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Strange metals possess highly unconventional transport characteristics, such as a linear-in-temperature ($T$) resistivity, an inverse Hall angle that varies as $T^2$ and a linear-in-field ($H$) magnetoresistance. Identifying the origin of these collective anomalies has proved profoundly challenging, even in materials such as the hole-doped cuprates that possess a simple band structure. The prevailing dogma is that strange metallicity in the cuprates is tied to a quantum critical point at a doping $p*$ inside the superconducting dome. Here, we study the high-field in-plane magnetoresistance of two superconducting cuprate families at doping levels beyond $p*$. At all dopings, the magnetoresistance exhibits quadrature scaling and becomes linear at high $H/T$ ratios. Moreover, its magnitude is found to be much larger than predicted by conventional theory and insensitive to both impurity scattering and magnetic field orientation. These observations, coupled with analysis of the zero-field and Hall resistivities, suggest that despite having a single band, the cuprate strange metal phase hosts two charge sectors, one containing coherent quasiparticles, the other scale-invariant `Planckian' dissipators., Comment: 20 pages, 9 figures and 3 tables (including Supplementary Information)

SrMnSb$_2$ is suggested to be a magnetic topological semimetal. It contains square, 2D Sb planes with non-symmorphic crystal symmetries that could protect band crossings, offering the possibility of a quasi-2D, robust Dirac semi-metal in the form of a stable, bulk (3D) crystal. Here, we report a combined and comprehensive experimental and theoretical investigation of the electronic structure of SrMnSb$_2$, including the first ARPES data on this compound. SrMnSb$_2$ possesses a small Fermi surface originating from highly 2D, sharp and linearly dispersing bands (the Y-states) around the (0,$\pi$/a)-point in $k$-space. The ARPES Fermi surface agrees perfectly with that from bulk-sensitive Shubnikov de Haas data from the same crystals, proving the Y$-$states to be responsible for electrical conductivity in SrMnSb$_2$. DFT and tight binding (TB) methods are used to model the electronic states, and both show good agreement with the ARPES data. Despite the great promise of the latter, both theory approaches show the Y-states to be gapped above E$_F$, suggesting trivial topology. Subsequent analysis within both theory approaches shows the Berry phase to be zero, indicating the non-topological character of the transport in SrMnSb$_2$, a conclusion backed up by the analysis of the quantum oscillation data from our crystals., Comment: 26 pages, 10 figures, revised submission to SciPost after including changes requested by referees. All referee reports are open and can be viewed here: https://scipost.org/submissions/1711.07165v2/

The main scientific activity in the field of topological insulators (TIs) consists of determining their electronic structure by means of magneto-transport and electron spectroscopy with a view to devices based on topological transport. There is however a caveat in this approach. There are systematic experimental discrepancies on the electronic structure of the most pristine surfaces of TI single crystals as determined by Shubnikov de Haas (SdH) oscillations and by Angle Resolved PhotoElectron Spectroscopy (ARPES). We identify intense ultraviolet illumination -that is inherent to an ARPES experiment- as the source for these experimental differences. We explicitly show that illumination is the key parameter, or in other words the trigger, for energetic shifts of electronic bands near the surface of a TI crystal. This finding revisits the common belief that surface decoration is the principal cause of surface band bending and explains why band bending is not a prime issue in the illumination-free magneto-transport studies. Our study further clarifies the role of illumination on the electronic band structure of TIs by revealing its dual effect: downward band bending on very small timescales followed by band flattening at large timescales. Our results therefore allow us to present and predict the complete evolution of the band structure of TIs in a typical ARPES experiment. By virtue of our findings, we pinpoint two alternatives of how to approach flat band conditions by means of photon-based techniques and we suggest a microscopic mechanism that can explain the underlying phenomena.

The recent rekindling of interest in the mixed valent Kondo insulator SmB$_{6}$ as candidate for a first correlated topological insulator has resulted in a wealth of new experimental observations. In particular, angle-resolved photoemission experiments have provided completely new insights into the formation of the low temperature Kondo insulating state starting from the high temperature correlated metal. Here, we report detailed temperature and energy dependent measurements of the optical constants of SmB$_6$ in order to provide a detailed study from the point of view of a bulk sensitive spectroscopic probe. We detect a previously unobserved infrared active optical phonon mode, involving the movement of the Sm ions against the boron cages. The changes taking place in the free carrier response with temperature and their connection to changes in optical transitions between different bands are discussed. We find that the free charge density starts to decrease rapidly below approximately 200 K. Below 60 K a small amount of spectral weight begins to accumulate in low lying interband transitions, indicating the formation of the Kondo insulating state; however, the total integrated spectral weight in our experimental window ($\sim 4.35$ eV) decreases. This indicates the involvement of a large Coulomb interaction ($>$ 5 eV) in the formation of the Kondo insulator., Comment: 10 pages, 7 figures (including supp.). Accepted for publication in New Journal of Physics

Obtaining high-quality thin films of 5d transition metal oxides is essential to explore the exotic semimetallic and topological phases predicted to arise from the combination of strong electron correlations and spin-orbit coupling. Here, we show that the transport properties of SrIrO3 thin films, grown by pulsed laser deposition, can be optimized by considering the effect of laser-induced modification of the SrIrO3 target surface. We further demonstrate that bare SrIrO3 thin films are subject to degradation in air and are highly sensitive to lithographic processing. A crystalline SrTiO3 cap layer deposited in-situ is effective in preserving the film quality, allowing us to measure metallic transport behavior in films with thicknesses down to 4 unit cells. In addition, the SrTiO3 encapsulation enables the fabrication of devices such as Hall bars without altering the film properties, allowing precise (magneto)transport measurements on micro- and nanoscale devices., Comment: 5 pages, 3 figures

We report a high-field magnetotransport study on selected low-carrier crystals of the topological insulator Bi$_{2-x}$Sb${_x}$Te$_{3-y}$Se$_{y}$. Monochromatic Shubnikov - de Haas (SdH) oscillations are observed at 4.2~K and their two-dimensional nature is confirmed by tilting the magnetic field with respect to the sample surface. With help of Lifshitz-Kosevich theory, important transport parameters of the surface states are obtained, including the carrier density, cyclotron mass and mobility. For $(x,y)=(0.50,1.3)$ the Landau level plot is analyzed in terms of a model based on a topological surface state in the presence of a non-ideal linear dispersion relation and a Zeeman term with $g_s = 70$ or $-54$. Input parameters were taken from the electronic dispersion relation measured directly by angle resolved photoemission spectroscopy on crystals from the same batch. The Hall resistivity of the same crystal (thickness of 40~$\mu$m) is analyzed in a two-band model, from which we conclude that the ratio of the surface conductance to the total conductance amounts to 32~\%., Comment: 16 pages, 5 figures, accepted for publication in Solid State Communications

Interfaces between a bulk-insulating topological insulator (TI) and metallic adatoms have been studied using high-resolution, angle-resolved and core-level photoemission. Fe, Nb and Ag were evaporated onto Bi1.5Sb0.5Te1.7Se1.3 (BSTS) surfaces both at room temperature and 38K. The coverage- and temperature-dependence of the adsorption and interfacial formation process have been investigated, highlighting the effects of the overlayer growth on the occupied electronic structure of the TI. For all coverages at room temperature and for those equivalent to less than 0.1 monolayer at low temperature all three metals lead to a downward shift of the TI's bands with respect to the Fermi level. At room temperature Ag appears to intercalate efficiently into the van der Waals gap of BSTS, accompanied by low-level substitution of the Te/Se atoms of the termination layer of the crystal. This Te/Se substitution with silver increases significantly for low temperature adsorption, and can even dominate the electrostatic environment of the Bi/Sb atoms in the BSTS near-surface region. On the other hand, Fe and Nb evaporants remain close to the termination layer of the crystal. On room temperature deposition, they initially substitute isoelectronically for Bi as a function of coverage, before substituting for Te/Se atoms. For low temperature deposition, Fe and Nb are too immobile for substitution processes and show a behaviour consistent with clustering on the surface. For both Ag and Fe/Nb, these differing adsorption pathways leads to the qualitatively similar and remarkable behavior for low temperature deposition that the chemical potential first moves upward (n-type dopant behavior) and then downward (p-type behavior) on increasing coverage., Comment: 10 pages, 4 figures. In our Phys. Rev. B manuscript an error was made in formulating the last sentence of the abstract that, unfortunately, was missed in the page proofs. Version 2 on arxiv has the correct formulation of this sentence

Combined in-situ x-ray photoemission spectroscopy, scanning tunnelling spectroscopy and angle resolved photoemission spectroscopy of molecular beam epitaxy grown Bi2Te3 on lattice mismatched substrates reveal high quality stoichiometric thin films with topological surface states without a contribution from the bulk bands at the Fermi energy. The absence of bulk states at the Fermi energy is achieved without counter doping. We observe that the surface morphology and electronic band structure of Bi2Te3 are not affected by in-vacuo storage and exposure to oxygen, whereas major changes are observed when exposed to ambient conditions. These films help define a pathway towards intrinsic topological devices., Comment: 8 pages, 5 figures

In 3D topological insulators achieving a genuine bulk-insulating state is an important research topic. Recently, the material system (Bi,Sb)$_{2}$(Te,Se)$_{3}$ (BSTS) has been proposed as a topological insulator with high resistivity and a low carrier concentration (Ren \textit{et al.} \cite{Ren2011}). Here we present a study to further refine the bulk-insulating properties of BSTS. We have synthesized Bi$_{2-x}$Sb${_x}$Te$_{3-y}$Se$_{y}$ single crystals with compositions around $x = 0.5$ and $y = 1.3$. Resistance and Hall effect measurements show high resistivity and record low bulk carrier density for the composition Bi$_{1.46}$Sb$_{0.54}$Te$_{1.7}$Se$_{1.3}$. The analysis of the resistance measured for crystals with different thicknesses within a parallel resistor model shows that the surface contribution to the electrical transport amounts to 97% when the sample thickness is reduced to $1 \mu$m. The magnetoconductance of exfoliated BSTS nanoflakes shows 2D weak antilocalization with $\alpha \simeq -1$ as expected for transport dominated by topological surface states., Comment: 16 pages, 6 figures, accepted for publication in New Journal of Physics

A combined experimental and theoretical investigation of the electronic structure of the archetypal oxide heterointerface system LaAlO3 on SrTiO3 is presented. High-resolution, hard x-ray photoemission is used to uncover the occupation of Ti 3d states and the relative energetic alignment - and hence internal electric fields - within the LaAlO3 layer. Firstly, the Ti 2p core level spectra clearly show occupation of Ti 3d states already for two unit cells of LaAlO3. Secondly, the LaAlO3 core levels were seen to shift to lower binding energy as the LaAlO3 overlayer thickness, n, was increased - agreeing with the expectations from the canonical electron transfer model for the emergence of conductivity at the interface. However, not only is the energy offset of only 300meV between n=2 (insulating interface) and n=6 (metallic interface) an order of magnitude smaller than the simple expectation, but it is also clearly not the sum of a series of unit-cell by unit-cell shifts within the LaAlO3 block. Both of these facts argue against the simple charge-transfer picture involving a cumulative shift of the LaAlO3 valence bands above the SrTiO3 conduction bands, resulting in charge transfer only for n>3. Turning to the theoretical data, our density functional simulations show that the presence of oxygen vacancies at the LaAlO3 surface at the 25% level reverses the direction of the internal field in the LaAlO3. Therefore, taking the experimental and theoretical results together, a consistent picture emerges for real-life samples in which nature does not wait until n=4 and already for n=2, mechanisms other than internal-electric-field-driven electron transfer from idealized LaAlO3 to near-interfacial states in the SrTiO3 substrate are active in heading off the incipient polarization catastrophe that drives the physics in these systems., Comment: 12 pages, 5 figures, submitted to Phys. Rev. B

We establish in a combination of ab initio theory and experiments that the tunneling process in scanning tunneling microscopy/spectroscopy on the A-122 iron pnictide superconductors - in this case BaFe$_{2-x}$Co$_x$As$_2$ - involve a strong adatom filtering of the differential conductance from the near-EF Fe3d states, which in turn originates from the top-most sub-surface Fe layer of the crystal. The calculations show that the dominance of surface Ba-related tunneling pathways leaves fingerprints found in the experimental differential conductance data, including large particle-hole asymmetry and an energy-dependent contrast inversion., Comment: 4.5 pages, 4 figures. To appear in Physical Review Letters

Cuprate high-T_c superconductors on the Mott-insulating side of "optimal doping" (with respect to the highest T_c's) exhibit enigmatic behavior in the non-superconducting state. Near optimal doping the transport and spectroscopic properties are unlike those of a Landau-Fermi liquid. For carrier concentrations below optimal doping a pseudogap removes quasi-particle spectral weight from parts of the Fermi surface, and causes a break-up of the Fermi surface into disconnected nodal and anti-nodal sectors. Here we show that the near-nodal excitations of underdoped cuprates obey Fermi liquid behavior. Our optical measurements reveal that the dynamical relaxation rate 1/tau(omega,T) collapses on a universal function proportional to (hbar omega)^2+(1.5 pi k_B T)^2. Hints at possible Fermi liquid behavior came from the recent discovery of quantum oscillations at low temperature and high magnetic field in underdoped YBa2Cu3O6+d and YBa2Cu4O8, from the observed T^2-dependence of the DC ({\omega}=0) resistivity for both overdoped and underdoped cuprates, and from the two-fluid analysis of nuclear magnetic resonance data. However, the direct spectroscopic determination of the energy dependence of the life-time of the excitations -provided by our measurements- has been elusive up to now. This observation defies the standard lore of non-Fermi liquid physics in high T_c cuprates on the underdoped side of the phase diagram., Comment: 15 pages, 11 figures

We study experimentally and theoretically the Fano-shaped phonon peak at 1590 cm$^{-1}$ (0.2 eV) in the in-plane optical conductivity of pristine graphite. We show that the anomalously large spectral weight and the Fano asymmetry of the peak can be qualitatively accounted for by a charged-phonon theory. A crucial role in this context is played by the particle-hole asymmetry of the electronic $\pi$-bands., Comment: 5 pages, 4 figures, 1 table

We present angle resolved photoemission experiments and scanning tunneling spectroscopy results on the doped topological insulator Cu0.2Bi2Te3. Quasi-particle interference (QPI) measurements, based on high resolution conductance maps of the local density of states show that there are three distinct energy windows for quasi-particle scattering. Using a model Hamiltonian for this system two new scattering channels are identified: the first between the surface states and the conduction band and the second between conduction band states. We also observe that the real space density modulation has a predominant three-fold symmetry, which rules out a simple, isotropic impurity potential. We obtain agreement between experiment and theory by considering a modified scattering potential that is consistent with having mostly Bi-Te anti-site defects as scatterers., Comment: Updated the discussion of results. New model for impurity scattering added to the discussion. Corrected labelling of some figures

The pseudogap state is one of the peculiarities of the cuprate high temperature superconductors. Here we investigate its presence in BaCo$_{x}$Fe$_{2-x}$As$_{2}$, a member of the pnictide family, with temperature dependent scanning tunneling spectroscopy. We observe that for under, optimally and overdoped systems the gap in the tunneling spectra always closes at the bulk T$_{c}$, ruling out the presence of a pseudogap state. For the underdoped case we observe superconducting gaps over large fields of view, setting a lower limit of tens of nanometers on the length scale of possible phase separated regions., Comment: 5 pages, 3 figures

We have studied the electronic structure of EuFe2As2-xPx using high resolution angle-resolved photoemission spectroscopy. Upon substituting As with the isovalent P, which leads to a chemical pressure and to superconductivity, we observe a non-rigid-band like change of the electronic structure along the center of the Brillouin zone (BZ): an orbital and kz dependent increase or decrease in the size of the hole pockets near the Gamma - Z line. On the other hand, the diameter of the Fermi surface cylinders at the BZ corner forming electron pockets, hardly changes. This is in stark contrast to p and n-type doped iron pnictides where, on the basis of ARPES experiments, a more rigid-band like behavior has been proposed. These findings indicate that there are different ways in which the nesting conditions can be reduced causing the destabilization of the antiferromagnetic order and the appearance of the superconducting dome., Comment: 5 pages, 3 figures

Using angle resolved photoemission it is shown that the low lying electronic states of the iron pnictide parent compound EuFe$_2$As$_2$ are strongly modified in the magnetically ordered, low temperature, orthorhombic state compared to the tetragonal, paramagnetic case above the spin density wave transition temperature. Back-folded bands, reflected in the orthorhombic/ anti-ferromagnetic Brillouin zone boundary hybridize strongly with the non-folded states, leading to the opening of energy gaps. As a direct consequence, the large Fermi surfaces of the tetragonal phase fragment, the low temperature Fermi surface being comprised of small droplets, built up of electron and hole-like sections. These high resolution ARPES data are therefore in keeping with quantum oscillation and optical data from other undoped pnictide parent compounds., Comment: 4 figures, 6 pages

We present detailed temperature dependent optical data on BaFe$_{2-x}$Co$_{x}$As$_{2}$ (BCFA), with x = 0.14, between 4 meV and 6.5 eV. We analyze our spectra to determine the main optical parameters and show that in this material the interband conductivity already starts around 10 meV. We determine the superfluid density to be 2.2 10^{7}$ cm^{-2}, which places optimally doped BFCA close to the Uemura line. Our experimental data shows clear signs of a superconducting gap with 2$\Delta_{1}$ = 6.2 $\pm$ 0.8 meV. In addition we show that the optical spectra are consistent with the presence of an additional band of strongly scattered carriers with a larger gap, 2$\Delta_{2}$ = 14 $\pm$ 2 meV., Comment: 5 pages, 4 figures

We elucidate the termination surface of cleaved single crystals of the BaFe_(2-x)Co_(x)As_(2) and Fe_(y)Se_(1-x)Te_(x) families of the high temperature iron based superconductors. By combining scanning tunneling microscopic data with low energy electron diffraction we prove that the termination layer of the Ba122 systems is a remnant of the Ba layer, which exhibits a complex diversity of ordered and disordered structures. The observed surface topographies and their accompanying superstructure reflections in electron diffraction depend on the cleavage temperature. In stark contrast, Fe_(y)Se_(1-x)Te_(x) possesses only a single termination structure - that of the tetragonally ordered Se_(1-x)Te_(x) layer., Comment: 4 pages, 4 figures

We analyze optical spectra of high temperature superconductors using a minimal model of electrons coupled to bosons. We consider the marginal Fermi liquid theory and the spin fluctuation theory, as well as a histogram representation of the bosonic spectral density. We find that the two theories can both be used to describe the experimental data provided that we allow for an additional scattering channel with an energy of 55 meV., Comment: 9 pages, 3 figures. proceedings of the 25th international conference on low temperature physics (LT25)

An experimental study of the in-plane optical conductivity of (Pb$_{x}$,Bi$_{2-x}$)(La$_{y}$Sr$_{2-y}$)CuO$_{6+\delta}$ (Bi2201) is presented for a broad doping and temperature range. The in-plane conductivity is analyzed within a strong coupling formalism. We address the interrelationship between the optical conductivity ($\sigma(\omega)$), the single particle self energy, and the electron-boson spectral function. We find that the frequency and temperature dependence can be well described within this formalism. We present a universal description of optical, ARPES and tunneling spectra. The full frequency and temperature dependence of the optical spectra and single particle self-energy is shown to result from an electron-boson spectral function, which shows a strong doping dependence and weak temperature dependence., Comment: 20 pages, 9 figures. To appear in special focus issue "Superconductors with Exotic Symmetries", New Journal of Physics

We take advantage of the connection between the free carrier optical conductivity and the glue function in the normal state, to reconstruct from the infrared optical conductivity the glue-spectrum of ten different high-Tc cuprates revealing a robust peak in the 50-60 meV range and a broad con- tinuum at higher energies for all measured charge carrier concentrations and temperatures up to 290 K. We observe that the strong coupling formalism accounts fully for the known strong temperature dependence of the optical spectra of the high Tc cuprates, except for strongly underdoped samples. We observe a correlation between the doping trend of the experimental glue spectra and the critical temperature. The data obtained on the overdoped side of the phase diagram conclusively excludes the electron-phonon coupling as the main source of superconducting pairing., Comment: Accepted for publication in Phys. Rev. B

We present infrared spectra (0.1-1 eV) of electrostatically gated bilayer graphene as a function of doping and compare it with tight binding calculations. All major spectral features corresponding to the expected interband transitions are identified in the spectra: a strong peak due to transitions between parallel split-off bands and two onset-like features due to transitions between valence and conduction bands. A strong gate voltage dependence of these structures and a significant electron-hole asymmetry is observed that we use to extract several band parameters. Surprisingly, the structures related to the gate-induced bandgap are much less pronounced in the experiment than predicted by the tight binding model., Comment: 4 pages, 3 figures

Classically the interaction between light and matter is given by the Maxwell relations. These are briefly reviewed and will be used as a basis to discuss several techniques that are used in optical spectroscopy. We then discuss the quantum mechanical description of the optical conductivity based on the Kubo formalism. This is used as a basis to understand how strong correlation effects can be observed using optical techniques. We will discuss the use of sum rules in the interpretation of optical experiments. Finally, we describe the effect of including interactions between electronic and collective degrees of freedom on optical spectra., Comment: Lecturenotes for "XI Training Course in the Physics of Strongly Correlated Systems", Vietri sul Mare, Italy, 2-13 October 2006. Published in Lectures On The Physics Of Strongly Correlated Systems XI: Eleventh Training Course in the Physics of Strongly Correlated Systems Editors F. Mancini and A. Avella. AIP Conference Proceedings 918 ISBN:978-0-7354-0428-1 (2006)

We take advantage of the connection between the free carrier optical conductivity and the glue function in the normal state, to reconstruct from the infrared optical conductivity the glue-spectrum of ten different high-Tc cuprates revealing a robust peak in the 50-60 meV range and a broad continuum at higher energies for all measured charge carrier concentrations and temperatures up to 290 K. We observe an intriguing correlation between the doping trend of the experimental glue spectra and the critical temperature., Comment: 6 pages, 5 figures. More concise discussion

We find experimentally that the optical sheet conductance of graphite per graphene layer is very close to $(\pi/2)e^2/h$, which is the theoretically expected value of dynamical conductance of isolated monolayer graphene. Our calculations within the Slonczewski-McClure-Weiss model explain well why the interplane hopping leaves the conductance of graphene sheets in graphite almost unchanged for photon energies between 0.1 and 0.6 eV, even though it significantly affects the band structure on the same energy scale. The f-sum rule analysis shows that the large increase of the Drude spectral weight as a function of temperature is at the expense of the removed low-energy optical spectral weight of transitions between hole and electron bands., Comment: 4 pages, 4 figures

A single band optical sum rule derived by Kubo can reveal a novel kind of superconducting state. It relies, however, on a knowledge of the single band contribution from zero to infinite frequency. A number of experiments over the past five years have used this sum rule; their data has been interpreted in support of 'kinetic energy-driven superconductivity'. However, because of the presence of unwanted interband optical spectral weight, they necessarily have to truncate their sum at a finite frequency. This work examines theoretical models where the impact of this truncation can be examined first in the normal state, and then in the superconducting state. The latter case is particularly important as previous considerations attributed the observed anomalous temperature dependence as an artifact of a non-infinite cutoff frequency. We find that this is in fact not the case, and that the sign of the corrections from the use of a non-infinite cutoff is such that the observed temperature dependence is even more anomalous when proper account is taken of the cutoff. On the other hand, in these same models, we find that the strong observed temperature dependence in the normal state can be attributed to the effect of a non-infinite cutoff frequency., Comment: 9 pages, 7 figures

Much attention has been given to a possible violation of the optical sum rule in the cuprates, and the connection this might have to kinetic energy lowering. The optical integral is composed of a cut-off independent term (whose temperature dependence is a measure of the sum rule violation), plus a cut-off dependent term that accounts for the extension of the Drude peak beyond the upper bound of the integral. We find that the temperature dependence of the optical integral in the normal state of the cuprates can be accounted for solely by the latter term, implying that the dominant contribution to the observed sum rule `violation' in the normal state is due to the finite cut-off. This cut-off dependent term is well modeled by a theory of electrons interacting with a broad spectrum of bosons., Comment: some clarifications and minor additions are offered in the final (published) version

In- and out-of-plane optical spectra and specific heat measurements for the single layer cuprate superconductor Hg-1201 at optimal doping (Tc = 97 K) are presented. Both the in-plane and out-of-plane superfluid density agree well with a recently proposed scaling relation rho_{s}=sigma_{dc}T_{c}. It is shown that there is a superconductivity induced increase of the in-plane low frequency spectral weight which follows the trend found in underdoped and optimally doped Bi-2212 and optimally doped Bi-2223. We observe an increase of optical spectral weight which corresponds to a change in kinetic energy of approximately 0.5 meV/Cu which is more than enough to explain the condensation energy. The specific heat anomaly is 10 times smaller than in YBCO and 3 times smaller than in Bi-2212. The shape of the anomaly is similar to the one observed in YBCO showing that the superconducting transition is governed by thermal fluctuations., Comment: 11 pages, 13 figures

We present the ab-plane optical conductivity of four single crystals of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (Bi2212) with different carrier doping levels from the strongly underdoped to the strongly overdoped range with $T_c$=66, 88, 77, and 67 K respectively. We focus on the redistribution of the low frequency optical spectral weight (SW) in the superconducting and normal states. The temperature dependence of the low-frequency spectral weight in the normal state is significantly stronger in the overdoped regime. In agreement with other studies, the superconducting order is marked by an increase of the low frequency SW for low doping, while the SW decreases for the highly overdoped sample. The effect crosses through zero at a doping concentration $\delta$=0.19 which is slightly to the right of the maximum of the superconducting dome. This sign change is not reproduced by the BCS model calculations, assuming the electron-momentum dispersion known from published ARPES data. Recent Cluster Dynamical Mean Field Theory (CDMFT) calculations based on the Hubbard and t-J models, agree in several relevant respects with the experimental data.

We examine the redistribution of the in-plane optical spectral weight in the normal and superconducting state in tri-layer \bbb (Bi2223) near optimal doping ($T_c$ = 110 K) on a single crystal via infrared reflectivity and spectroscopic ellipsometry. We report the temperature dependence of the low-frequency integrated spectral weight $W(\Omega_c)$ for different values of the cutoff energy $\Omega_c$. Two different model-independent analyses consistently show that for $\Omega_c$ = 1 eV, which is below the charge transfer gap, $W(\Omega_c)$ increases below $T_c$, implying the lowering of the kinetic energy of the holes. This is opposite to the BCS scenario, but it follows the same trend observed in the bi-layer compound \bb (Bi2212). The size of this effect is larger in Bi2223 than in Bi2212, approximately scaling with the critical temperature. In the normal state, the temperature dependence of $W(\Omega_c)$ is close to $T^2$ up to 300 K.