inside the sample and does not change if the total length of the sample is increased by, for example, adding more scatterers on the sides. We show that the total number of cavities $N_{\mathrm{cav}}$ and resonances $N_{\mathrm{res}}$ per unit frequency interval is uniquely determined by the size of the disordered system and is independent of the strength of the disorder. In an active amplifying medium, part of the cavities may host lasing modes whose number is less than $N_{\mathrm{res}}$. The ensemble of lasing cavities behaves as distributed feedback lasers, provided that the gain in the medium exceeds the lasing threshold, which is specific for each cavity. We present the results of experiments carried out with single-mode optical fibers with gain and randomly located resonant Bragg reflectors (periodic gratings). When the fiber was illuminated by a pumping laser with an intensity high enough to overcome the lasing threshold, the resonances revealed themselves by peaks in the emission spectrum. Our experimental results are in good agreement with the theory presented here.

Motivated by recent experiments, we study theoretically the full counting statistics of radiation emitted below the threshold of parametric resonance in a Josephson-junction circuit. In contrast to most optical systems, a significant part of emitted radiation can be collected and converted to an output signal. This permits studying the correlations of the radiation. To quantify the correlations, we derive a closed expression for full counting statistics in the limit of long measurement times. We demonstrate that the statistics can be interpreted in terms of uncorrelated bursts, each encompassing $2N$ photons; this accounts for the bunching of the photon pairs produced in the course of the parametric resonance. We present the details of the burst rates. In addition, we study the time correlations within the bursts and discuss experimental signatures of the statistics deriving the frequency-resolved cross-correlations.

We consider interfacial phenomena accompanying bulk quantum phase transitions in the presence of surface fields. On general grounds we argue that the surface contribution to the system free energy involves a line of singularities characteristic of an interfacial phase transition, occurring below the bulk transition temperature $T_c$ down to $T=0$. This implies the occurrence of an interfacial quantum critical regime extending into finite temperatures and located within the portion of the phase diagram where the bulk is ordered. Even in situations where the bulk order sets in discontinuously at $T=0$, the system's behavior at the boundary may be controlled by a divergent length scale if the tricritical temperature is sufficiently low. Relying on an effective interfacial model we compute the surface phase diagram in bulk spatial dimensionality $d⩾2$ and extract the values of the exponents describing the interfacial singularities in $d⩾3$.

Semiconducting nanowires (NWs) are good candidates for new optoelectronic or photovoltaic devices due to their excellent ability to guide, scatter, or absorb light, from near ultraviolet to near infrared. The existence of morphology-dependent optical resonances opens a promising route to overcome the intrinsic limitations of the constituent material and optimize their interaction with light. We propose a thorough investigation of the optical properties of Si${}_{1-x}$Ge${}_x$ alloy nanowires addressing the influence of NW diameter, composition, light polarization, and angle of incidence on their scattering and absorption. Our results clearly show that the Ge composition provides an additional degree of freedom to tailor the optical response of these one-dimensional nano-objects and that resonant enhancement of both absorption and scattering can be obtained in the infrared range at relatively small diameters compared to pure Si nanowires. These results are confirmed by complementary light scattering and Raman spectroscopy experiments using confocal dark field optical microscopy on individual nanowires fabricated by Au-catalyzed vapor-liquid-solid synthesis.

Directed assembly of an array of Ru nanoclusters (NCs) is achieved by deposition of Ru at around room temperature on a single layer of graphene supported on Ru(0001). In this system, directed assembly is guided by the periodic moiré structure of the buckled graphene sheet. Behavior is analyzed utilizing both scanning tunneling microscopy and atomistic lattice-gas modeling together with kinetic Monte Carlo simulation. We elucidate the kinetics of NC nucleation and growth, specifically assessing the coverage dependence of the NC density and height distribution. In addition, we provide a detailed characterization of the development of short-range spatial order within the NC array, identifying a tendency for row formation.

One of the most successful theories of a non-Fermi-liquid metallic state is the composite Fermi-liquid (CFL) theory of the half-filled Landau level. In this paper, we study continuous quantum phase transitions out of the CFL state and into a Landau Fermi liquid, in the limit of no disorder and fixed particle number. This transition can be induced by tuning the bandwidth of the Landau level relative to the interaction energy, for instance through an externally applied periodic potential. We find a transition to the Landau Fermi liquid through a gapless Mott insulator with a Fermi surface of neutral fermionic excitations. In the presence of spatial symmetries, we also find a direct continuous transition between the CFL and the Landau Fermi liquid. The transitions have a number of characteristic observable signatures, including the presence of two crossover temperature scales, resistivity jumps, and vanishing compressibility. When the composite fermions are paired instead, our results imply quantum critical points between various non-Abelian topological states, including the $\nu =1/2$ Moore-Read Pfaffian [Ising $\times$ $U\left(1\right)$ topological order], a version of the Kitaev B phase (Ising topological order), and paired electronic superconductors. To study such transitions, we use a projective construction of the CFL, which goes beyond the conventional framework of flux attachment to include a broader set of quantum fluctuations. These considerations suggest a possible route to fractionalized Mott insulators by starting with fractional quantum Hall states and tuning the Landau-level bandwidth.

Near a critical point, the equilibrium relaxation time of a system diverges and any change of control/thermodynamic parameters leads to nonequilibrium behavior. The Kibble-Zurek problem is to determine the dynamical evolution of the system parametrically close to its critical point when the change is parametrically slow. The nonequilibrium behavior in this limit is controlled entirely by the critical point and the details of the trajectory of the system in parameter space (the protocol) close to the critical point. Together, they define a universality class consisting of critical exponents, discussed in the seminal work by Kibble and Zurek, and scaling functions for physical quantities, which have not been discussed hitherto. In this article, we give an extended and pedagogical discussion of the universal content in the Kibble-Zurek problem. We formally define a scaling limit for physical quantities near classical and quantum transitions for different sets of protocols. We report computations of a few scaling functions in model Gaussian and large-$N$ problems and prove their universality with respect to protocol choice. We also introduce a protocol in which the critical point is approached asymptotically at late times with the system marginally out of equilibrium, wherein logarithmic violations to scaling and anomalous dimensions occur even in the simple Gaussian problem.