For the antiferromagnetic $J_1$-$J_2$ quantum spin chain with an even number of sites, the point $J_2^d=J_1/2$ is a disorder point. It marks the onset of incommensurate real space correlations for $J_2>J_2^d$. At a distinct larger value of $J_2^L=0.52036\left(6\right)J_1$, the Lifshitz point, the peak in the static structure factor begins to move away from $k=\pi$. Here, we focus on chains with an odd number of sites. In this case, the disorder point is also at $J_2^d=J_1/2$ but the behavior close to the Lifshitz point, $J_2^L\simeq 0.538J_1$, is quite different: starting at $J_2^L$, the ground state goes through a sequence of level crossings as its momentum changes away from $k=\pi /2$. An even length chain, on the other hand, is gapped for any $J_2>0.24J_1$ and has the ground-state momentum $k=0$. This gradual change in the ground-state wave function for chains with an odd number of sites is reflected in a dramatic manner directly in the ground-state on-site magnetization as well as in the bipartite von Neumann entanglement entropy. Our results are based on DMRG calculations and variational calculations performed in a restricted Hilbert space defined in the valence bond picture. In the vicinity of the point $J_2=J_1/2$, we expect the variational results to be very precise.

In order to identify and quantify characteristics of the magnetoelectric coupling at ferromagnetic/ferroelectric interfaces, epitaxial La${}_{1-x}$Sr${}_x$MnO${}_3$/Pb(Zr,Ti)O${}_3$ (LSMO/PZT) heterostructures were deposited by large-distance magnetron sputtering. The remarkably high lateral uniformity achieved in such films allowed for a ferroelectric device area of more than 6 mm${}^2$. This has enabled for superconductive quantum interference device (SQUID) measurements of the magnetic response to the systematically, completely in situ, varied remanent ferroelectric polarization. Temperature dependence of the magnetic modulation upon charging and the magnetic response to the ferroelectric stimulation indicate a field-effect dominated coupling mechanism and generally confirm the concept of electrostatic hole ($h^{+}$) doping of LSMO. The modulation of magnetization was comprehensively analyzed for a broad range of electrostatically induced surface charge concentrations. For small charge modulations at low temperature a linear tuning coefficient of $\approx -3.6{\mu }_{\mathrm{B}}/h^{+}$ has been determined. This suggests the activation of an antiferromagnetic coupling, even for very small surface charge densities. Simultaneously, a shift in the magnetic transition temperature at higher surface charge concentration indicates the presence of a ferromagnetic phase at the LSMO/PZT interface. Eventually, a physical picture of magnetoelectric coupling is proposed in which these quantitative results are consistently interpreted, in terms of a surface-charge dependent electronic phase separation with the coexistence of antiferromagnetic and ferromagnetic regions at the ferromagnetic/ferroelectric interface.

We classify distinct types of quantum number fractionalization occurring in two-dimensional topologically ordered phases, focusing in particular on phases with ${\mathbb{Z}}_2$ topological order, that is, on gapped ${\mathbb{Z}}_2$ spin liquids. We find that the fractionalization class of each anyon is an equivalence class of projective representations of the symmetry group, corresponding to elements of the cohomology group $H^2(G,{\mathbb{Z}}_2)$. This result leads us to a symmetry classification of gapped ${\mathbb{Z}}_2$ spin liquids, such that two phases in different symmetry classes cannot be connected without breaking symmetry or crossing a phase transition. Symmetry classes are defined by specifying a fractionalization class for each type of anyon. The fusion rules of anyons play a crucial role in determining the symmetry classes. For translation and internal symmetries, braiding statistics plays no role, but can affect the classification when point group symmetries are present. For square lattice space group, time-reversal, and $\mathrm{SO}\left(3\right)$ spin rotation symmetries, we find $2098176\approx 2^{21}$ distinct symmetry classes. Our symmetry classification is not complete, as we exclude, by assumption, permutation of the different types of anyons by symmetry operations. We give an explicit construction of symmetry classes for square lattice space group symmetry in the toric code model. Via simple examples, we illustrate how information about fractionalization classes can, in principle, be obtained from the spectrum and quantum numbers of excited states. Moreover, the symmetry class can be partially determined from the quantum numbers of the four degenerate ground states on the torus. We also extend our results to arbitrary Abelian topological orders (limited, though, to translations and internal symmetries), and compare our classification with the related projective symmetry group classification of parton mean-field theories. Our results provide a framework for understanding and probing the sharp distinctions among symmetric ${\mathbb{Z}}_2$ spin liquids and are a first step toward a full classification of symmetric topologically ordered phases.

We study the Hall effect in Ni${}_x$Pt${}_{1-x}$ thin films. It is observed that the ordinary Hall coefficient is always negative (electron-like). The anomalous Hall coefficient is also negative, except in the vicinity of the ferromagnetic quantum phase transition, where it exhibits a sign reversal and turns positive (hole-like). This leads to an “anti-ordinary” Hall effect with opposite signs of ordinary and anomalous contributions. It clearly shows that the anomalous Hall effect does not reflect the overall topology of the Fermi surface (which remains unchanged), but originates from singular hot spots. We attribute the anti-ordinary contribution to the intrinsic (Berry-phase) origin and propose a spectroscopic explanation of its tunability as a function of temperature and composition.

Recent work [Appl. Phys. Lett. 100, 193108 (2012)] has demonstrated that uniaxial strain applied to wurtzite (WZ) GaAs nanowires leads to an interesting direct-indirect band gap transition. Here, we explored the potential of strain engineering on electronic structures of one-dimensional WZ and zinc-blende (ZB) GaAs nanowires along the [0001] and [111] directions, respectively. The studied strain includes uniaxial strain, radial strain, and strain along zigzag and armchair directions in the cross section of the nanowires and shear strains. It was found that the WZ and ZB GaAs nanowires with a diameter of ∼2 nm have an indirect band gap, whereas, bulk GaAs has a direct gap. The near-gap states (valence-band maximum/conduction-band minimum) are dominated by $s$ or $p$ orbitals of Ga or As atoms. The energies of these states respond very differently to the applied strains. For example, the energy increases with a positive uniaxial expansion while decreasing with a negative uniaxial compression for a state dominated by bonding s orbitals. However, for a state dominated by antibonding s orbitals, an opposite trend of its energy response to strain is observed. Furthermore, the energy response to strain of bonding p orbitals was found to be different from that of bonding s orbitals. Due to the different responses of the near-gap state energies with respect to strain, the direct-indirect band gap transition was produced. It was further found that whether a strain can trigger the direct-indirect band gap transition in the GaAs nanowires depends strongly on the type of applied strain. It requires less strain energy to convert the indirect gap to be direct in both the WZ and the ZB nanowires through applying a radial strain in the cross section, compared with applying a strain in the zigzag direction.

In a Bernal-stacked graphene bilayer, an electronic state in Landau level $N=0$ is described by its guiding-center index $X$ (in the Landau gauge) and by its valley, spin, and orbital indices $\xi =\pm K,\sigma =\pm 1,$ and $n=0,1.$ When Coulomb interaction is taken into account, the chiral two-dimensional electron gas (C2DEG) in this system can support a variety of quantum Hall ferromagnetic ground states where the spins and/or valley pseudospins and/or orbital pseudospins collectively align in space. In this work, we give a comprehensive account of the phase diagram of the C2DEG at integer filling factors $\nu \in [-3,3]$ in Landau level $N=0$ when an electrical potential difference ${\Delta }_B$ between the two layers is varied. We consider states with or without layer, spin, or orbital coherence. For each phase, we discuss the behavior of the transport gap as a function of ${\Delta }_B,$ the spectrum of collective excitations, and the optical absorption due to orbital pseudospin-wave modes. We also study the effect of an external in-plane electric field on a coherent state that has both valley and spin coherence and show that it is possible, in such a state, to control the spin polarization by varying the strength of the external in-plane electric field.

We examine electronic transport in a spin-blockaded double quantum dot. We show that by tuning the strength of the spin-orbit interaction the current flowing through the double dot exhibits a dip at zero magnetic field or a peak at a magnetic field for which the two-electron energy levels anticross. This behavior is due to the dependence of the singlet-triplet mixing on the field and spin-orbit amplitude. We derive approximate expressions for the current as a function of the amplitudes of the states involved in the transport. We also consider an alternative model that takes into account a finite number of nuclear spins and study the resulting coupled dynamics between electron and nuclear spins. We show that if the spin ensemble is in a thermal state there are regular oscillations in the transient current followed by quasichaotic revivals akin to those seen in a thermal Jaynes-Cummings model.

Using terahertz spectroscopy in external magnetic fields, we investigate the low-temperature charge dynamics of strained HgTe, a three-dimensional topological insulator. In resonator experiments, we observe quantum Hall oscillations at terahertz frequencies, which offer direct access to the unusual electrodynamic properties of the surface states of topological insulators. The 2D density estimated from the period of the quantum Hall oscillations agrees well with dc transport experiments on the topological surface state. The Dirac character of the surface state is further evidenced by the observation of the characteristic Berry phase in the dependence of the Landau levels on magnetic field.

Here we present linear-polarization-dependent soft x-ray absorption spectroscopy data at the Ce $M_{4,5}$ edges of CeOs${}_2$Al${}_{10}$ and CeFe${}_2$Al${}_{10}$. Despite the strong hybridization between $4f$ and conduction electrons and the existence of spin gaps as seen in inelastic neutron scattering, we were able to determine the crystal field ground state wave functions by combining our spectroscopy data with magnetization measurements. The results quantitatively explain the small ordered moment along $c$ and the measured magnetic moment along the easy $a$ axis in CeOs${}_2$Al${}_{10}$.

We successfully synthesized verdazyl biradical crystals of $p$-BIP-V${}_2$ [4,4${}^{\prime }$-bis(1,5-diphenylverdazyl-3-yl)biphenyl]. Two types of intermolecular interactions are deduced from the spin-density distribution and molecular packing in the crystal, and these interactions are considered to result in the formation of a honeycomb lattice. The $\mathit{ab}$ $\mathit{initio}$ molecular orbital calculation also indicated such an exchange network of intermolecular interactions. The intramolecular interaction acts as a diagonal bridge across the honeycomb lattice to form a square lattice. We evaluated the intramolecular antiferromagnetic (AF) interaction $J_1$ to be about 8.8 K from an analysis of the magnetic susceptibility of isolated $p$-BIP-V${}_2$ molecules in terms of an isolated $S$ $=$ 1/2 AF dimer. We analyzed the magnetic susceptibility of the crystals using the quantum Monte Carlo method. Consequently, two types of intermolecular AF interactions, $J_2$ and $J_3$, were found to be almost comparable and about 4.5 times larger than the intramolecular interaction $J_1$. Thus, we confirmed that $p$-BIP-V${}_2$ has a slightly distorted $S=1/2$ honeycomb-like lattice.

We report the pressure response of charge-density-wave (CDW) and ferromagnetic (FM) phases of the rare-earth intermetallic SmNiC${}_2$ up to 5.5 GPa. The CDW transition temperature ($T_{\text{CDW}}$), which is reflected as a sharp inflection in the electrical resistivity, is almost independent of pressure up to 2.18 GPa but is strongly enhanced at higher pressures, increasing from 155.7 K at 2.2 GPa to 279.3 K at 5.5 GPa. Commensurate with the sharp increase in $T_{\text{CDW}}$, the first-order FM phase transition, which decreases with applied pressure, bifurcates into the upper ($T_{M1}$) and lower ($T_c$) phase transitions and the lower transition changes its nature to second order above 2.18 GPa. Enhancement both in the residual resistivity and the Fermi-liquid $T^2$ coefficient $A$ near 3.8 GPa suggests abundant magnetic quantum fluctuations that arise from the possible presence of a FM quantum critical point.

We study the electronic properties of a twisted trilayer graphene, where two of the layers have Bernal stacking and the third one has a relative rotation with respect to the AB-stacked layers. Near the Dirac point, the AB-twisted trilayer graphene spectrum shows two parabolic Bernal-like bands and a twistedlike Dirac cone. For small twist angles, the parabolic bands present a gap that increases for decreasing rotation angle. There is also a shift in the twistedlike Dirac cone with a similar angle dependence. We correlate the gap in the trilayer with the shift of the Dirac cone in an isolated twisted bilayer, which is due to the loss of electron-hole symmetry caused by sublattice mixing in the rotated geometry. Using a tight-binding and a continuum model, we derive an effective Hamiltonian which accounts for the relevant low-energy properties of this system.

Motivated by recent experimental observations of Tongay et al. [Nano Lett. 12, 5576 (2012)] we show how the electronic properties and Raman characteristics of single layer MoSe${}_2$ are affected by elastic biaxial strain. We found that with increasing strain: (1) the $E^{\prime }$ and $E^{\prime \prime }$ Raman peaks ($E_{2g}$ and $E_{1g}$ in bulk) exhibit significant redshifts (up to $\sim$30 cm${}^{-1}$), (2) the position of the $A_1^{\prime }$ peak remains at $\sim$180 cm${}^{-1}$ ($A_{1g}$ in bulk) and does not change considerably with further strain, (3) the dispersion of low energy flexural phonons crosses over from quadratic to linear, and (4) the electronic band structure undergoes a direct to indirect band gap crossover under $\sim$3$\%$ biaxial tensile strain. Thus the application of strain appears to be a promising approach for a rapid and reversible tuning of the electronic, vibrational, and optical properties of single layer MoSe${}_2$ and similar MX${}_2$ dichalcogenides.

We derive a spin diffusion equation for a spin-orbit coupled two-dimensional electron gas including the Hartree-Fock field resulting from first order electron-electron interactions. We find that the lifetime of the persistent spin helix, which emerges for equal linear Rashba and Dresselhaus spin-orbit interactions, can be enhanced considerably for large initial spin polarizations due to the Hartree-Fock field. The reason is a reduction of the symmetry-breaking cubic Dresselhaus scattering rate by the Hartree-Fock field. Also higher harmonics are generated and the polarization of the persistent spin helix rotates out of the ($S_y$,$S_z$) plane acquiring a finite $S_x$ component. This effect becomes more pronounced when the cubic Dresselhaus spin-orbit interaction is large.

We present the results of anelastic and dielectric spectroscopy measurements performed on large-grain, ceramic PbZr${}_{1-x}$Ti${}_x$O${}_3$ (PZT) compositions located near the two morphotropic phase boundaries (MPBs) that separate the ferroelectric (FE) rhombohedral (R) phase from the Zr-rich antiferroelectric and Ti-rich FE tetragonal phases. Additional evidence is provided of the existence of a temperature $T_{\mathrm{IT}}$, which we interpret as the onset of the tilt instability in the R phase, where tilting is initially frustrated by lattice disorder but achieves long-range order at the lower temperature $T_{\mathrm{T}}$. The $T_{\mathrm{IT}}\left(x\right)$ line is observed for $x<0.17$, beginning at the $T_{\mathrm{T}}\left(x\right)$ line at the point where $T_{\mathrm{T}}\left(x\right)$ drops abruptly and then continuing up to the $T_{\mathrm{C}}\left(x\right)$ line. If $T_{\mathrm{IT}}\left(x\right)$ indeed signals the onset of short-range ordered tilting, then it follows that the tilt instability lines should tend to be attracted and merge with those of the polar instabilities. Not only does the $T_{\mathrm{IT}}\left(x\right)$ line bend toward and then merge with the $T_{\mathrm{C}}\left(x\right)$ line but, in our series of samples, the temperature $T_{\mathrm{MPB}}$ defined by the dielectric and anelastic maxima at the rhombohedral/tetragonal MPB does not cross the $T_{\mathrm{T}}\left(x\right)$ line. Instead it gradually bends downward to become parallel to, and possibly merges with, the $T_{\mathrm{T}}\left(x\right)$line. An abrupt change is found in the shape of the anelastic anomaly at $T_{\mathrm{T}}$ when $x$ passes from $0.465$ to 0.48, possibly indicative of a rhombohedral/monoclinic boundary.

The development of a new era of quantum devices requires an understanding of how paramagnetic dopants or impurity spins behave in crystal hosts. Here, we describe a spectroscopic technique which uses traditional electron spin resonance (ESR) combined with the measurement of a large population of electromagnetic whispering gallery modes. This allows the characterization of the physical parameters of paramagnetic impurity ions in the crystal at low temperatures. We present measurements of two ultrahigh-purity sapphires cooled to 20 mK in temperature, and determine the concentration of Fe${}^{3+}$ ions and their frequency sensitivity to a dc magnetic field. Our method is different from ESR in that it is possible to track the resonant frequency of the ion from zero applied magnetic field to any arbitrary value, allowing excellent measurement precision. This high precision reveals anisotropic behavior of the Zeeman splitting. In both crystals, each Zeeman component demonstrates a different $g$ factor.

The robustness of the topological color code, which is a class of error-correcting quantum codes, is investigated under the influence of a uniform magnetic field on the honeycomb lattice. Our study relies on two high-order series expansions using perturbative continuous unitary transformations in the limit of low and high fields, exact diagonalization, and a classical approximation. We show that the topological color code in a single parallel field is isospectral to the Baxter-Wu model in a transverse field on the triangular lattice. It is found that the topological phase is stable up to a critical field beyond which it breaks down to the polarized phase by a first-order phase transition. The results also suggest that the topological color code is more robust than the toric code in the parallel magnetic field.

The recent discovery of a Skyrmion crystal phase in an insulating multiferroic compound Cu${}_2$OSeO${}_3$ calls for new ways and ideas to manipulate the Skyrmions in the absence of spin transfer torque from the conduction electrons. It is shown here that the position-dependent electric field, pointed along the direction of the average induced dipole moment of the Skyrmion, can induce the Hall motion of the Skyrmion with its velocity orthogonal to the field gradient. Finite Gilbert damping produces longitudinal motion. Inter-Skyrmion interaction leads to the reduction of the drift speed. We find a rich variety of resonance modes excited by an ac electric field.

We have studied the thermal quenching of the ultraviolet luminescence band with a maximum at about 3.25 eV in $p$-type Mg-doped GaN. The characteristic temperature of the thermal quenching of photoluminescence (PL) gradually shifted to higher temperatures with increasing excitation intensity. This effect is explained by a population inversion of charge carriers at low temperatures, which suddenly converts into a quasiequilibrium population as the temperature increases above the characteristic value. Tunable quenching of PL has been observed only in some of the GaN:Mg samples. The absence of the tunable quenching of PL in another group of GaN:Mg samples is preliminarily attributed to different types of dominant nonradiative defects in the two groups of samples.

Intermetallic clathrates are known for their high thermoelectric efficiency. However, to realize mass market applications, efficient low-cost representatives have to be found. Here we investigate the candidate material Ba${}_8$Cu${}_5$Si${}_x$Ge${}_{41-x}$, $0\le x\le 41$ by x-ray powder diffraction (XPD), energy dispersive x-ray spectroscopy, and electrical and thermal transport property measurements. Polycrystalline samples are prepared by high frequency melting and subsequent ball milling and hot pressing. The type-I clathrate structure is confirmed in all samples by XPD. The structural details are evaluated by the Rietveld method. The results show that when Ge is replaced by Si, linear variations can be observed for the lattice parameter, cages size, atomic displacement parameters of Ba in the large cage, and atomic parameters $x$ of $16i(x,x,x)$ and $z$ of $24k(0,y,z)$. However, the atomic parameters $y$ of $24k(0,y,z)$ and interatomic distance between the atoms at the $24k$ site vary nonlinearly with the Si content $x_{\text{Si}}$. Nonlinear behavior also appears for the Si occupation at the $24k$ site. These nonlinear variations result in the electronic band structure changing nonmonotonically with $x_{\text{Si}}$, which explains the observed nonmonotonic variations of the transport properties. The lattice thermal conductivity shows $x_{\text{Si}}$ independence, which escapes from our anticipation that the larger the tetrakaidecahedra cage, the lower the lattice thermal conductivity in clathrates. The insignificance of resonant scattering for the lattice thermal conductivity might be the reason for the observed independence. The highest dimensionless thermoelectric figure of merit $ZT$ of 0.5 at about $550{}^{\circ }\mathrm{C}$ is achieved for Ba${}_8$Cu${}_5$Si${}_3$Ge${}_{38}$.