Optical spectroscopy is performed for $c$-plane homoepitaxial aluminum nitride (AlN) films. The temperature dependence of the polarization-resolved photoluminescence spectra reveals the exciton fine structure. The experimental results demonstrate that the electron-hole exchange interaction energy ($j$) in AlN is $j=6.8\text{meV}$, which is the largest value for typical III-V and II-VI compound semiconductors. We propose the effective interatomic distance as the criterion of the electron-hole exchange interaction energy, revealing a universal rule. This study should encourage potential applications of excitonic optoelectronic devices in nitride semiconductors similar to those using II-VI compound semiconductors.

We study a class of $\text{SU}\left(N\right)$ Heisenberg models, describing Mott insulators of fermionic ultracold alkaline earth atoms on the three-dimensional simple cubic lattice. Based on an earlier semiclassical analysis, magnetic order is unlikely, and we focus instead on a solvable large-$N$ limit designed to address the competition among nonmagnetic ground states. We find a rich phase diagram as a function of the filling parameter $k$, composed of a variety of ground states spontaneously breaking lattice symmetries, and in some cases also time-reversal symmetry. One particularly striking example is a state spontaneously breaking lattice rotation symmetry, where the cubic lattice breaks up into bilayers, each of which forms a two-dimensional chiral spin liquid state.

We study the charge response of conformal field theories (CFTs) at nonzero temperature in 2+1 dimensions using the anti-de Sitter (AdS)/CFT correspondence. A central role is played by the quasinormal modes (QNMs), specifically, the poles and zeros of the current correlators. We generalize our recent study of the QNMs of the ac charge conductivity to include momentum dependence. This sheds light on the various excitations in the CFT. We begin by discussing the $R$-current correlators of the $\mathcal{N}=8$ SU$\left(N_c\right)$ super-Yang-Mills theory at its conformal fixed point using holography. For instance, transitions in the QNM spectrum as a function of momentum clearly identify “hydrodynamic-to-relativistic” crossovers. We then extend our study to include four-derivative terms in the gravitational description allowing us to study more generic charge response as well as the role of the S duality, which plays a central role in understanding the correlators. The presence of special purely damped QNMs can lead to new behavior, distinct from what occurs in the aforementioned gauge theory. We also extend previous conductivity sum rules to finite momentum and discuss their interpretation in the gravity picture. A comparison is finally made with the conformal fixed point of the vector O($N$) model in the large-$N$ limit.

As a long-lived theme in solid-state physics, the Kondo effect reflects the many-body physics involving the short-range Coulomb interactions between itinerant electrons and localized spins in metallic materials. Here we show that the Kondo effect is present in ZnO, a prototypical wide-band-gap oxide, doped with a rare-earth element (Gd). The localized 4$f$ electrons of Gd ions do not produce remanent magnetism, but interact strongly with the host electrons, giving rise to a saturating resistance upturn and negative magnetoresistance at low temperatures. Furthermore, the Kondo temperature and resistance can be electrostatically modulated using electric-double-layer gating with liquid ionic electrolyte. Our experiments provide the experimental evidence of tunable Kondo effect in ZnO, underscoring the magnetic interactions between localized and itinerant electrons and the emergent transport behaviors in such doped wide-band-gap oxides.

Topological superconductors are gapped superconductors with gapless and topologically robust quasiparticles propagating on the boundary. In this paper, we present a topological field theory description of three-dimensional time-reversal invariant topological superconductors. In our theory the topological superconductor is characterized by a topological coupling between the electromagnetic field and the superconducting phase fluctuation, which has the same form as the coupling of “axions” with an Abelian gauge field. As a physical consequence of our theory, we predict the level crossing induced by the crossing of special “chiral” vortex lines, which can be realized by considering $s$-wave superconductors in proximity with the topological superconductor. Our theory can also be generalized to the coupling with a gravitational field.

It is well known that the Haldane phase of a one-dimensional spin-1 chain is a symmetry-protected topological (SPT) phase, which is described by a nonlinear sigma model (NLSM) with a $\Theta$ term at $\Theta =2\pi$. In this work we study a three-dimensional (3d) SPT phase of a SU(2$N$) antiferromagnetic spin system with a self-conjugate representation on every site. The spin-ordered Néel phase of this system has a ground state manifold $\mathcal{M}=\frac{\mathrm{U}\left(2N\right)}{\mathrm{U}\left(N\right)\times \mathrm{U}\left(N\right)}$, and this system is described by a NLSM defined with manifold $\mathcal{M}$. Since the homotopy group ${\pi }_4\left[\mathcal{M}\right]=\mathbb{Z}$ for $N>1$, this NLSM can naturally have a $\Theta$ term. We will argue that when $\Theta =2\pi$ this NLSM describes a SPT phase. This SPT phase is protected by the SU(2$N$) spin symmetry, or its subgroup SU($N$)$\times$SU$\left(N\right)⋊Z_2$, without assuming any other discrete symmetry. We will also construct a trial SU(2$N$) spin state on a 3d lattice; we argue that the long-wavelength physics of this state is precisely described by the aforementioned NLSM with $\Theta =2\pi$.

Electronic nematic phases have been proposed to occur in various correlated electron systems and were recently claimed to have been detected in scanning tunneling microscopy (STM) conductance maps of the pseudogap states of the cuprate high-temperature superconductor ${\text{Bi}}_2{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_{8+\delta }$ (Bi-2212). We investigate the influence of anisotropic STM tip structures on such measurements and establish, with a model calculation, the presence of a tunneling interference effect within an STM junction that induces energy-dependent symmetry-breaking features in the conductance maps. We experimentally confirm this phenomenon on different correlated electron systems, including measurements in the pseudogap state of Bi-2212, showing that the apparent nematic behavior of the imaged crystal lattice is likely not due to nematic order but is related to how a realistic STM tip probes the band structure of a material. We further establish that this interference effect can be used as a sensitive probe of changes in the momentum structure of the sample's quasiparticles as a function of energy.

The thermally activated glide of screw dislocations in bcc crystals proceeds through the formation of kinks by pairs, a mechanism named after Peierls for his early work on dislocation theory. A method is proposed to compute the dislocation kink-pair formation enthalpy from density functional theory (DFT) calculations. This method consists of properly adjusting the parameters of a one-dimensional line tension model from atomistic calculations performed in small simulation cells. This model is applied to bcc iron to determine the kink-pair formation enthalpy at different applied stresses from DFT calculations.

We analyze the evolution of the superconducting gap structure in strongly hole-doped Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ between $x=1$ and $x\sim 0.4$ (optimal doping). In the latter case, the pairing state is most likely $s\pm$, with different gap signs on hole and electron pockets, but with the same signs of the gap on the two $\Gamma$-centered hole pockets (a $++$ state on hole pockets). In a pure KFe${}_2$As${}_2$ ($x=1$), which has only hole pockets, laser ARPES data suggested another $s\pm$ state, in which the gap changes sign between hole pockets (a $+-$ state). We analyze how a $++$ gap transforms into a $+-$ gap as $x\to 1$. We found that this transformation occurs via an intermediate $s+is$ state in which the gaps on the two hole pockets differ in phase by $\varphi$, which gradually involves from $\varphi =\pi$ (the $+-$ state) to $\varphi =0$ (the $++$ state). This state breaks time-reversal symmetry and has huge potential for applications. We compute the dispersion of collective excitations and show that two different Leggett-type phase modes soften at the two end points of the time-reversal-symmetry-breaking state.

Gated terahertz cyclotron resonance measurements on epitaxial Bi${}_2$Se${}_3$ thin films capped with In${}_2$Se${}_3$ enable the first spectroscopic characterization of a single topological interface state from the vicinity of the Dirac point to above the conduction band edge. A precipitous drop in the scattering rate with Fermi energy is observed, which is interpreted as the surface state decoupling from bulk states and evidence of a shift of the Dirac point towards mid-gap. Near the Dirac point, potential fluctuations of 50 meV are deduced from an observed loss of differential optical spectral weight near the Dirac point. Potential fluctuations are reduced by a factor of two at higher surface Fermi levels in the vicinity of the conduction band edge inferred from the width of the scattering rate step. The passivated topological interface state attains a high mobility of 3500 cm${}^2$/V s near the Dirac point.

We show that the lack of inversion symmetry in monolayer MoS${}_2$ allows strong optical second harmonic generation. The second harmonic of an 810-nm pulse is generated in a mechanically exfoliated monolayer, with a nonlinear susceptibility on the order of 10${}^{-7}$ m/V. The susceptibility reduces by a factor of seven in trilayers, and by about two orders of magnitude in even layers. A proof-of-principle second harmonic microscopy measurement is performed on samples grown by chemical vapor deposition, which illustrates potential applications of this effect in the fast and noninvasive detection of crystalline orientation, thickness uniformity, layer stacking, and single-crystal domain size of atomically thin films of MoS${}_2$ and similar materials.

We present a theory of the spin Hall magnetoresistance (SMR) in multilayers made from an insulating ferromagnet F, such as yttrium iron garnet (YIG), and a normal metal N with spin-orbit interactions, such as platinum (Pt). The SMR is induced by the simultaneous action of spin Hall and inverse spin Hall effects and therefore a nonequilibrium proximity phenomenon. We compute the SMR in F$|$N and F$|$N$|$F layered systems, treating N by spin-diffusion theory with quantum mechanical boundary conditions at the interfaces in terms of the spin-mixing conductance. Our results explain the experimentally observed spin Hall magnetoresistance in N$|$F bilayers. For F$|$N$|$F spin valves we predict an enhanced SMR amplitude when magnetizations are collinear. The SMR and the spin-transfer torques in these trilayers can be controlled by the magnetic configuration.

The influence of defects on the local structural, electronic, and chemical properties of a surface oxide on Cu(100) were investigated using atomic resolution three-dimensional force mapping combined with tunneling current measurements and ab initio density functional theory. Results reveal that the maximum attractive force between tip and sample occurs above the oxygen atoms; theory indicates that the tip, in this case, terminates in a Cu atom. Meanwhile, simultaneously acquired tunneling current images emphasize the positions of Cu atoms, thereby, providing species-selective contrast in the two complementary data channels. One immediate outcome is that defects due to the displacement of surface copper are exposed in the current maps, even though force maps only reflect a well-ordered oxygen sublattice. The exact nature of the defects is confirmed by the simulations, which also reveal that the arrangement of the oxygen atoms is not disrupted by the copper displacement. In addition, the experimental force maps uncover a position-dependent modulation of the attractive forces between the surface oxygen and the copper-terminated tips, which is found to reflect the surface's inhomogeneous chemical and structural environment. As a consequence, the demonstrated method has the potential to directly probe how defects affect surface chemical interactions.

We propose and analyze a mesoscopic device producing on-demand entangled pairs of electrons. The system consists of two capacitively coupled Mach-Zehnder interferometers implemented in a quantum Hall structure. A pair of electron wave packets is injected into the chiral edge states of two (of the four) incoming arms; scattering on the incoming interferometers splits the wave packets into four components, of which two interact. The resulting interaction phase associated with this component leads to the entanglement of the state; the latter is scattered at the outgoing beam splitter and analyzed in a Bell violation test measuring the presence of particles in the four outgoing leads. We study the two-particle case and determine the conditions to reach and observe full entanglement. We extend our two-particle analysis to include the underlying Fermi seas in the quantum Hall device; the change in shape of the wave function, the generation of electron-hole pairs in the interaction regime, and a time delay between the pulses all reduce the degree of visible entanglement and the violation of the Bell inequality, effects which we analyze quantitatively. We determine the device settings optimizing the entanglement and the Bell test and find that violation is still possible in the presence of the Fermi seas, with a maximal Bell parameter reaching $\mathcal{B}=2.18>2$ in our setup.

Noise measurements are a probe beyond simple electronic transport that can reveal additional information about electronic correlations and inelastic processes. Here we report noise measurements in individual electromigrated nanojunctions, examining the evolution from the many-channel regime to the tunneling regime, using a radio frequency technique. While we generally observe the dependence of noise on bias expected for shot noise, in approximately 12$\%$ of junction configurations we find discrete changes in the bias dependence at threshold values of the bias, consistent with electronic excitation of local vibrational modes. Moreover, with some regularity we find significant mesoscopic variation in the magnitude of the noise in particular junctions even with small changes in the accompanying conductance. In another $\sim$17$\%$ of junctions we observe pronounced asymmetries in the inferred noise magnitude as a function of bias polarity, suggesting that investigators should be concerned about current-driven ionic motion in the electrodes even at biases well below those used for deliberate electromigration.

We introduce and study a class of anyon models that are a natural generalization of Ising anyons and Majorana fermion zero modes. These models combine an Ising anyon sector with a sector associated with $\mathit{\text{SO}}{\left(m\right)}_2$ Chern-Simons theory. We show how they can arise in a simple scenario for electron fractionalization and give a complete account of their quasiparticle types, fusion rules, and braiding. We show that the image of the braid group is finite for a collection of $2n$ fundamental quasiparticles and is a proper subgroup of the metaplectic representation of $Sp(2n-2,{\mathbb{F}}_m)⋉H(2n-2,{\mathbb{F}}_m)$, where $Sp(2n-2,{\mathbb{F}}_m)$ is the symplectic group over the finite field ${\mathbb{F}}_m$ and $H(2n-2,{\mathbb{F}}_m)$ is the extra special group (also called the $(2n-1)$-dimensional Heisenberg group) over ${\mathbb{F}}_m$. Moreover, the braiding of fundamental quasiparticles combined with a restricted set of measurements can be efficiently simulated classically. However, computing the result of braiding a certain type of composite quasiparticle followed by fusion into the identity is $\#P$-hard. It is not universal for quantum computation because it has a finite braid group image. This is a rare example of a topological phase that is not universal for quantum computation through braiding but nevertheless has $\#P$-hard link invariants. We argue that our models are closely related to recent analyses finding non-Abelian anyonic properties for defects in quantum Hall systems, generalizing Majorana zero modes in quasi-1D systems.

Building on the generalization of the exactly dimerized Majumdar-Ghosh ground state to arbitrary spin $S$ for the Heisenberg chain with a three-site term $({\mathbf{S}}_{i-1}·{\mathbf{S}}_i)({\mathbf{S}}_i·{\mathbf{S}}_{i+1})+\text{H.c.}$, we use density-matrix renormalization group simulations and exact diagonalizations to determine the nature of the dimerization transition for $S=1$, $3/2$, and 2. The resulting central charge and critical exponent are in good agreement with the $\text{SU}{\left(2\right)}_{k=2S}$ Wess-Zumino-Witten values $c=3k/(2+k)$ and $\eta =3/(2+k)$. Since the three-site term that induces dimerization appears naturally if exchange interactions are calculated beyond second order, these results suggest that $\text{SU}{\left(2\right)}_{k>1}$ Wess-Zumino-Witten models might finally be realized in actual spin chains.

We consider the thermal phase transition from a paramagnetic to a stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions $J_1<0$ (nearest neighbor, ferromagnetic) and $J_2>0$ (second neighbor, antiferromagnetic). The striped phase breaks a $Z_4$ symmetry and is stabilized at low temperatures for $g=J_2/\left|J_1\right|>1/2$. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. [Phys. Rev. Lett. 108, 045702 (2012)]. Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster mean-field theory, Monte Carlo simulations, and transfer-matrix calculations. The $J_1$-$J_2$ model has a line of very weak first-order phase transitions in the whole region $1/2<g<g^{*}$, where $g^{*}=0.67\pm 0.01$. Thereafter, the transitions from $g=g^{*}$ to $g\to \infty$ are continuous and can be fully mapped, using universality arguments, to the critical line of the well-known Ashkin-Teller model from its four-state Potts point to the decoupled Ising limit. We also comment on the pseudo-first-order behavior at the Potts point and its neighborhood in the Ashkin-Teller model on finite lattices, which in turn leads to the appearance of similar effects in the vicinity of the multicritical point $g^{*}$ in the $J_1$-$J_2$ model. The continuous transitions near $g^{*}$ can therefore be mistaken for first-order transitions, and this realization was the key to understanding the paramagnetic-striped transition for the full range of $g>1/2$. Most of our conclusions are based on Monte Carlo calculations, while the cluster mean-field and transfer-matrix results provide useful methodological benchmarks for weakly first-order behaviors and Ashkin-Teller criticality.

Recent theoretical and numerical evidence suggests that localization can survive in disordered many-body systems with very high energy density, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in extended quantum systems far from the zero-temperature limit. It separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present numerical evidence that many-body localization also occurs in models without disorder but rather a quasiperiodic potential. In one dimension, these systems already have a single-particle localization transition, and we show that this transition becomes a many-body localization transition upon the introduction of interactions. We also comment on possible relevance of our results to experimental studies of many-body dynamics of cold atoms and nonlinear light in quasiperiodic potentials.

Optical gyrotropy, the lifting of degeneracy between left and right circularly polarized light, can be generated by either time-reversal or chiral symmetry breaking. In the high-$T_c$ superconductor La${}_{2-x}$Ba${}_x$CuO${}_4$ (LBCO), gyrotropy onsets at the same temperature as charge stripe order, suggesting that the rotation of the stripe direction from one plane to the next generates a helical pattern that breaks chiral symmetry. In order to further test this chiral stacking hypothesis it is necessary to develop an understanding of the physical mechanisms by which chirality generates gyrotropy. In this paper we show that, in chiral metals, optical gyrotropy is a consequence of Berry curvature in momentum space. We describe a physical picture showing that gyrotropy in chiral metals is closely related to the anomalous Hall effect in itinerant ferromagnets. We then calculate the magnitude of the gyrotropic response for a given Berry curvature using the semiclassical picture of anomalous velocity and Boltzmann transport theory. To connect this physical picture with experiment, we calculate the Berry curvature in two tight-binding models. The first model is motivated by the structure of LBCO and illustrates how gyrotropy is created when stripe perturbations are added to a simple cubic model. In the second model, we examine the dramatic enhancement of the gyrotropic coefficient when Rashba spin-orbit coupling is introduced. The magnitude of the rotation of polarization on reflection expected based on these models is calculated and compared with experimental data.