We investigate the entanglement spectra of topological insulators, which manifest edge states on a lattice with spatial boundaries. In the physical energy spectrum, a subset of the edge states that intersect the Fermi level translates to discontinuities in the trace of the single-particle entanglement spectrum, which we call a “trace index.” We find that any free-fermion topological insulator that exhibits spectral flow has a nonvanishing trace index, which provides us with a new description of topological invariants. In addition, we identify the signatures of spectral flow in the single-particle and many-body entanglement spectrum; in the process we present new methods to extract topological invariants and establish a connection between entanglement and quantum Hall physics.

There is evidence that the photo-generated singlet exciton in polycrystalline pentacene films undergoes rapid and efficient fission to form two triplet excitons. However, the role of exciton fission in pentacene has been controversial, with previous studies putting forward alternate relaxation pathways for the singlet exciton, such as excimer or charge formation, or internal conversion to a doubly excited exciton. We report temperature- and angular-dependent ultrafast transient optical absorption measurements in a wide spectral and temporal window. Angular-dependent transient spectra identify a common origin to photo-induced absorptions at 530 and 860 nm, which we associate with triplet excitons. These constitute the dominant relaxation channel for singlet excitons. Other features, particularly near 620 nm, previously assigned to excimers or electronic charges, are shown to be caused by thermal modulation from the optical pump.

By using density-functional theory in combination with the coherent-potential approximation and the disordered local magnetic moment picture, we demonstrate that the competing high-temperature cubic phases of paramagnetic Fe correspond to two distinct total energy minima in the tetragonal (Bain) configurational space. Both the face-centered-cubic (fcc) and the body-centered-cubic (bcc) lattices are dynamically stable, and at static conditions the fcc structure is found to be the thermodynamically stable phase. The theoretical bcc and fcc bulk parameters are in agreement with the experimental data. Due to the shallow energy minimum around the bcc structure, increasing temperature is predicted to stabilize the bcc ($\delta$) phase against the fcc ($\gamma$) one.

Despite intense efforts during the last 25 years, the physics of unconventional superconductors, including the cuprates with a very high transition temperature, is still a controversial subject. It is believed that superconductivity in many of these strongly correlated metallic systems originates in the physics of quantum phase transitions, but quite diverse perspectives have emerged on the fundamentals of the electron-pairing physics, ranging from Hertz-style critical spin fluctuation glue to the holographic superconductivity of string theory. Here we demonstrate that the gross energy scaling differences that are behind these various pairing mechanisms are directly encoded in the frequency and temperature dependence of the dynamical pair susceptibility. This quantity can be measured directly via the second-order Josephson effect and it should be possible employing modern experimental techniques to build a “pairing telescope” that gives a direct view on the origin of quantum critical superconductivity.

We analyze the infrared behavior of effective $N$-point interactions between order parameter fluctuations for nematic and other quantum critical electron systems with a scalar order parameter in two dimensions. The interactions exhibit a singular momentum and energy dependence and thus can not be represented by local vertices. They diverge for all $N\ge 4$ in a collinear low-energy limit, where energy variables scale to zero faster than momenta, and momenta become increasingly collinear. The degree of divergence is not reduced by any cancellations and renders all $N$-point interactions marginal. A truncation of the order parameter action at quartic or any other finite order is therefore not justified. The same conclusion can be drawn for the effective action describing fermions coupled to a U$\left(1\right)$ gauge field in two dimensions.

I propose a new type of capacitor with a very high volumetric capacitance. It is based on the known phenomenon of the sharp increase of the dielectric constant of a metal-insulator composite in the vicinity of the percolation threshold on the insulator side. The optimization suggests that the sizes of the metallic particles should fall within the nanoscale. The distance between planar electrodes should be somewhat larger than the correlation length of the percolation theory and $\approx$10–20 times larger than the size of the particles while the area of the electrodes could be unlimited. The random electric field in the capacitor is calculated and is shown to be larger than the average field corresponding to the potential difference of the electrodes. This random field is potentially responsible for the dielectric breakdown. The estimated breakdown voltage of the capacitor shows that the stored energy density might be significantly larger than that of electrolytic capacitors while the volumetric capacitances might be comparable. The charging and discharging times should be significantly smaller than the corresponding times of batteries and even electrolytic capacitors.

We have quantitatively tested the theoretical model on the collapse of spin slitting in the quantum Hall effect regime proposed by Fogler and Shklovskii [Phys. Rev. B 52, 17366 (1995)] in a high-mobility two-dimensional electron system (2DES) realized in a heterojunction insulated-gate field-effect transistor. In the 2DES density range between $n$ $=$ 2 × 10${}^{10}$ and 2 × 10${}^{11}$ cm${}^{-2}$, the Landau level number $N$ displays a power-law dependence on the critical electron density $n_{\mathrm{c}}$ where the spin splitting collapses and $N$ $=$ 11.47 × $n_{\mathrm{c}}$${}^{0.64\pm 0.01}$ ($n_{\mathrm{c}}$ is in units of 10${}^{11}$ cm${}^{-2}$). This power-law dependence is in good agreement with the theoretical prediction in the low-density regime.

We study multiband semiconducting nanowires proximity coupled with an $s$-wave superconductor and calculate the topological phase diagram as a function of the chemical potential and magnetic field. The nontrivial topological state corresponds to a superconducting phase supporting an odd number of pairs of Majorana modes localized at the ends of the wire, whereas the nontopological state corresponds to a superconducting phase with no Majoranas or with an even number of pairs of Majorana modes. Our key finding is that multiband occupancy not only lifts the stringent constraint of one-dimensionality, but also allows having higher carrier density in the nanowire. Consequently, multiband nanowires are better suited for stabilizing the topological superconducting phase and for observing the Majorana physics. We present a detailed study of the parameter space for multiband semiconductor nanowires focusing on understanding the key experimental conditions required for the realization and detection of Majorana fermions in solid-state systems. We include various sources of disorder and characterize their effects on the stability of the topological phase. Finally, we calculate the local density of states as well as the differential tunneling conductance as functions of external parameters and predict the experimental signatures that would establish the existence of emergent Majorana zero-energy modes in solid-state systems.

We analyze doping dependence of the spin resonance of an $s^{\pm }$ superconductor and its sensitivity to the ellipticity of electron pockets, to magnetic and nonmagnetic impurities, and to the angle dependence of the superconducting gap along electron Fermi surfaces. We show that the maximum intensity of the resonance shifts from commensurate to incommensurate momentum above some critical doping which decreases with increasing ellipticity. Angle dependence of the gap and particularly the presence of accidental nodes lowers the overall intensity of the resonance peak and shifts its position toward the onset of the particle-hole continuum. Still, however, the resonance remains a true $\delta$ function in the clean limit. When nonmagnetic or magnetic impurities are present, the resonance broadens and its position shifts. The shift depends on the type of impurities and on the ratio of intraband and interband scattering components. The ratio ${\Omega }_{\mathrm{res}}$/T${}_c$ increases almost linearly with the strength of the interband impurity scattering, in agreement with the experimental data. We also compare spin response of $s^{\pm }$ and $s^{++}$ superconductors. We show that there is no resonance for $s^{++}$ gap, even when there is a finite mismatch between electron and hole Fermi surfaces shifted by the antiferromagnetic momentum.

We report a multiband transport study of bilayer graphene at high carrier densities. Employing a poly(ethylene)oxide-CsClO${}_4$ solid polymer electrolyte gate we demonstrate the filling of the high-energy subbands in bilayer graphene samples at carrier densities $\left|n\right|⩾2.4\times {10}^{13}$ cm${}^{-2}$. We observe a sudden increase of resistance and the onset of a second family of Shubnikov–de Haas (SdH) oscillations as these high-energy subbands are populated. From simultaneous Hall and magnetoresistance measurements, together with SdH oscillations in the multiband conduction regime, we deduce the carrier densities and mobilities for the higher-energy bands separately and find the mobilities to be at least a factor of 2 higher than those in the low-energy bands.

We show numerically that near-field heat flux can be modulated by orders of magnitude upon switching from the metallic to the insulating phase of vanadium dioxide. Furthermore, the resonant phonon polariton interaction for the insulating phase enhances near-field thermal transfer by three orders of magnitude. The effect should therefore be measurable with existing experimental setups and could find broad applications for systems where thermal control at the nanoscale is required.

Four $s{p}^3$ carbon allotropes with six, eight, and 16 atoms per primitive cell have been derived using a combination of metadynamics simulations and topological scan. A chiral orthorhombic phase $o$C16 ($C{222}_1$) was found to be harder than monoclinic M-carbon and shows excellent stability in the high-pressure range. A second orthorhombic phase of $Cmmm$ symmetry, by $\sim$0.028 eV/atom energetically lower than W-carbon, can be formed from graphite at $\sim$9 GPa. In general, the mechanical response under pressure was found to depend on the structure topology, which reflects the way rings are formed from an initial graphene layer stacking.

We present a theoretical approach to describing the Mott transition of electrons on a two-dimensional lattice that begins with the low-energy effective theory of the Fermi liquid. The approach to the Mott transition must be characterized by the suppression of density and current fluctuations that correspond to specific shape deformations of the Fermi surface. We explore the nature of the Mott insulator and the corresponding Mott transition when these shape fluctuations of the Fermi surface are suppressed without making any a priori assumptions about other Fermi surface shape fluctuations. Building on insights from the theory of the Mott transition of bosons, we implement this suppression by identifying and condensing vortex degrees of freedom in the phase of the low-energy electron operator. We show that the resulting Mott insulator is a quantum spin liquid with a spinon Fermi surface coupled to a $U\left(1\right)$ gauge field, which is usually described within a slave particle formulation. Our approach thus provides a coarse-grained treatment of the Mott transition and the proximate spin liquid that is nevertheless equivalent to the standard slave particle construction. This alternate point of view provides further insight into the novel physics of the Mott transition and the spin liquid state that is potentially useful. We describe a generalization that suppresses spin antisymmetric fluctuations of the Fermi surface that leads to a spin-gapped charge metal previously also discussed in terms of slave particle constructions.

The theory of the spectra of coupled magnetoelastic waves in ferromagnetic shape-memory alloys (FSMA) is developed. The possibility of an abnormally strong coupling of spin waves with the soft elastic mode at approaching the martensitic transformation (MT) temperature is disclosed. In particular the magnetoelastic waves in Ni–Mn–Ga single crystals are considered. A considerable (by an order of magnitude) reduction of the shear elastic modulus and an appropriate lowering of the transversal velocity of sound in the applied magnetic field are predicted. Optimum conditions for the experimental observation of the predicted effects are specified.

Surface plasmon modes supported by graphene ribbon waveguides are studied and classified. The properties of both modes with the field concentration within the ribbon area (waveguiding modes) and on the edges (edge modes) are discussed. The waveguide and edge modes are shown to be separated from each other by a gap in wave numbers. The even-parity hybridized edge mode results to be the fundamental electromagnetic mode of the ribbon, possessing also the lowest losses. All of the plasmonic modes in the ribbons have an optimum frequency, at which the absorption losses are minimum, due to compromise between the plasmon confinement and the decrease of the group velocity close to the modal cutoff. The presented results show that the diffraction limit in graphene ribbons can be surpassed.

We report the observation of the superconducting proximity effect in nanoribbons of a candidate topological insulator (Bi${}_2$Se${}_3$), which is interfaced with superconducting (tungsten) contacts. We observe a supercurrent and multiple Andreev reflections for channel lengths that are much longer than the inelastic and diffusive thermal lengths deduced from normal-state transport. This suggests that the proximity effect couples preferentially to a ballistic surface transport channel, even in the presence of a coexisting diffusive bulk channel. When a magnetic field is applied perpendicular to the plane of the nanoribbon, we observe magnetoresistance oscillations that are periodic in magnetic field. Quantitative comparison with a model of vortex blockade relates the occurrence of these oscillations to the formation of Pearl vortices in the region of proximity-induced superconductivity.

Motivated by recent Fermi-surface and transport measurements on LaNiO${}_3$, we study the Mott metal-insulator transitions of perovskite nickelates, with the chemical formula $R$NiO${}_3$, where $R$ is a rare-earth ion. We introduce and study a minimal two-band model, which takes into account only the e${}_g$ bands. In the weak to intermediate correlation limit, a Hartree-Fock analysis predicts charge and spin order consistent with experiments on $R=\text{Pr}$, Nd, driven by Fermi surface nesting. It also produces an interesting semimetallic electronic state in the model when an ideal cubic structure is assumed. We also study the model in the strong-interaction limit and find that the charge and magnetic order observed in experiment exist only in the presence of very large Hund’s coupling, suggesting that additional physics is required to explain the properties of the more insulating nickelates, $R=\text{Eu}$, Lu, Y. Next, we extend our analysis to slabs of finite thickness. In ultrathin slabs, quantum confinement effects substantially change the nesting properties and the magnetic ordering of the bulk, driving the material to exhibit highly anisotropic transport properties. However, pure confinement alone does not significantly enhance insulating behavior. Based on these results, we discuss the importance of various physical effects and propose some experiments.

The need for faster magnetic recording devices has driven researchers to seek more efficient ways to reverse the magnetization. A large variety of methods and materials has been investigated to accomplish the most rapid spin reorientation, ranging from magnetic field pulses in ferromagnetic compounds to ultrashort optical excitations in ferrimagnetic and antiferromagnetic materials. To date, the precessional motion in an external field is the most effective route to control the magnetization in ferromagnets. Reversible switching under simple experimental conditions, i.e., in air and at room temperature, with a moderate optical excitation is a goal that has not been reached so far. Here we demonstrate that, using short laser pulses, the magnetization of a thin biaxial ferromagnetic layer can be optically and repeatedly commuted between well-defined directions on a time scale of 100 ps.

We present Lu${}_2$MnCoO${}_6$, a multiferroic member of the double perovskites that we have investigated using x-ray and neutron diffraction, specific heat, magnetization, electric polarization, and dielectric constant measurements. This material possesses a net electric polarization strongly coupled to a net magnetization below 35 K, despite the antiferromagnetic ordering of the $S=3/2$ Mn${}^{4+}$ and Co${}^{2+}$ spins in an $\uparrow \uparrow \downarrow \downarrow$ configuration along the $c$ direction. We discuss the magnetic order in terms of a condensation of domain boundaries between $\uparrow \uparrow$ and $\downarrow \downarrow$ ferromagnetic domains, with each domain boundary producing an electric polarization due to spatial inversion symmetry breaking. In an applied magnetic field the domain boundaries slide, controlling the size of the magnetization, electric polarization, and magnetoelectric coupling.

The $ab$ plane resistivity of Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ ($x=0.00$, 0.09, 0.16, 0.21, and 0.28) was studied under nearly hydrostatic pressures, up to 7.4 GPa, in order to explore the $T-P$ phase diagram and to compare the combined effects of isoelectronic Ru substitution and pressure. The parent compound BaFe${}_2$As${}_2$ exhibits a structural/magnetic phase transition near 134 K. At ambient pressure, progressively increasing Ru concentration suppresses this phase transition to lower temperatures at an approximate rate of $\sim$5 K/% Ru correlated with the emergence of superconductivity. By applying pressure to this system, a similar behavior is seen for each concentration: the structural/magnetic phase transition is further suppressed and superconductivity induced and ultimately, for larger $x$ Ru and $P$, suppressed. A detailed comparison of the $T-P$ phase diagrams for all Ru concentrations shows that 3 GPa of pressure is roughly equivalent to $10\%$ Ru substitution. Furthermore, due to the sensitivity of Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ to pressure conditions, the melting of the liquid media, $4:6$ light mineral oil : $n$-pentane and $1:1$ isopentane : $n$-pentane, used in this study could be readily seen in the resistivity measurements. This feature was used to determine the freezing curves for these media and to infer their room temperature, hydrostatic limits: 3.5 and 6.5 GPa, respectively.