Studies of Majorana bound states in semiconducting nanowires frequently neglect the orbital effect of a magnetic field. Systematically studying its role leads us to several conclusions for designing Majoranas in this system. Specifically, we show that for experimentally relevant parameter values the orbital effect of a magnetic field has a stronger impact on the dispersion relation than the Zeeman effect. While Majoranas do not require the presence of only one dispersion subband, we observe that the size of the Majoranas becomes unpractically large, and the band gap unpractically small, when more than one subband is filled. Since the orbital effect of a magnetic field breaks several symmetries of the Hamiltonian, it leads to the appearance of large regions in parameter space with no band gap whenever the magnetic field is not aligned with the wire axis. The reflection symmetry of the Hamiltonian with respect to the plane perpendicular to the wire axis guarantees that the wire stays gapped in the topologically nontrivial region as long as the field is aligned with the wire.

We present a systematic study of the variables affecting the electronic and optical properties of two-dimensional (2D) crystals within ab initio $GW$ and $GW$ plus Bethe-Salpeter equation ($GW$-BSE) calculations. As a prototypical 2D transition metal dichalcogenide material, we focus our study on monolayer ${\mathrm{MoS}}_2$. We find that the reported variations in $GW$-BSE results in the literature for monolayer ${\mathrm{MoS}}_2$ and related systems arise from different treatments of the long-range Coulomb interaction in supercell calculations and convergence of $k$-grid sampling and cutoffs for various quantities such as the dielectric screening. In particular, the quasi-2D nature of the system gives rise to fast spatial variations in the screening environment, which are computationally challenging to resolve. We also show that common numerical treatments to remove the divergence in the Coulomb interaction can shift the exciton continuum leading to false convergence with respect to $k$-point sampling. Our findings apply to $GW$-BSE calculations on any low-dimensional semiconductors.

We study spontaneous dimerization transitions in a Heisenberg spin-1 chain with additional next-nearest-neighbor and three-site interactions using extensive numerical simulations and a conformal field-theory analysis. We show that the transition can be second order in the Wess-Zumino-Witten (WZW) $\mathrm{SU}{\left(2\right)}_2$ or Ising universality class, or first order. We argue that these features are generic because of a marginal operator in the WZW $\mathrm{SU}{\left(2\right)}_2$ model and because of two topologically distinct nondimerized phases with or without edge states. We also provide explicit numerical evidence of conformal towers of singlets inside the spin gap at the Ising transition. Implications for other models are briefly discussed.

Unlike most quantum systems which rapidly become incoherent as temperature is raised, strong correlations persist at elevated temperatures in $S=\frac{1}{2}$ dimer magnets, as revealed by the unusual asymmetric line shape of their excitations at finite temperatures. Here, we quantitatively explore and parametrize the strongly correlated magnetic excitations at finite temperatures using high-resolution inelastic neutron scattering of the model compound ${\mathrm{BaCu}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ which we show to be an alternating antiferromagnetic-ferromagnetic $\mathrm{spin}-\frac{1}{2}$ chain. Comparison to state of the art computational techniques shows excellent agreement over a wide temperature range. Our findings hence demonstrate the possibility to quantitatively predict coherent behavior at elevated temperatures in quantum magnets.

Motivated by the high superconducting transition temperature of monolayer FeSe on ${\mathrm{SrTiO}}_3$, we propose a potential three-dimensional high-temperature superconductor superlattice FeSe-${\mathrm{SrTiO}}_3$ and study its structural stability and electronic structure using density functional theory. We find that the binding energy between the FeSe and ${\mathrm{SrTiO}}_3$ layers is about $\sim 0.7$ eV per (${\mathrm{Fe}}_2{\mathrm{Se}}_2$) unit and that it saturates already within a single ${\mathrm{TiO}}_2$ atomic layer of ${\mathrm{SrTiO}}_3$. In addition we analyzed the dynamical stability of the superlattice and compared it to the case of bulk ${\mathrm{SrTiO}}_3$.

We present a study of the tetragonal to collapsed-tetragonal transition of ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ using angle-resolved photoemission spectroscopy and dynamical mean field theory-based electronic structure calculations. We observe that the collapsed-tetragonal phase exhibits reduced correlations and a higher coherence temperature due to the stronger Fe-As hybridization. Furthermore, a comparison of measured photoemission spectra and theoretical spectral functions shows that momentum-dependent corrections to the density functional band structure are essential for the description of low-energy quasiparticle dispersions. We introduce those using the recently proposed combined “screened exchange + dynamical mean field theory” scheme.

We develop an approach based on edge theories to calculate the entanglement entropy and related quantities in (2+1)-dimensional topologically ordered phases. Our approach is complementary to, e.g., the existing methods using replica trick and Witten's method of surgery, and applies to a generic spatial manifold of genus $g$, which can be bipartitioned in an arbitrary way. The effects of fusion and braiding of Wilson lines can be also straightforwardly studied within our framework. By considering a generic superposition of states with different Wilson line configurations, through an interference effect, we can detect, by the entanglement entropy, the topological data of Chern-Simons theories, e.g., the $R$ symbols, monodromy, and topological spins of quasiparticles. Furthermore, by using our method, we calculate other entanglement/correlation measures such as the mutual information and the entanglement negativity. In particular, it is found that the entanglement negativity of two adjacent noncontractible regions on a torus provides a simple way to distinguish Abelian and non-Abelian topological orders.

The strange correlator [Phys. Rev. Lett. 112, 247202 (2014)] has been proposed as a measure of symmetry protected topological order in one- and two-dimensional systems. It takes the form of a spin-spin correlation function, computed as a mixed overlap between the state of interest and a trivial local product state. We demonstrate that it can be computed exactly (asymptotically, in the Monte Carlo sense) for various Affleck-Kennedy-Lieb-Tasaki states by direct evaluation of the wave function within the valence bond loop gas framework. We present results for lattices with chain, square, honeycomb, cube, diamond, and hyperhoneycomb geometries. In each case, the spin quantum number $S$ is varied such that $2S$ (the number of valence bonds emerging from each site) achieves various integer multiples of the lattice coordination number. We introduce the concept of strange correlator loop winding number and point to its utility in testing for the presence of symmetry protected topological order.

We develop the theory of quantum transport and magnetoconductivity for two-dimensional electrons with an arbitrarily large (even exceeding the Fermi energy), linear-in-momentum Rashba or Dresselhaus spin-orbit splitting. For short-range disorder potentials, we derive the analytical expression for the quantum conductivity correction, which accounts for interference processes with an arbitrary number of scattering events and is valid beyond the diffusion approximation. We demonstrate that the zero-field conductivity correction is given by the sum of the universal logarithmic “diffusive” term and a “ballistic” term. The latter is temperature independent and encodes information about the spectrum properties. This information can be extracted experimentally by measuring the conductivity correction at different temperatures and electron concentrations. We calculate the quantum correction in the whole range of classically weak magnetic fields and find that the magnetoconductivity is negative both in the diffusive and in the ballistic regimes, for an arbitrary relation between the Fermi energy and the spin-orbit splitting. We also demonstrate that the magnetoconductivity changes with the Fermi energy when the Fermi level is above the “Dirac point” and does not depend on the Fermi energy when it goes below this point.

Majorana bound states (MBSs) nested in a topological nanowire are predicted to manifest nonlocal correlations in the presence of a finite energy splitting between the MBSs. However, the signal of the nonlocal correlations has not yet been detected in experiments. A possible reason is that the energy splitting is too weak and seriously affected by many system parameters. Here we investigate the charging energy induced nonlocal correlations in a hybrid device of MBSs and quantum dots. The nanowire that hosts the MBSs is assumed in proximity to a mesoscopic superconducting island with a finite charging energy. Each end of the nanowire is coupled to one lead via a quantum dot with resonant levels. With a floating superconducting island, the devices show a negative differential conductance and giant super-Poissonian shot noise, due to the interplay between the nonlocality of the MBSs and dynamical Coulomb blockade effect. When the island is strongly coupled to a bulk superconductor, the current cross correlations at small lead chemical potentials are negative by tuning the dot energy levels. In contrast, the cross correlation is always positive in a non-Majorana setup. This difference may provide a signature for the existence of the MBSs.

We obtain analytic expressions for the conductivity of pristine (pure) graphene in the framework of the Dirac model using the polarization tensor in (2+1) dimensions defined along the real frequency axis. It is found that at both zero and nonzero temperature $T$ the in-plane and out-of-plane conductivities of graphene are equal to each other with a high precision and essentially do not depend on the wave vector. At $T=0$ the conductivity of graphene is real and equal to ${\sigma }_0=e^2/\left(4\hslash \right)$ up to small nonlocal corrections in accordance with many authors. At some fixed $T\ne 0$ the real part of the conductivity varies between zero at low frequencies $\omega$ and ${\sigma }_0$ for optical $\omega$. If $\omega$ is fixed, the conductivity varies between ${\sigma }_0$ at low $T$ and zero at high $T$. The imaginary part of the conductivity of graphene is shown to depend on the ratio of $\omega$ to $T$. In accordance with the obtained asymptotic expressions, at fixed $T$ it varies from infinity at $\omega =0$ to a negative minimum value reached at some $\omega$, and then approaches to zero with further increase of $\omega$. At fixed $\omega$ the imaginary part of the conductivity varies from zero at $T=0$, reaches a negative minimum at some $T$, and then goes to infinity together with $T$. The numerical computations of both the real and imaginary parts of the conductivity are performed. The above results are obtained in the framework of quantum electrodynamics at nonzero temperature and can be generalized for graphene samples with nonzero mass gap parameter and chemical potential.

Bottom-up fabrication of graphene antidot lattices (GALs) has previously yielded atomically precise structures with subnanometer periodicity. Focusing on this type of experimentally realized GAL, we perform density functional theory calculations on the pristine structure as well as GALs with edge carbon atoms substituted with boron or nitrogen. We show that $p$- and $n$-type doping levels emerge with activation energies that depend on the level of hydrogenation at the impurity. Furthermore, a tight-binding parametrization together with a Green's function method are used to describe more dilute doping. Finally, random configurations of impurities in moderately doped systems are considered to show that the doping properties are robust against disorder.

Using a polaron master equation approach, we investigate the resonance fluorescence spectra from coherently driven quantum dots (QDs) coupled to an acoustic phonon bath and photonic crystal waveguides with a rich local density of photon states (LDOS). Resonance fluorescence spectra from QDs in semiconductor crystals are known to show strong signatures of electron-phonon interactions, but when coupled to a structured photonic reservoir, the QD emission properties are also determined by the frequency dependence of the LDOS of the photon reservoir. Here, we investigate the simultaneous role of coupled photon and phonon baths on the characteristic Mollow triplet spectra from a strongly driven QD. As an example structured photonic reservoir, we first study a photonic crystal coupled cavity waveguide, and find that photons and phonons have counterinteracting effects near the upper mode edge of the coupled-cavity waveguide, thus establishing the importance of their separate roles in determining the emission spectra. The general theory is developed for arbitrary photonic reservoirs and is further applied to determine the resonance fluorescence spectra from a realistic, disordered W1 photonic crystal waveguide showing important photon-phonon interaction effects that are directly relevant to emerging experiments and theoretical proposals.

Motivated by questions about the open-system dynamics of topological quantum matter, we investigated the quantum Brownian motion of an electron in a homogeneous magnetic field. When the Fermi length $l_F=\hslash /\left(v_F{m}_{\text{eff}}\right)$ becomes much longer than the magnetic length $l_B={(\hslash c/eB)}^{1/2}$, then the spatial coordinates $X,Y$ of the electron cease to commute, $[X,Y]=i{l}_B^2$. As a consequence, localization of the electron becomes limited by Heisenberg uncertainty, and the linear bath-electron coupling becomes unconventional. Moreover, because the kinetic energy of the electron is quenched by the strong magnetic field, the electron has no energy to give to or take from the bath, and so the usual connection between frictional forces and dissipation no longer holds. These two features make quantum Brownian motion topological, in the regime $l_F\gg l_B$, which is at the verge of current experimental capabilities. We model topological quantum Brownian motion in terms of an unconventional operator Langevin equation derived from first principles, and solve this equation with the aim of characterizing diffusion. While diffusion in the noncommutative plane turns out to be conventional, with the mean displacement squared being proportional to $t^{\alpha }$ and $\alpha =1$, there is an exotic regime for the proportionality constant in which it is directly proportional to the friction coefficient and inversely proportional to the square of the magnetic field: in this regime, friction helps diffusion and the magnetic field suppresses all fluctuations. We also show that quantum tunneling can be completely suppressed in the noncommutative plane for suitably designed metastable potential wells, a feature that might be worth exploiting for storage and protection of quantum information.

We study and compare two analytic models of graphene quantum dots for calculating charge relaxation times due to electron-phonon interaction. Recently, charge relaxation processes in graphene quantum dots have been probed experimentally and here we provide a theoretical estimate of relaxation times. By comparing a model with pure edge confinement to a model with electrostatic confinement, we find that the latter features much larger relaxation times. Interestingly, relaxation times in electrostatically defined quantum dots are predicted to exceed the experimentally observed lower bound of $\sim 100$ ns.

Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were proposed, but few of them (if any) are derived from microscopic considerations through systematic and controlled averaging procedures. In this paper we present a two-dimensional continuum theory that is obtained by systematic averaging of the equations of motion of discrete dislocations. It is shown that in the evolution equations of the dislocation densities diffusionlike terms neglected in earlier considerations play a crucial role in the length scale selection of the dislocation density fluctuations. It is also shown that the formulated continuum theory can be derived from an averaged energy functional using the framework of phase field theories. However, in order to account for the flow stress one has in that case to introduce a nontrivial dislocation mobility function, which proves to be crucial for the instability leading to patterning.

Because of the enormous range of time and space scales involved in dislocation dynamics, plastic modeling at macroscale requires a continuous formulation. In this paper, we present a rigorous formulation of the transition between the discrete, where plastic flow is resolved at the scale of individual dislocations, and the continuum, where dislocations are represented by densities. First, we focus on the underlying coarse-graining procedure. Our work reveals that both a spatiotemporal convolution and an ensemble average are required and that the emerging correlation-induced stresses are scale dependent. Each of these stresses can be expanded into the sum of two components. The first one depends on the local values of the dislocation densities and always opposes the sum of the applied stress and long-range mean field stress generated by the geometrically necessary dislocation (GND) density; this stress acts as a friction stress. The second component depends on the local gradients of the dislocation densities and is inherently associated to a translation of the elastic domain; therefore, it acts as a back stress. Finally, we show that that these friction and back stresses contain symmetry-breaking components that were missing in previous continuous formulations and that make, at mesoscale, the local stress experienced by dislocations depend on the sign of their Burgers vectors.

The intermediate-valent polymorphs $\alpha$- and $\beta -{\mathrm{YbAlB}}_4$ exhibit quantum criticality and other novel properties not usually associated with intermediate valence. Iron doping induces quantum criticality in $\alpha -{\mathrm{YbAlB}}_4$ and magnetic order in both compounds. We report results of muon spin relaxation ($\mu \mathrm{SR}$) experiments in $\alpha -{\mathrm{YbAl}}_{1-x}{\mathrm{Fe}}_x{\mathrm{B}}_4, x=0.014$ and 0.25. For $x=0.014$ we find no evidence for magnetic order down to 25 mK. The dynamic muon spin relaxation rate ${\lambda }_d$ exhibits a power-law temperature dependence ${\lambda }_d\propto T^{-a}, a=0.40\left(4\right)$, in the temperature range 100 mK–2 K, in disagreement with predictions by theories of antiferromagnetic (AFM) or valence quantum critical behavior. For $x=0.25$, where AFM order develops in the temperature range 7.5–10 K, we find coexistence of meso- or macroscopically segregated paramagnetic and AFM phases, with considerable disorder in the latter down to 2 K.