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Using density functional theory, we study the lattice dynamical properties of magnetite (Fe$_3$O$_4$) in the high-temperature cubic and low-temperature monoclinic phases. The calculated phonon dispersion curves and phonon density of states are compared with the available experimental data obtained by inelastic neutron, inelastic x-ray, and nuclear inelastic scattering. We find a very good agreement between the theoretical and experimental results for the monoclinic $Cc$ structure revealing the strong coupling between charge-orbital (trimeron) order and specific phonon modes. For the cubic phase, clear discrepancies arise which, remarkably, can be understood assuming that the strong trimeron-phonon coupling can be extended above the Verwey transition, with lattice dynamics influenced by the short-range trimeron order instead of the average cubic structure. Our results establish the validity of trimerons (and trimeron-phonon coupling) in explaining the physics of magnetite much beyond their original formulation., Comment: 11 pages, 9 figures, 1 table

Topological semimetals with different types of band crossings provide a rich platform to realize novel fermionic excitations, known as topological fermions. In particular, some fermionic excitations can be direct analogues of elementary particles in quantum field theory when both obey the same laws of physics in the low-energy limit. Examples include Dirac and Weyl fermions, whose solid-state realizations have provided new insights into long-sought phenomena in high-energy physics. Recently, theorists predicted new types of fermionic excitations in condensed-matter systems without any high-energy counterpart, and their existence is protected by crystalline symmetries. By studying the topology of the electronic structure in PdBiSe using density functional theory calculations and bulk-sensitive soft X-ray angle-resolved photoemission spectroscopy, we demonstrate a coexistence of four different types of topological fermions: Weyl, Rarita-Schwinger-Weyl, double class-II three-component, and charge-2 fourfold fermions. Our discovery provides a remarkable platform to realize multiple novel fermions in a single solid, charting the way forward to studies of their potentially exotic properties as well as their interplay.

We used femtosecond optical pump-probe spectroscopy to study the photoinduced change in reflectivity of thin films of the electron-doped cuprate La$_{2-x}$Ce$_x$CuO$_4$ (LCCO) with dopings of x$=$0.08 (underdoped) and x$=$0.11 (optimally doped). Above T$_c$, we observe fluence-dependent relaxation rates which onset at a similar temperature that transport measurements first see signatures of antiferromagnetic correlations. Upon suppressing superconductivity with a magnetic field, it is found that the fluence and temperature dependence of relaxation rates is consistent with bimolecular recombination of electrons and holes across a gap (2$\Delta_{AF}$) originating from antiferromagnetic correlations which comprise the pseudogap in electron-doped cuprates. This can be used to learn about coupling between electrons and high-energy ($\omega>2\Delta_{AF}$) excitations in these compounds and set limits on the timescales on which antiferromagnetic correlations are static.

The condensation of an electron superfluid from a conventional metallic state at a critical temperature $T_c$ is described well by the BCS theory. In the underdoped copper-oxides, high-temperature superconductivity condenses instead from a nonconventional metallic "pseudogap" phase that exhibits a variety of non-Fermi liquid properties. Recently, it has become clear that a charge density wave (CDW) phase exists within the pseudogap regime, appearing at a temperature $T_{CDW}$ just above $T_c$. The near coincidence of $T_c$ and $T_{CDW}$, as well the coexistence and competition of CDW and superconducting order below $T_c$, suggests that they are intimately related. Here we show that the condensation of the superfluid from this unconventional precursor is reflected in deviations from the predictions of BSC theory regarding the recombination rate of quasiparticles. We report a detailed investigation of the quasiparticle (QP) recombination lifetime, $\tau_{qp}$, as a function of temperature and magnetic field in underdoped HgBa$_{2}$CuO$_{4+\delta}$ (Hg-1201) and YBa$_{2}$Cu$_{3}$O$_{6+x}$ (YBCO) single crystals by ultrafast time-resolved reflectivity. We find that $\tau_{qp}(T)$ exhibits a local maximum in a small temperature window near $T_c$ that is prominent in underdoped samples with coexisting charge order and vanishes with application of a small magnetic field. We explain this unusual, non-BCS behavior by positing that $T_c$ marks a transition from phase-fluctuating SC/CDW composite order above to a SC/CDW condensate below. Our results suggest that the superfluid in underdoped cuprates is a condensate of coherently-mixed particle-particle and particle-hole pairs.

Optical excitation typically enhances electrical conduction and low-frequency radiation absorption in semiconductors. We have, however, observed a pronounced transient decrease of conductivity in doped monolayer molybdenum disulfide (MoS2), a two-dimensional (2D) semiconductor, under femtosecond laser excitation. In particular, the conductivity is reduced dramatically down to only 30% of its equilibrium value with high pump fluence. This anomalous phenomenon arises from the strong many-body interactions in the system, where photoexcited electron-hole pairs join the doping-induced charges to form trions, bound states of two electrons and one hole. The resultant increase of the carrier effective mass substantially diminishes the carrier conductivity.

We investigated the transient photoconductivity of graphene at various gate-tuned carrier densities by optical-pump terahertz-probe spectroscopy. We demonstrated that graphene exhibits semiconducting positive photoconductivity near zero carrier density, which crosses over to metallic negative photoconductivity at high carrier density. Our observations are accounted for by considering the interplay between photo-induced changes of both the Drude weight and the carrier scattering rate. Notably, we observed multiple sign changes in the temporal photoconductivity dynamics at low carrier density. This behavior reflects the non-monotonic temperature dependence of the Drude weight, a unique property of massless Dirac fermions.

The unique electronic properties of the surface electrons in a topological insulator are protected by time-reversal symmetry. Circularly polarized light naturally breaks time-reversal symmetry, which may lead to an exotic surface quantum Hall state. Using time- and angle-resolved photoemission spectroscopy, we show that an intense ultrashort mid-infrared pulse with energy below the bulk band gap hybridizes with the surface Dirac fermions of a topological insulator to form Floquet-Bloch bands. These photon dressed surface bands exhibit polarization-dependent band gaps at avoided crossings. Circularly polarized photons induce an additional gap at the Dirac point, which is a signature of broken time-reversal symmetry on the surface. These observations establish the Floquet-Bloch bands in solids and pave the way for optical manipulation of topological quantum states of matter., Comment: 23 pages including supplementary materials

Motivated by recent photoemission experiments on the surface of topological insulators we compute the spectrum of driven topological surface excitations in the presence of an external light source. We completely characterize the spectral function of these non-equilibrium electron excitations for both linear and circular polarizations of the incident light. We find that in the latter case, the circularly polarized light gaps out the surface states, whereas linear polarization gives rise to an anisotropic metal with multiple Dirac cones. We compare the sizes of the gaps with recent pump-probe photoemission measurements and find good agreement. We also identify theoretically several new features in the time-dependent spectral function, such as shadow Dirac cones., Comment: 6 pages, 3 figures, references updated, appendices added, typos corrected, published version

When light is absorbed by a semiconductor, photoexcited charge carriers enhance the absorption of far-infrared radiation due to intraband transitions. We observe the opposite behavior in monolayer graphene, a zero-gap semiconductor with linear dispersion. By using time domain terahertz (THz) spectroscopy in conjunction with optical pump excitation, we observe a reduced absorption of THz radiation in photoexcited graphene. The measured spectral shape of the differential optical conductivity exhibits non-Drude behavior. We discuss several possible mechanisms that contribute to the observed low-frequency non-equilibrium optical response of graphene.

We perform time- and angle-resolved photoemission spectroscopy of a prototypical topological insulator Bi$_2$Se$_3$ to study the ultrafast dynamics of surface and bulk electrons after photo-excitation. By analyzing the evolution of surface states and bulk band spectra, we obtain their electronic temperature and chemical potential relaxation dynamics separately. These dynamics reveal strong phonon-assisted surface-bulk coupling at high lattice temperature and total suppression of inelastic scattering between the surface and the bulk at low lattice temperature. In this low temperature regime, the unique cooling of Dirac fermions in TI by acoustic phonons is manifested through a power law dependence of the surface temperature decay rate on carrier density., Comment: Accepted to Phys. Rev. Lett

We perform a time-resolved optical study of Sr$_2$IrO$_4$ to understand the influence of magnetic ordering on the low energy electronic structure of a strongly spin-orbit coupled $J_{eff}$=1/2 Mott insulator. By studying the recovery dynamics of photo-carriers excited across the Mott gap, we find that upon cooling through the N\'{e}el temperature $T_N$ the system evolves continuously from a metal-like phase with fast ($\sim$50 fs) and excitation density independent relaxation dynamics to a gapped phase characterized by slower ($\sim$500 fs) excitation density dependent bimolecular recombination dynamics. The development of the insulating gap is accompanied by a transfer of in-gap spectral weight to energies far in excess of the gap and occurs over an unusually broad temperature window, which suggests Sr$_2$IrO$_4$ to be a Slater- rather than Mott-Hubbard type insulator and naturally explains the absence of anomalies at $T_N$ in transport and thermodynamic measurements.

Three-dimensional topological insulators represent a new quantum phase of matter with spin-polarized surface states that are protected from backscattering. The static electronic properties of these surface states have been comprehensively imaged by both photoemission and tunneling spectroscopies. Theorists have proposed that topological surface states can also exhibit novel electronic responses to light, such as topological quantum phase transitions and spin-polarized electrical currents. However, the effects of optically driving a topological insulator out of equilibrium have remained largely unexplored experimentally, and no photocurrents have been measured. Here we show that illuminating the topological insulator Bi2Se3 with circularly polarized light generates a photocurrent that originates from topological helical Dirac fermions, and that reversing the helicity of the light reverses the direction of the photocurrent. We also observe a photocurrent that is controlled by the linear polarization of light, and argue that it may also have a topological surface state origin. This approach may allow the probing of dynamic properties of topological insulators and lead to novel opto-spintronic devices., Comment: Accepted in Nature Nanotechnology, November 2 2011

Topological insulators possess completely different spin-orbit coupled bulk and surface electronic spectra that are each predicted to exhibit exotic responses to light. Here we report time-resolved fundamental and second harmonic optical pump-probe measurements on the topological insulator Bi2Se3 to independently measure its photo-induced charge and spin dynamics with bulk and surface selectivity. Our results show that a transient net spin density can be optically induced in both the bulk and surface, which may drive spin transport in topological insulators. By utilizing a novel rotational anisotropy analysis we are able to separately resolve the spin de-polarization, intraband cooling and interband recombination processes following photo-excitation, which reveal that spin and charge degrees of freedom relax on very different time scales owing to strong spin-orbit coupling., Comment: Accepted to Phys. Rev. Lett

A differential coupling of topological surface states to left- versus right-circularly polarized light is the basis of many opto-spintronics applications of topological insulators. Here we report direct evidence of circular dichroism from the surface states of Bi$_2$Se$_3$ using a laser-based time-of-flight angle-resolved photoemission spectroscopy. By employing a novel sample rotational analysis, we resolve unusual modulations in the circular dichroism photoemission pattern as a function of both energy and momentum, which perfectly mimic the predicted but hitherto un-observed three-dimensional warped spin-texture of the surface states. By developing a microscopic theory of photoemission from topological surface states, we show that this correlation is a natural consequence of spin-orbit coupling. These results suggest that our technique may be a powerful probe of the spin-texture of spin-orbit coupled materials in general., Comment: 16 pages, 4 figures

We use ultrafast laser pulses to experimentally demonstrate that the second-order optical response of bulk single crystals of the topological insulator Bi$_2$Se$_3$ is sensitive to its surface electrons. By performing surface doping dependence measurements as a function of photon polarization and sample orientation we show that second harmonic generation can simultaneously probe both the surface crystalline structure and the surface charge of Bi$_2$Se$_3$. Furthermore, we find that second harmonic generation using circularly polarized photons reveals the time-reversal symmetry properties of the system and is surprisingly robust against surface charging, which makes it a promising tool for spectroscopic studies of topological surfaces and buried interfaces.

The phonon-mediated attractive interaction between carriers leads to the Cooper pair formation in conventional superconductors. Despite decades of research, the glue holding Cooper pairs in high-temperature superconducting cuprates is still controversial, and the same is true as for the relative involvement of structural and electronic degrees of freedom. Ultrafast electron crystallography (UEC) offers, through observation of spatio-temporally resolved diffraction, the means for determining structural dynamics and the possible role of electron-lattice interaction. A polarized femtosecond (fs) laser pulse excites the charge carriers, which relax through electron-electron and electron-phonon coupling, and the consequential structural distortion is followed diffracting fs electron pulses. In this review, the recent findings obtained on cuprates are summarized. In particular, we discuss the strength and symmetry of the directional electron-phonon coupling in Bi2Sr2CaCu2O8+\delta (BSCCO), as well as the c-axis structural instability induced by near-infrared pulses in La2CuO4 (LCO). The theoretical implications of these results are discussed with focus on the possibility of charge stripes being significant in accounting for the polarization anisotropy of BSCCO, and cohesion energy (Madelung) calculations being descriptive of the c-axis instability in LCO.

An electron propagating through a solid carries spin angular momentum in addition to its mass and charge. Of late there has been considerable interest in developing electronic devices based on the transport of spin, which offer potential advantages in dissipation, size, and speed over charge-based devices. However, these advantages bring with them additional complexity. Because each electron carries a single, fixed value (-e) of charge, the electrical current carried by a gas of electrons is simply proportional to its total momentum. A fundamental consequence is that the charge current is not affected by interactions that conserve total momentum, notably collisions among the electrons themselves. In contrast, the electron's spin along a given spatial direction can take on two values, "up" and "down", so that the spin current and momentum need not be proportional. Although the transport of spin polarization is not protected by momentum conservation, it has been widely assumed that, like the charge current, spin current is unaffected by electron-electron (e-e) interactions. Here we demonstrate experimentally not only that this assumption is invalid, but that over a broad range of temperature and electron density, the flow of spin polarization in a two-dimensional gas of electrons is controlled by the rate of e-e collisions.

We report time-resolved measurements of the photoinduced change in reflectivity, Delta R, in the Bi2Sr2Ca(1-y)Dy(y)Cu2O(8+delta) (BSCCO) system of cuprate superconductors as a function of hole concentration. We find that the kinetics of quasiparticle decay and the sign of Delta R both change abruptly where the superconducting transition temperature Tc is maximal. These coincident changes suggest that a sharp transition in quasiparticle dynamics takes place precisely at optimal doping in the BSCCO system., Comment: 10 pages, 4 figures

We report a transport study of nonequilibrium quasiparticles in a high-Tc cuprate superconductor using the transient grating technique. Low-intensity laser excitation (at photon energy 1.5 eV) was used to introduce a spatially periodic density of quasiparticles into a high-quality untwinned single crystal of YBa2Cu3O6.5. Probing the evolution of the initial density through space and time yielded the quasiparticle diffusion coefficient, and both inelastic and elastic scattering rates. The technique reported here is potentially applicable to precision measurement of quasiparticle dynamics, not only in cuprate superconductors, but in other electronic systems as well., Comment: 5 pages, 4 figures

We report results and analysis of time-resolved photoinduced reflectivity experiments on the cuprate superconductor YBa2Cu3O6.5. The sample, which has Tc=45 K, was characterized by a high degree of purity and Ortho II ordering. The change in reflectivity (Delta R) was induced and probed using pulses of 100 femtosecond duration and photon energy 1.55 eV from a Ti:Sapphire laser. We provide a detailed picture of the decay rate (gamma) of Delta R as a function of temperature T and pump intensity I. At low T, gamma decreases linearly with decreasing I, extrapolating to nearly zero in the limit that I tends to zero. At higher temperatures gamma has the same linear dependence, but with nonzero limit as I goes to zero. In the interpretation of these results we assume that Delta R is proportional to the nonequilibrium quasiparticle density created by the laser. From an analysis of the gamma vs. I we estimate beta, the coefficient of proportionality relating the quasiparticle decay rate to the density. The intercept of gamma vs. I yields the thermal equilibrium quasiparticle decay rate. In a discussion section, we argue that the quasiparticles induced by the laser occupy primarily states near the antinodal regions of the Brillouin zone. We explain the divergence of the lifetime as T and I both tend to zero as a consequence of momentum and energy conservation in electron-electron scattering. We discuss the significance of the measured value of beta (approximately 0.1 cm2/s) in terms of the electron-phonon interactions., Comment: 14 pages, 10 figures

We report measurements of the photoinduced change in reflectivity of an untwinned single crystal of YBa2Cu3O6.5 in the ortho II structure. The decay rate of the transient change in reflectivity is found to decrease rapidly with decreasing temperature and, below Tc, with decreasing laser intensity. We interpret the decay as a process of thermalization of antinodal quasiparticles, whose rate is determined by an inelastic scattering rate of quasiparticle pairs., Comment: 4 pages, 4 figures