We investigate the effect of magnetic field and charge noise on the generation of entanglement between two Heisenberg exchange-coupled electron spins in a double quantum dot. We focus on exchange-driven evolution that would ideally take an initial unentangled tensor product state to a maximally entangled state in the absence of noise. The presence of noise obviously adversely affects the attainment of maximal entanglement, which we study quantitatively and exactly. To quantify the effects of noise, we calculate two-qubit coherence times and entanglement fidelity, both of which can be extracted from simulations or measurements of the return probability as a function of interaction time, i.e., the time period during which the exchange coupling remains effective between the two spins. We perform these calculations for a broad range of noise strengths that includes the regime of recent experiments. We find that the two types of noise reduce the amount of entanglement in qualitatively distinct ways and that, although charge noise generally leads to faster decoherence, the relative importance of the two types of noise in entanglement creation depends sensitively on the strength of the exchange coupling. Our results can be used to determine the level of noise suppression needed to reach quantum error correction thresholds. We provide quantitative guidance for the requisite noise constraints necessary to eventually reach the $>99\%$ fidelity consistent with the quantum error correction threshold.

Density functional theory applied to small-diameter boron nitride nanotubes (BNNTs) finds out-of-plane structural buckling in contrast to large-diameter tubes that exhibit faceting. Buckling significantly affects interlayer interactions in commensurate double-walled BNNTs. Energy corrugation amplitudes in relative motions of BNNT walls change up to fourfold, depending on interlayer registry relaxation, in marked contrast to carbon nanotubes. Large differences between relaxed and unrelaxed energy corrugations of BNNTs could yield energy dissipation via the strain-induced anelastic relaxation of interlayer locking (or “lattice kinks”), which can be exploited for mechanical damping applications.

Boron carbide exhibits intrinsic substitutional disorder over a broad composition range. The structure consists of 12-atom icosahedra placed at the vertices of a rhombohedral lattice, together with a 3-atom chain along the threefold axis. In the high-carbon limit, one or two carbon atoms can replace boron atoms on the icosahedra while the chains are primarily of type C-B-C. We fit an interatomic pair interaction model to density-functional-theory total energies to investigate the substitutional carbon disorder. Monte Carlo simulations with sampling improved by replica exchange and augmented by two-dimensional multiple histogram analysis predict three phases. The low-temperature, high-carbon-composition monoclinic $Cm$ structure disorders through a pair of phase transitions, first via an Ising-like transition to a monoclinic centrosymmetric state with space group $C2/m$, then via a first-order three-state Potts-like transition to the experimentally observed rhombohedral $R\overline{3}m$ symmetry.

The melting curve of Sn initially rises steeply as a function of pressure but exhibits a decrease in slope ($d{T}_m/dP$) above 40 GPa to become nearly flat above 50 GPa. Previous studies have argued that a body-centered tetragonal (bct) to cubic (bcc) phase transition occurs in this range at room temperature. However, our investigations have shown that the phase behavior is more complex in this region with orthorhombic (bco) splitting of reflections occurring in the x-ray diffraction pattern above 32 GPa and coexisting diffraction signatures of bco and bcc structures are observed between 40 and 70 GPa. Here we have documented the simultaneous presence of bco and bcc reflections up to the melting point, negating the possibility that their coexistence might indicate a kinetically hindered first-order phase transformation. In this paper we have extended the observation of Sn melting relations into the megabar ($P>100$ GPa) range using the appearance of liquid diffuse scattering in x-ray diffraction patterns and discontinuities during thermal signal processing to diagnose the occurrence of melting. Both techniques yield consistent results that indicate the melting line maintains the same low slope up to the highest pressure examined and does not flatten. The results below approximately 40 GPa agree well with the melting relations produced recently using a multiphase equation of state fitted to available or assumed data. Above this pressure the experimental melting points lie increasingly below the predicted crystal-liquid phase boundary, but above the flat melting from past studies, indicating that the thermodynamic properties of the body-centered “$\gamma$”-Sn structure remain to be clarified.

The structural and magnetic properties of 30% and 50% Co-doped ZnO have been investigated in order to determine the influence of the presence of ${\mathrm{Co}}^{3+}$ as a potential $p$-type dopant. For 30% doping, ${\mathrm{Co}}^{3+}$ could be stabilized in the wurtzite lattice of ZnO without phase separation by providing high oxygen partial pressures during growth. At 50% Co concentration, the crystal lattice destabilizes. X-ray absorption spectroscopy and simulations are used to substantiate the valence and local structure of ${\mathrm{Co}}^{3+}$. Integral and element selective magnetometry reveals uncompensated antiferromagnetism of the Co atoms irrespective of being present as ${\mathrm{Co}}^{2+}$ or ${\mathrm{Co}}^{3+}$.

We use transport and neutron scattering to study the electronic phase diagram and spin excitations of ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ single crystals. Similar to Co- and Ni-doped NaFeAs, a bulk superconducting phase appears near $x\approx 2\%$ with the suppression of stripe-type magnetic order in NaFeAs. Upon further increasing Cu concentration the system becomes insulating, culminating in an antiferromagnetically ordered insulating phase near $x\approx 50\%$. Using transport measurements, we demonstrate that the resistivity in ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ exhibits non-Fermi-liquid behavior near $x\approx 1.8\%$. Our inelastic neutron scattering experiments reveal a single neutron spin resonance mode exhibiting weak dispersion along $c$ axis in ${\mathrm{NaFe}}_{0.98}{\mathrm{Cu}}_{0.02}\mathrm{As}$. The resonance is high in energy relative to the superconducting transition temperature $T_{\mathrm{c}}$ but weak in intensity, likely resulting from impurity effects. These results are similar to other iron pnictides superconductors despite that the superconducting phase in ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ is continuously connected to an antiferromagnetically ordered insulating phase near $x\approx 50\%$ with significant electronic correlations. Therefore, electron correlations is an important ingredient of superconductivity in ${\mathrm{NaFe}}_{1-x}{\mathrm{Cu}}_x\mathrm{As}$ and other iron pnictides.

The fractional Josephson effect has been observed in many instances as a signature of a topological superconducting state containing zero-energy Majorana modes. We present a nontopological scenario which can produce a fractional Josephson effect generically in semiconductor-based Josephson junctions, namely, a resonant impurity bound state weakly coupled to a highly transparent channel. We show that the fractional ac Josephson effect can be generated by the Landau-Zener processes which flip the electron occupancy of the impurity bound state. The Josephson effect signature for Majorana modes become distinct from this nontopological scenario only at low frequency. We prove that a variant of the fractional ac Josephson effect, namely, the low-frequency doubled Shapiro steps, can provide a more reliable signature of the topological superconducting state.

Inelastic neutron scattering measurements have been performed to investigate the spin waves of the quasi-one-dimensional antiferromagnetic ladder compound ${\mathrm{BaFe}}_2{\mathrm{S}}_3$, where a superconducting transition was observed under pressure [H. Takahashi et al., Nat. Mater. 14, 1008 (2015); T. Yamauchi et al., Phys. Rev. Lett. 115, 246402 (2015)]. By fitting the spherically averaged experimental data collected on a powder sample to a Heisenberg Hamiltonian, we find that the one-dimensional antiferromagnetic ladder exhibits a strong nearest-neighbor ferromagnetic exchange interaction ($S{J}_R=-71\pm 4$ meV) along the rung direction, an antiferromagnetic $S{J}_L=49\pm 3$ meV along the leg direction, and a ferromagnetic $S{J}_2=-15\pm 2$ meV along the diagonal direction. Our data demonstrate that the antiferromagnetic spin excitations are a common characteristic for the iron-based superconductors, while specific relative values for the exchange interactions do not appear to be unique for the parent states of the superconducting materials.

We study the transport properties of a topological system coupled to an ac electric field by means of Floquet-Keldysh formalism. We consider a semi-infinite chain of dimers coupled to a semi-infinite metallic lead and obtain the density of states and current when the system is out of equilibrium. Our formalism is nonperturbative and allows us to explore, in the thermodynamic limit, a wide range of regimes for the ac field, arbitrary values of the coupling strength to the metallic contact and corrections to the wide-band limit (WBL). We find that hybridization with the contact can change the dimerization phase, and that the current dependence on the field amplitude can be used to discriminate between them. We also show the appearance of side bands and nonequilibrium zero-energy modes, characteristic of the Floquet systems. Our results directly apply to the stability of nonequilibrium topological phases, when transport measurements are used for their detection.

The low energy magnetic excitation spectrum of charge stripe ordered ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_4, x=0.4$ and $x=0.45$ samples, were studied by neutron scattering. Two excitation modes are observed in both materials, one from the ordered magnetic moments, and a second mode consistent with pseudo-one-dimensional antiferromagnetic excitations of the charge stripe electrons (q-1D). The dispersion of the q-1D excitation follows the same relation as in $x=1/3$ composition, with even spectral weight in the two counterpropagating branches of the $x=0.4$ sample, however in the $x=0.45$ sample only one dispersion branch has any measurable spectral weight. The evolution of the q-1D excitations on doping to the checkerboard charge ordered phase is discussed.

By taking into account the charge and spin orderings and the exchange interactions between all the Landau levels, we investigate the integer quantum Hall effect of electrons in graphene using the mean-field theory. We find that the fourfold degeneracy of the Landau levels cannot be completely lifted by the Coulomb interactions. In particular, at fillings $\nu =4n+2$ with $n=0,1,...$, there is no splitting between the fourfold degenerated Landau levels. We show that with doping the degenerated lowest empty level can be sequentially filled one by one; the filled level is lower than the empty ones because of the Coulomb-exchange interactions. This result explains the step $\mathrm{\Delta }\nu =1$ in the quantized Hall conductivity. We present a highly efficient method for dealing with a huge number of the Coulomb couplings between all the Landau levels of the Dirac fermions.

We develop the formalism of fermionic matrix product states (fMPS) and show how irreducible fMPS fall in two different classes, related to the different types of simple ${\mathbb{Z}}_2$ graded algebras, which are physically distinguished by the absence or presence of Majorana edge modes. The local structure of fMPS with Majorana edge modes also implies that there is always a twofold degeneracy in the entanglement spectrum. Using the fMPS formalism, we make explicit the correspondence between the ${\mathbb{Z}}_8$ classification of time-reversal-invariant spinless superconductors and the modulo 8 periodicity in the representation theory of real Clifford algebras. Studying fMPS with general onsite unitary and antiunitary symmetries allows us to define invariants that label symmetry-protected phases of interacting fermions. The behavior of these invariants under stacking of fMPS is derived, which reveals the group structure of such interacting phases. We also consider spatial symmetries and show how the invariant phase factor in the partition function of reflection-symmetric phases on an unorientable manifold appears in the fMPS framework.

Interplay of Pomeranchuk instability (spontaneous symmetry breaking of the Fermi surface) and $d$-wave superconductivity is studied for the repulsive Hubbard model on the square lattice with the dynamical mean-field theory combined with the fluctuation exchange approximation (FLEX+DMFT). We show that the fourfold symmetric Fermi surface becomes unstable against a spontaneous distortion into twofold near the van Hove filling, where the symmetry of superconductivity coexisting with the Pomeranchuk-distorted Fermi surface is modified from the $d$-wave pairing to the $(d+s)$ wave. By systematically shifting the position of van Hove filling with varied second- and third-neighbor hoppings, we find that the transition temperature $T_{\mathrm{c}}^{\mathrm{PI}}$ for the Pomeranchuk instability is more sensitively affected by the position of van Hove filling than the superconducting $T_{\mathrm{c}}^{\mathrm{SC}}$. This implies that the filling region for strong Pomeranchuk instability and that for the $T_{\mathrm{c}}^{\mathrm{SC}}$ dome can be separated, and that Pomeranchuk instability can appear even if the peak of $T_{\mathrm{c}}^{\mathrm{PI}}$ is lower than the peak of $T_{\mathrm{c}}^{\mathrm{SC}}$. An interesting finding is that the Fermi surface distortion can enhance the superconducting $T_{\mathrm{c}}^{\mathrm{SC}}$ in the overdoped regime, which is explained with a perturbational picture for small distortions.

We have carried out a detailed first-principles study of the copper pyrovanadate ${\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$ which crystallizes in at least three different polymorphs $\alpha , \beta$, and $\gamma$. The magnetic properties of these systems are analyzed by calculating various exchange interactions and deriving the relevant spin Hamiltonian. Our detailed analysis based on the derived spin model suggests the crucial role of the crystal structure in governing the electronic and magnetic properties of the three different phases of the system. In particular, our calculations reveal that a subtle difference in the crystal structure has a substantial impact on the magnetic properties of the $\alpha$ phase. The important role of spin-orbit coupling (SOC) is also investigated for the three different phases of ${\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$. Although SOC stabilizes magnetic order in all the phases, the absence of inversion symmetry leads to an appreciable Dzyaloshinski-Moriya interaction in the $\alpha$ phase which in turn causes the canting of the spins and adds to the stabilization of the long-range order. Finally, from the symmetry analysis and total energy calculation we have obtained the magnetic ground state for the different phases of ${\mathrm{Cu}}_2{\mathrm{V}}_2{\mathrm{O}}_7$. While the symmetry-allowed magnetic ground states for the $\alpha$ and $\beta$ phases are in agreement with the experimental observations, the theoretically predicted magnetic ground state for the $\gamma$ phase is found to be a realization of a dimeric system with the potential to host novel physics.

We theoretically investigate the effects of backscattering and superconducting proximity terms between the edges of two multilayer fractional quantum Hall (FQH) systems. While the different layers are strongly interacting, we assume that tunneling between them is absent. Studying the boundaries between regions gapped by the two mechanisms in an $N$-layer system, we find $N$ localized zero-mode operators, realizing a generalized parafermionic algebra. We further propose an experiment capable of probing imprints of the generalized parafermionic bound states. This is done by coupling different superconducting contacts to different layers and examining the periodicity of the Josephson effect as a function of the various relative superconducting phases. Remarkably, even if we apply a phase difference between the superconductors in one layer, we induce a Josephson current at the other layers due to interlayer interactions. Furthermore, while the Josephson effect is commonly used to probe only charged degrees of freedom, the possibility of independently controlling the superconducting phase differences between the layers allows us to find imprints of the neutral modes of the underlying multilayer system. In particular, we propose two configurations, one of which is capable of isolating the signal associated with the charge modes while the other probes the neutral modes.

We investigate direct energy and heat transfer between two distant sites of a triple quantum dot connected to reservoirs, where one of the edge dots is driven by an ac-gate voltage. We theoretically propose how to implement heat and cooling engines mediated by long-range photoassisted transport. Additionally, we propose a simple setup to heat up coherently the two reservoirs symmetrically and a mechanism to store energy in the closed system. The present proposals can be experimentally implemented and easily controlled by tuning the external parameters.

The band alignment of prototypical semiconductors and insulators is investigated using first-principles calculations. A dielectric-dependent hybrid functional, where the nonlocal Fock exchange mixing is set at the reciprocal of the static electronic dielectric constant and the exchange correlation is otherwise treated as in the Perdew-Burke-Ernzerhof (PBE0) hybrid functional, is used as well as the Heyd-Scuseria-Ernzerhof (HSE06) hybrid and PBE semilocal functionals. In addition, these hybrid functionals are applied non-self-consistently to accelerate calculations. The systems considered include C and Si in the diamond structure, BN, AlP, AlAs, AlSb, GaP, GaAs, InP, ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe in the zinc-blende structure, MgO in the rocksalt structure, and GaN and ZnO in the wurtzite structure. Surface band positions with respect to the vacuum level, i.e., ionization potentials and electron affinities, and band offsets at selected zinc-blende heterointerfaces are evaluated as well as band gaps. The non-self-consistent approach speeds up hybrid functional calculations by an order of magnitude, while it is shown using HSE06 that the resultant band gaps and surface band positions are similar to the self-consistent results. The dielectric-dependent hybrid functional improves the band gaps and surface band positions of wide-gap systems over HSE06. The interfacial band offsets are predicted with a similar degree of precision. Overall, the performance of the dielectric-dependent hybrid functional is comparable to the $G{W}_0$ approximation based on many-body perturbation theory in the prediction of band gaps and alignments for most systems. The present results demonstrate that the dielectric-dependent hybrid functional, particularly when applied non-self-consistently, is promising for applications to systematic calculations or high-throughput screening that demand both computational efficiency and sufficient accuracy.

Motivated by recent experimental progress in the field of dipolar-Fermi gases, we investigate the quantum phases of dipolar fermions on a triangular ladder at half filling. Using density matrix renormalization group method, in the presence of onsite repulsion and intersite attractive interaction, we find an exotic spin-triplet superfluid phase in addition to the usual spin-density and charge-density waves. We examine the stability of the spin-triplet superfluid phase by varying hopping along the rungs of the triangle. The possibility of fermionic supersolidity has also been discussed, by considering three-body interaction in the Hamiltonian. We also study the effect of spin-dependent hopping on the stability of the spin-triplet superfluid phase.

${\mathrm{CePd}}_2{\mathrm{Al}}_{2-x}{\mathrm{Ga}}_x$ compounds crystallizing in the tetragonal ${\mathrm{CaBe}}_2{\mathrm{Ge}}_2$-type structure (space group $P4/nmm$) and undergoing a structural phase transition to an orthorhombic structure ($Cmme$) at low temperatures were studied by means of neutron scattering. The amplitude-modulated magnetic structure of ${\mathrm{CePd}}_2{\mathrm{Al}}_2$ is described by an incommensurate propagation vector $\vec{k}=({\delta }_x,\frac{1}{2}+{\delta }_y,0)$ with ${\delta }_x=0.06$ and ${\delta }_y=0.04$. The magnetic moments order antiferromagnetically within the $ab$ planes stacked along the $c$ axis and are arranged along the direction close to the orthorhombic $a$ axis with a maximum value of 1.5(1) ${\mu }_{\mathrm{B}}/{\mathrm{Ce}}^{3+}$. ${\mathrm{CePd}}_2{\mathrm{Ga}}_2$ reveals a magnetic structure composed of two components: the first is described by the propagation vector $\overrightarrow{k_1}=(\frac{1}{2},\frac{1}{2},0)$, and the second one propagates with $\overrightarrow{k_2}=(0,\frac{1}{2},0)$. The magnetic moments of both components are aligned along the same direction—the orthorhombic [100] direction—and their total amplitude varies depending on the mutual phase of magnetic moment components on each Ce site. The propagation vectors $\overrightarrow{k_1}$ and $\overrightarrow{k_2}$ describe also the magnetic structure of substituted ${\mathrm{CePd}}_2{\mathrm{Al}}_{2-x}{\mathrm{Ga}}_x$ compounds, except the one with $x=0.1.{\mathrm{CePd}}_2{\mathrm{Al}}_{1.9}{\mathrm{Ga}}_{0.1}$ with magnetic structure described by $\vec{k}$ and $\overrightarrow{k_1}$ stays on the border between pure ${\mathrm{CePd}}_2{\mathrm{Al}}_2$ and the rest of the series. Determined magnetic structures are compared with other Ce 112 compounds. Inelastic neutron scattering experiments disclosed three nondispersive magnetic excitations in the paramagnetic state of ${\mathrm{CePd}}_2{\mathrm{Al}}_2$, while only two crystal field (CF) excitations are expected from the splitting of ground state $J=\frac{5}{2}$ of the ${\mathrm{Ce}}^{3+}$ ion in a tetragonal/orthorhombic point symmetry. Three magnetic excitations at 1.4, 7.8, and 15.9 meV are observed in the tetragonal phase of ${\mathrm{CePd}}_2{\mathrm{Al}}_2$. A structural phase transition to an orthorhombic structure shifts the first excitation up to 3.7 meV, while the other two excitations remain at almost the same energy. The presence of an additional magnetic peak is discussed and described within the Thalmeier-Fulde CF-phonon coupling (i.e., magnetoelastic coupling) model generalized to the tetragonal point symmetry. The second parent compound ${\mathrm{CePd}}_2{\mathrm{Ga}}_2$ does not display any sign of additional magnetic excitation. The expected two CF excitations were observed. The development of magnetic excitations in the ${\mathrm{CePd}}_2{\mathrm{Al}}_{2-x}{\mathrm{Ga}}_x$ series is discussed and crystal field parameters determined.