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We revisit a method for mapping arbitrary single-mode pure states into superpositions of N00N states using an asymmetric non-linear Mach-Zehnder interferometer (ANLMZI). This method would allow for one to tailor-make superpositions of N00N states where each axis of the two-mode joint-photon number distribution is weighted by the statistics of any single-mode pure state. The non-linearity of the ANLMZI comes in the form of a $\chi^{\left(3\right)}$ self-Kerr interaction occurring on one of the intermediary modes of the interferometer. Motivated by the non-classical interference effects that occur at a beam splitter, we introduce inverse-engineering techniques aimed towards extrapolating optimal transformations for generating N00N state superpositions. These techniques are general enough so as to be employed to probe the means of generating states of any desired quantum properties., Comment: This paper was prepared for AVS Quantum as part of a commemorative issue for Jonathan Dowling

The 40-70 meV band-structure renormalization (so-called kink) in high-temperature cuprate superconductors - which has been mainly interpreted in terms of electron-boson coupling - is observed to be strongly suppressed both above the superconducting transition temperature and under optical excitation. We employ equilibrium and time- and angle-resolved photoemission spectroscopy, in combination with Migdal-Eliashberg simulations, to investigate the suppression of the near-nodal kink in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. We show that the $\sim$30$\%$ decrease of the kink strength across the superconducting-to-normal-state phase transition can be entirely accounted for by the filling of the superconducting gap, without additional consideration of temperature-dependent electron-boson coupling. Our findings demonstrate that consideration of changes in the density of states is essential to quantitatively account for the band structure renormalization effects in cuprates.

In the study of dynamic charge order correlations in the cuprates, most high energy-resolution resonant inelastic x-ray scattering (RIXS) measurements have focused on momenta along the high-symmetry directions of the copper oxide plane. However, electron scattering along other in-plane directions should not be neglected as they may contain information relevant, for example, to the origin of charge order correlations or to our understanding of the isotropic scattering responsible for strange metal behavior in cuprates. We report high-resolution resonant inelastic x-ray scattering (RIXS) experiments that reveal the presence of dynamic electron correlations over the $q_x$-$q_y$ scattering plane in underdoped $\textrm{Bi}_2\textrm{Sr}_2\textrm{Ca}\textrm{Cu}_2\textrm{O}_{8+\delta}$ with $T_c=54$ K. We use the softening of the RIXS-measured bond stretching phonon line as a marker for the presence of charge-order-related dynamic electron correlations. The experiments show that these dynamic correlations exist at energies below approximately $70$ meV and are centered around a quasi-circular manifold in the $q_x$-$q_y$ scattering plane with radius equal to the magnitude of the charge order wave vector, $q_{CO}$. We also demonstrate how this phonon-tracking procedure provides the necessary experimental precision to rule out fluctuations of short-range directional charge order (i.e. centered around $[q_x=\pm q_{CO}, q_y=0]$ and $[q_x=0, q_y=\pm q_{CO}]$) as the origin of the observed correlations., Comment: Submitted and under review

In the doped topological insulator Sr$_x$Bi$_2$Se$_3$, a pronounced in-plane two-fold symmetry is observed in electronic properties below the superconducting transition temperature $T_c \sim$ 3 K, despite the three-fold symmetry of the observed $R\bar{3}m$ space group. The axis of two-fold symmetry is nominally pinned to one of three rotational equivalent directions and crystallographic strain has been proposed to be the origin of this pinning. We carried out multimodal synchrotron diffraction and resistivity measurements down to $\sim$0.68 K and in magnetic fields up to 45 kG on a single crystal of Sr$_{0.1}$Bi$_2$Se$_3$ to probe the effect of superconductivity on the crystallographic distortion. Our results indicate that there is no in-plane crystallographic distortion at the level of $1x10^{-5}$ associated with the superconducting transition. These results further support the model that the large two-fold in-plane anisotropy of superconducting properties of Sr$_x$Bi$_2$Sr$_3$ is not structural in origin but electronic, namely it is caused by a nematic superconducting order parameter of Eu symmetry., Comment: 7 pages, 6 figures

In strongly correlated systems the strength of Coulomb interactions between electrons, relative to their kinetic energy, plays a central role in determining their emergent quantum mechanical phases. We perform resonant x-ray scattering on Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, a prototypical cuprate superconductor, to probe electronic correlations within the CuO$_2$ plane. We discover a dynamic quasi-circular pattern in the $x$-$y$ scattering plane with a radius that matches the wave vector magnitude of the well-known static charge order. Along with doping- and temperature-dependent measurements, our experiments reveal a picture of charge order competing with superconductivity where short-range domains along $x$ and $y$ can dynamically rotate into any other in-plane direction. This quasi-circular spectrum, a hallmark of Brazovskii-type fluctuations, has immediate consequences to our understanding of rotational and translational symmetry breaking in the cuprates. We discuss how the combination of short- and long-range Coulomb interactions results in an effective non-monotonic potential that may determine the quasi-circular pattern., Comment: This is a post-peer-review, pre-copyedit version of an article published in Nature Communications. The final authenticated version is available online at: https://doi.org/10.1038/s41467-020-20824-7. Supplementary materials are available through the published version in Nature Communications

High-temperature superconducting cuprates exhibit an intriguing phenomenology for the low-energy elementary excitations. In particular, an unconventional temperature dependence of the coherent spectral weight (CSW) has been observed in the superconducting phase by angle-resolved photoemission spectroscopy (ARPES), both at the antinode where the d-wave paring gap is maximum, as well as along the gapless nodal direction. Here, we combine equilibrium and time-resolved ARPES to track the temperature dependent meltdown of the nodal CSW in Bi-based cuprates with unprecedented sensitivity. We find the nodal suppression of CSW upon increasing temperature to be ubiquitous across single- and double-layer Bi cuprates, and uncorrelated to superconducting and pseudogap onset temperatures. We quantitatively model both the lineshape of the nodal spectral features and the anomalous suppression of CSW within the Fermi-Liquid framework, establishing the key role played by the normal state electrodynamics in the description of nodal quasiparticles in superconducting cuprates., Comment: 6 pages, 3 figures; Supplementary Materials available upon request

We observe proximity-induced superconductivity in the \textit{in situ} prepared heterostructures constructed by topological insulator Bi$_{2}$Te$_{3}$ thin films and high-temperature cuprate superconductors Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$. The superconducting gap maximum is about 7.6 meV on the surface of Bi$_{2}$Te$_{3}$ thin films with a thickness of two quintuple layers, and the gap value decreases with an increase in the film thickness. Moreover, the quasiparticle interference data show a clear evidence of a twofold symmetric superconducting gap with gap minima along one pair of the principal crystalline axes of Bi$_{2}$Te$_{3}$. This gap form is consistent with the $\Delta_{4y}$ notation of the topological superconductivity proposed in such systems. Our results provide fruitful information of the possible topological superconductivity induced by the proximity effect in high-temperature superconducting cuprates., Comment: 6 pages, 4 figures

Superconducting topological crystalline insulators (TCI) are predicted to host new topological phases protected by crystalline symmetries, but available materials are insufficiently suitable for surface studies. To induce superconductivity at the surface of a prototypical TCI SnTe, we use molecular beam epitaxy to grow a heterostructure of SnTe and a high-Tc superconductor Fe(Te,Se), utilizing a 'buffer' layer to bridge the large lattice mismatch between SnTe and Fe(Te,Se). Using low-temperature scanning tunneling microscopy and spectroscopy, we measure a prominent spectral gap on the surface of SnTe, and demonstrate its superconducting origin by its dependence on temperature and magnetic field. Our work provides a new platform for atomic-scale investigations of emergent topological phenomena in superconducting TCIs., Comment: to appear in Physical Review B

A normal metal exhibits a valence plasmon, which is a sound wave in its conduction electron density. The mysterious strange metal is characterized by non-Boltzmann transport and violates most fundamental Fermi liquid scaling laws. A fundamental question is: Do strange metals have plasmons? Using momentum-resolved inelastic electron scattering (M-EELS) we recently showed that, rather than a plasmon, optimally-doped Bi$_{2.1}$Sr$_{1.9}$Ca$_{1.0}$Cu$_{2.0}$O$_{8+x}$ (Bi-2212) exhibits a featureless, temperature-independent continuum with a power-law form over most energy and momentum scales [M. Mitrano, PNAS 115, 5392-5396 (2018)]. Here, we show that this continuum is present throughout the fan-shaped, strange metal region of the phase diagram. Outside this region, dramatic changes in spectral weight are observed: In underdoped samples, spectral weight up to 0.5 eV is enhanced at low temperature, biasing the system towards a charge order instability. The situation is reversed in the overdoped case, where spectral weight is strongly suppressed at low temperature, increasing quasiparticle coherence in this regime. Optimal doping corresponds to the boundary between these two opposite behaviors at which the response is temperature-independent. Our study suggests that plasmons do not exist as well-defined excitations in Bi-2212, and that a featureless continuum is a defining property of the strange metal, which is connected to a peculiar crossover where the spectral weight change undergoes a sign reversal., Comment: 10 pages, 6 figures, two appendices

Establishing the presence and the nature of a quantum critical point in their phase diagram is a central enigma of the high-temperature superconducting cuprates. It could explain their pseudogap and strange metal phases, and ultimately their high superconducting temperatures. Yet, while solid evidences exist in several unconventional superconductors of ubiquitous critical fluctuations associated to a quantum critical point, in the cuprates they remain undetected until now. Here using symmetry-resolved electronic Raman scattering in the cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, we report the observation of enhanced electronic nematic fluctuations near the endpoint of the pseudogap phase. While our data hint at the possible presence of an incipient nematic quantum critical point, the doping dependence of the nematic fluctuations deviates significantly from a canonical quantum critical scenario. The observed nematic instability rather appears to be tied to the presence of a van Hove singularity in the band structure., Comment: 28 pages, 7 figures, including SM

Cooper pairs of mutually attracting electrons form the building blocks of superconductivity. Thirty years after the discovery of high-temperature superconductivity in cuprates, many details of the pairs remain unknown, including their size and shape. Here we apply brand new ARPES-based methods that allow us to reconstruct the shape and size of the pairs in Bi$_2$Sr$_2$CaCu$_2$O$_{8+{\delta}}$. The pairs are seen to form a characteristic starfish shape that is very long (>50{\AA}) in the near-nodal direction but extremely short (~4.5{\AA}) in the antinodal (Cu-O) direction. We find that this ultrashort antinodal length scale, which is of order a lattice constant, is approximately constant over a wide range of doping levels even as many other parameters including the pairing strength change. This suggests that this new length scale, along with the pair shape, is one of the most fundamental characteristics of the pairs. Further, the shape and ultrashort length scale should make the pairs create or intertwine with variations in charge and pair density, center on various types of lattice positions, and potentially explain aspects of the nematic order in these materials.

Symmetry, dimensionality, and interaction are crucial ingredients for phase transitions and quantum states of matter. As a prominent example, the integer quantum Hall effect (QHE) represents a topological phase generally regarded as characteristic for two-dimensional (2D) electronic systems, and its many aspects can be understood without invoking electron-electron interaction. The intriguing possibility of generalizing QHE to three-dimensional (3D) systems was proposed decades ago, yet it remains elusive experimentally. Here, we report clear experimental evidence for the 3D QHE observed in bulk ZrTe5 crystals. Owing to the extremely high sample quality, the extreme quantum limit with only the lowest Landau level occupied can be achieved by an applied magnetic field as low as 1.5 T. Remarkably, in this regime, we observe a dissipationless longitudinal resistivity rho_xx=0 accompanied with a well-developed Hall resistivity plateau rho_xy=(1\pm0.1) h/e^2 (\lambda_(F,z)/2), where \lambda_(F,z) is the Fermi wavelength along the field direction (z axis). This striking result strongly suggests a Fermi surface instability driven by the enhanced interaction effects in the extreme quantum limit. In addition, with further increasing magnetic field, both rho_xx and rho_xy increase dramatically and display an interesting metal-insulator transition, representing another magnetic field driven quantum phase transition. Our findings not only unambiguously reveal a novel quantum state of matter resulting from an intricate interplay among dimensionality, interaction, and symmetry breaking, but also provide a promising platform for further exploration of more exotic quantum phases and transitions in 3D systems.

Interest in the superconducting proximity effect has recently been reignited by theoretical predictions that it could be used to achieve topological superconductivity. Low-T$_{c}$ superconductors have predominantly been used in this effort, but small energy scales of ~1 meV have hindered the characterization of the emergent electronic phase, limiting it to extremely low temperatures. In this work, we use molecular beam epitaxy to grow topological insulator Bi$_{2}$Te$_{3}$ in a range of thicknesses on top of a high-T$_{c}$ superconductor Fe(Te,Se). Using scanning tunneling microscopy and spectroscopy, we detect {\Delta}$_{ind}$ as high as ~3.5 meV, which is the largest reported gap induced by proximity to an s-wave superconductor to-date. We find that {\Delta}$_{ind}$ decays with Bi$_{2}$Te$_{3}$ thickness, but remains finite even after the topological surface states had been formed. Finally, by imaging the scattering and interference of surface state electrons, we provide a microscopic visualization of the fully gaped Bi$_{2}$Te$_{3}$ surface state due to Cooper pairing. Our results establish Fe-based high-T$_{c}$ superconductors as a promising new platform for realizing high-T$_{c}$ topological superconductivity.

We study the behavior of the pseudogap in overdoped Bi$_{2}$Sr$_2$CaCu$_2$O$_{8+d}$ by electronic Raman scattering (ERS) and angle-resolved photoemission spectroscopy (ARPES) on the same single crystals. Using both techniques we find that, unlike the superconducting gap, the pseudogap related to the anti-bonding band vanishes above the critical doping p$_c$ = 0.22. Concomitantly, we show from ARPES measurements that the Fermi surface of the anti-bonding band is hole-like below pc and becomes electron-like above p$_c$. This reveals that the appearance of the pseudogap depends on the Fermi surface topology in Bi$_{2}$Sr$_2$CaCu$_2$O$_{8+d}$ , and more generally, puts strong constraint on theories of the pseudogap phase., Comment: 6 pages , 3 figures

In as-grown bulk crystals of Fe$_{1+y}$Te$_{1-x}$Se$_{x}$ with $x\lesssim0.3$, excess Fe ($y>0$) is inevitable and correlates with a suppression of superconductivity. At the same time, there remains the question as to whether the character of the antiferromagnetic correlations associated with the enhanced anion height above the Fe planes in Te-rich samples is compatible with superconductivity. To test this, we have annealed as-grown crystals with $x=0.1$ and 0.2 in Te vapor, effectively reducing the excess Fe and inducing bulk superconductivity. Inelastic neutron scattering measurements reveal low-energy magnetic excitations consistent with short-range correlations of the double-stripe type; nevertheless, cooling into the superconducting state results in a spin gap and a spin resonance, with the extra signal in the resonance being short-range with a mixed single-stripe/double-stripe character, which is different than other iron-based superconductors. The mixed magnetic character of these superconducting samples does not appear to be trivially explainable by inhomogeneity., Comment: 6 pages, 6 figures

We report the direct observation of a "resonance" mode in the lowest-energy optic phonon very near the zone center around (111) in the multiferroic BiFeO$_3$ using neutron scattering methods. The phonon scattering intensity is enhanced when antiferromagnetic (AFM) order sets in at T$_N = 640$~K, and it increases on cooling. This "resonance" is confined to a very narrow region in energy-momentum space where no spin-wave excitation intensity is expected, and it can be modified by an external magnetic field. Our results suggest the existence of a novel coupling between the lattice and spin fluctuations in this multiferroic system in which the spin-wave excitations are mapped onto the lattice vibrations via the Dzyaloshinskii-Moriya (DM) interaction.

We report a study of magnetic susceptibility and electrical resistivity as a function of temperature and magnetic field in superconducting crystals of La$_{2-x}$Ca$_{1+x}$Cu$_{2}$O$_{6}$ with $x=0.10$ and 0.15 and transition temperature $T_{c}^{\rm m} = 54$ K (determined from the susceptibility). When an external magnetic field is applied perpendicular to the CuO$_2$ bilayers, the resistive superconducting transition measured with currents flowing perpendicular to the bilayers is substantially lower than that found with currents flowing parallel to the bilayers. Intriguingly, this anisotropic behavior is quite similar to that observed for the magnetic irreversibility points with the field applied either perpendicular or parallel to the bilayers. We discuss the results in the context of other studies that have found evidence for the decoupling of superconducting layers induced by a perpendicular magnetic field., Comment: 8 pages, 5 figures; version accepted for publication in PRB

Sr$_x$Bi$_2$Se$_3$ and the related compounds Cu$_x$Bi$_2$Se$_3$ and Nb$_x$Bi$_2$Se$_3$ have attracted considerable interest, as these materials may be realizations of unconventional topological superconductors. Superconductivity with T$_c$ ~ 3 K in Sr$_x$Bi$_2$Se$_3$ arises upon intercalation of Sr into the layered topological insulator Bi$_2$Se$_3$. Here we elucidate the anisotropy of the normal and superconducting state of Sr$_{0.1}$Bi$_2$Se$_3$ with angular dependent magnetotransport and thermodynamic measurements. High resolution x-ray diffraction studies underline the high crystalline quality of the samples. We demonstrate that the normal state electronic and magnetic properties of Sr$_{0.1}$Bi$_2$Se$_3$ are isotropic in the basal plane while we observe a large two-fold in-plane anisotropy of the upper critical field in the superconducting state. Our results support the recently proposed odd-parity nematic state characterized by a nodal gap of $E_u$ symmetry in Sr$_x$Bi$_2$Se$_3$., Comment: 10 pages, 7 figures, 3 supplemental pages

The temperature dependence of the London penetration depth $\Delta\lambda(T)$ in the superconducting doped topological crystalline insulator Sn$_{1-x}$In$_x$Te was measured down to 450 mK for two different doping levels, x $\approx$ 0.45 (optimally doped) and x $\approx$ 0.10 (underdoped), bookending the range of cubic phase in the compound. The results indicate no deviation from fully gapped BCS-like behavior, eliminating several candidate unconventional gap structures. Critical field values below 1 K and other superconducting parameters are also presented. The introduction of disorder by repeated particle irradiation with 5 MeV protons does not enhance $T_c$, indicating that ferroelectric interactions do not compete with superconductivity., Comment: 6 pages, 7 figures

Large crystals of La$_{2-x}$Ca$_{1+x}$Cu$_2$O$_{6}$ (La-Ca-2126) with $x=0.10$ and 0.15 have been grown and converted to bulk superconductors by high-pressure oxygen annealing. The superconducting transition temperature, $T_c$, is as high as 55~K; this can be raised to 60~K by post-annealing in air. Here we present structural and magnetic characterizations of these crystals using neutron scattering and muon spin rotation techniques. While the as-grown, non-superconducting crystals are single phase, we find that the superconducting crystals contain 3 phases forming coherent domains stacked along the $c$ axis: the dominant La-Ca-2126 phase, very thin (1.5 unit-cell) intergrowths of La$_2$CuO$_4$, and an antiferromagnetic La$_8$Cu$_8$O$_{20}$ phase. We propose that the formation and segregation of the latter phases increases the Ca concentration of the La-Ca-2126, thus providing the hole-doping that supports superconductivity., Comment: 9 pages, 8 figures, version accepted in PRMaterials

We have combined elastic and inelastic neutron scattering techniques, magnetic susceptibility and resistivity measurements to study single-crystal samples of K$_x$Fe$_{2-y}$Se$_2$, which contain the superconducting phase that has a transition temperature of $\sim$31 K. In the inelastic neutron scattering measurements, we observe both the spin-wave excitations resulting from the block antiferromagnetic ordered phase and the resonance that is associated with the superconductivity in the superconducting phase, demonstrating the coexistence of these two orders. From the temperature dependence of the intensity of the magnetic Bragg peaks, we find that well before entering the superconducting state, the development of the magnetic order is interrupted, at $\sim$42 K. We consider this result to be evidence for the physical separation of the antiferromagnetic and superconducting phases; the suppression is possibly due to the proximity effect of the superconducting fluctuations on the antiferromagnetic order., Comment: To appear in PRB

A central mystery in high temperature superconductivity is the origin of the so-called "strange metal," i.e., the anomalous conductor from which superconductivity emerges at low temperature. Measuring the dynamic charge response of the copper-oxides, $\chi''(q,\omega)$, would directly reveal the collective properties of the strange metal, but it has never been possible to measure this quantity with meV resolution. Here, we present the first measurement of $\chi''(q,\omega)$ for a cuprate, optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ ($T_c=91$ K), using momentum-resolved inelastic electron scattering. In the medium energy range 0.1-2 eV relevant to the strange metal, the spectra are dominated by a featureless, temperature- and momentum-independent continuum persisting to the eV energy scale. This continuum displays a simple power law form, exhibiting $q^2$ behavior at low energy and $q^2/\omega^2$ behavior at high energy. Measurements of an overdoped crystal ($T_c=50$ K) showed the emergence of a gap-like feature at low temperature, indicating deviation from power law form outside the strange metal regime. Our study suggests the strange metal exhibits a new type of charge dynamics in which excitations are local to such a degree that space and time axes are decoupled., Comment: 21 pages, 8 figures

The possibility of driving phase transitions in low-density condensates through the loss of phase coherence alone has far-reaching implications for the study of quantum phases of matter. This has inspired the development of tools to control and explore the collective properties of condensate phases via phase fluctuations. Electrically-gated oxide interfaces, ultracold Fermi atoms, and cuprate superconductors, which are characterized by an intrinsically small phase-stiffness, are paradigmatic examples where these tools are having a dramatic impact. Here we use light pulses shorter than the internal thermalization time to drive and probe the phase fragility of the Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ cuprate superconductor, completely melting the superconducting condensate without affecting the pairing strength. The resulting ultrafast dynamics of phase fluctuations and charge excitations are captured and disentangled by time-resolved photoemission spectroscopy. This work demonstrates the dominant role of phase coherence in the superconductor-to-normal state phase transition and offers a benchmark for non-equilibrium spectroscopic investigations of the cuprate phase diagram., Comment: 24 pages, 9 figures, Main Text and Supplementary Information

We apply the first-order reversal curve (FORC) method, borrowed from studies of ferromagnetic materials, to the magneto-structural phase transition of FeTe. FORC measurements reveal two features in the hysteretic phase transition, even in samples where traditional temperature measurements display only a single transition. For Fe1.13Te, the influence of magnetic field suggests that the main feature is primarily structural while a smaller, slightly higher-temperature transition is magnetic in origin. By contrast Fe1.03Te has a single transition which shows a uniform response to magnetic field, indicating a stronger coupling of the magnetic and structural phase transitions. We also introduce uniaxial stress, which spreads the distribution width without changing the underlying energy barrier of the transformation. The work shows how FORC can help disentangle the roles of the magnetic and structural phase transitions in FeTe., Comment: 8 pages

We report inelastic neutron scattering measurements of low energy ($\hbar \omega < 10$ meV) magnetic excitations in the "11" system Fe$_{1+y}$Te$_{1-x}$Se$_{x}$. The spin correlations are two-dimensional (2D) in the superconducting samples at low temperature, but appear much more three-dimensional when the temperature rises well above $T_c \sim 15$ K, with a clear increase of the (dynamic) spin correlation length perpendicular to the Fe planes. The spontaneous change of dynamic spin correlations from 2D to 3D on warming is unexpected and cannot be naturally explained when only the spin degree of freedom is considered. Our results suggest that the low temperature physics in the "11" system, in particular the evolution of low energy spin excitations towards %better satisfying the nesting condition for mediating superconducting pairing, is driven by changes in orbital correlations.

Combining electronic Raman scattering experiments with cellular dynamical mean field theory, we present evidence of the pseudogap in the superconducting state of various hole-doped cuprates. In Bi2Sr2CaCu2O8+d we track the superconducting pseudogap hallmark, a peak-dip feature, as a function of temperature T and doping p, well beyond the optimal one. We show that, at all temperatures under the superconducting dome, the pseudogap disappears at the doping pc, between 0.222 and 0.226, where also the normal-state pseudogap collapses at a Lifshitz transition. This demonstrates that the superconducting pseudogap boundary forms a vertical line in the T-p phase diagram., Comment: 8 pages and 8 figures

Topological superconductivity is the quantum condensate of paired electrons with an odd parity of the pairing function. One of the candidates is the triplet pairing superconductor derived from topological insulator Bi2Se3 by chemical doping. Theoretically it was predicted that a two-fold superconducting order parameter may exist in this kind of bulk topological superconductor. Earlier experiments by nuclear magnetic resonance and angle-resolved magnetocaloric measurements seem to support this picture. By using a Corbino-shape like electrode configuration, we measure the c-axis resistivity without the influence of the vortex motion and find clear evidence of two-fold superconductivity in the recently discovered topological superconductor SrxBi2Se3. The Laue diffraction measurements on these samples show that the maximum gap direction is either parallel or perpendicular to the main crystallographic axis., Comment: 21 pages, 6 figures, including the Supplementary Notes

The detailed temperature dependence of the infrared-active mode in Fe$_{1.03}$Te ($T_N\simeq 68$ K) and Fe$_{1.13}$Te ($T_N\simeq 56$ K) has been examined, and the position, width, strength, and asymmetry parameter determined using an asymmetric Fano profile superimposed on an electronic background. In both materials the frequency of the mode increases as the temperature is reduced; however, there is also a slight asymmetry in the line shape, indicating that the mode is coupled to either spin or charge excitations. Below $T_N$ there is an anomalous decrease in frequency and the mode shows little temperature dependence, at the same time becoming more symmetric, suggesting a reduction in spin- or electron-phonon coupling. The frequency of the infrared-active mode and the magnitude of the shift below $T_N$ are predicted reasonably well by first-principles calculations; however, the predicted splitting of the mode is not observed. In superconducting FeTe$_{0.55}$Se$_{0.45}$ ($T_c\simeq 14$ K) the infrared-active $E_u$ mode displays asymmetric line shape at all temperatures, which is most pronounced between 100 - 200 K, indicating the presence of either spin- or electron-phonon coupling, which may be a necessary prerequisite for superconductivity in this class of materials., Comment: 9 pages, 5 figures and 3 tables, one page of supplemental information. Updated to reflect the published version

It has recently been demonstrated that dynamical magnetic correlations measured by neutron scattering in iron chalcogenides can be described with models of short-range correlations characterized by particular {choices of four-spin plaquettes, where the appropriate choice changes as the} parent material is doped towards superconductivity. Here we apply such models to describe measured maps of magnetic scattering as a function of two-dimensional wave vectors obtained for optimally superconducting crystals of FeTe$_{1-x}$Se$_x$. We show that the characteristic antiferromagnetic wave vector evolves from that of the bicollinear structure found in underdoped chalcogenides (at high temperature) to that associated with the stripe structure of antiferromagnetic iron arsenides (at low temperature); {these can both be described with the same local plaquette, but with different inter-plaquette correlations}. While the magnitude of the low-energy magnetic spectral weight is substantial at all temperatures, it actually weakens somewhat at low temperature, where the charge carriers become more itinerant. The observed change in spin correlations is correlated with the dramatic drop in the electronic scattering rate and the growth of the bulk nematic response on cooling. Finally, we also present powder neutron diffraction results for lattice parameters in FeTe$_{1-x}$Se$_x$ indicating that the tetrahedral bond angle tends to increase towards the ideal value on cooling, in agreement with the increased screening of the crystal field by more itinerant electrons and the correspondingly smaller splitting of the Fe $3d$ orbitals.

Understanding the mechanism of high transition temperature (Tc) superconductivity in cuprates has been hindered by the apparent complexity of their multilayered crystal structure. Using a cryogenic scanning tunneling microscopy, we report on layer-by-layer probing of the electronic structures of all ingredient planes (BiO, SrO, CuO2) of Bi2Sr2CaCu2O8+{\delta} superconductor prepared by argon-ion bombardment and annealing technique. We show that the well-known pseudogap (PG) feature observed by STM is inherently a property of the BiO planes and thus irrelevant directly to Cooper pairing. The SrO planes exhibit an unexpected Van Hove singularity near the Fermi level, while the CuO2 planes are exclusively characterized by a smaller gap inside the PG. The small gap becomes invisible near Tc, which we identify as the superconducting gap. The above results constitute severe constraints on any microscopic model for high Tc superconductivity in cuprates., Comment: 7 pages, 10 figures

We present a magneto-infrared spectroscopy study on a newly identified three-dimensional (3D) Dirac semimetal ZrTe$_5$. We observe clear transitions between Landau levels and their further splitting under magnetic field. Both the sequence of transitions and their field dependence follow quantitatively the relation expected for 3D \emph{massless} Dirac fermions. The measurement also reveals an exceptionally low magnetic field needed to drive the compound into its quantum limit, demonstrating that ZrTe$_5$ is an extremely clean system and ideal platform for studying 3D Dirac fermions. The splitting of the Landau levels provides a direct and bulk spectroscopic evidence that a relatively weak magnetic field can produce a sizeable Zeeman effect on the 3D Dirac fermions, which lifts the spin degeneracy of Landau levels. Our analysis indicates that the compound evolves from a Dirac semimetal into a topological line-node semimetal under current magnetic field configuration., Comment: Editors' Suggestion

In complex materials various interactions play important roles in determining the material properties. Angle Resolved Photoelectron Spectroscopy (ARPES) has been used to study these processes by resolving the complex single particle self energy $\Sigma(E)$ and quantifying how quantum interactions modify bare electronic states. However, ambiguities in the measurement of the real part of the self energy and an intrinsic inability to disentangle various contributions to the imaginary part of the self energy often leave the implications of such measurements open to debate. Here we employ a combined theoretical and experimental treatment of femtosecond time-resolved ARPES (tr-ARPES) and show how measuring the population dynamics using tr-ARPES can be used to separate electron-boson interactions from electron-electron interactions. We demonstrate the analysis of a well-defined electron-boson interaction in the unoccupied spectrum of the cuprate Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ characterized by an excited population decay time constant $\tau_{QP}$ that maps directly to a discrete component of the equilibrium self energy not readily isolated by static ARPES experiments., Comment: 19 pages with 6 figures

We used low-energy, momentum-resolved inelastic electron scattering to study surface collective modes of the three-dimensional topological insulators Bi$_2$Se$_3$ and Bi$_{0.5}$Sb$_{1.5}$Te$_{3-x}$Se$_{x}$. Our goal was to identify the "spin plasmon" predicted by Raghu and co-workers [S. Raghu, et al., Phys. Rev. Lett. 104, 116401 (2010)]. Instead, we found that the primary collective mode is a surface plasmon arising from the bulk, free carrers in these materials. This excitation dominates the spectral weight in the bosonic function of the surface, $\chi "(\textbf{q},\omega)$, at THz energy scales, and is the most likely origin of a quasiparticle dispersion kink observed in previous photoemission experiments. Our study suggests that the spin plasmon may mix with this other surface mode, calling for a more nuanced understanding of optical experiments in which the spin plasmon is reported to play a role., Comment: 5 pages, 4 figures

Superconductors derived from topological insulators and topological crystalline insulators by doping have long been considered to be candidates as topological superconductors. Pb$_{0.5}$Sn$_{0.5}$Te is a topological crystalline insulator with mirror symmetry protected surface states on (001), (011) and (111) oriented surfaces. The superconductor (Pb$_{0.5}$Sn$_{0.5}$)$_{0.7}$In$_{0.3}$Te is induced by In doping in Pb$_{0.5}$Sn$_{0.5}$Te, and is thought to be a topological superconductor. Here we report the first scanning tunneling spectroscopy measurement of the superconducting state as well as the superconducting energy gap in (Pb$_{0.5}$Sn$_{0.5}$)$_{0.7}$In$_{0.3}$Te on a (001)-oriented surface. The spectrum can be well fitted by an anisotropic $s$-wave gap function of $\Delta=0.72+0.18\cos4\theta$ meV using Dynes model. The results show that the quasi-particle density of states seem to be fully gapped without any in-gap states, in contradiction with the expectation of a topological superconductor., Comment: 5 pages, 4 figures

Three dimensional (3D) topological Dirac materials are under intensive study recently. The layered compound ZrTe$_5$ has been suggested to be one of them by transport and ARPES experiments. Here, we perform infrared reflectivity measurement to investigate the underlying physics of this material. The derived optical conductivity exhibits linear increasing with frequency below normal interband transitions, which provides the first optical spectroscopic proof of a 3D Dirac semimetal. Apart from that, the plasma edge shifts dramatically to lower energy upon temperature cooling, which might be associated with the consequence of lattice parameter shrinking. In addition, an extremely sharp peak shows up in the frequency dependent optical conductivity, indicating the presence of a Van Hove singularity in the joint density of state., Comment: 5 pages, 4 figures

Topological superconductivity, implying gapless protected surface states, has recently been proposed to exist in the compound CuxBi2Se3. Unfortunately, low diamagnetic shielding fractions and considerable inhomogeneity have been reported in this compound. In an attempt to understand and improve on the finite superconducting volume fractions, we have investigated the effects of various growth and post-annealing conditions. With a melt-growth (MG) method, diamagnetic shielding fractions of up to 56% in Cu0.3Bi2Se3 have been obtained, the highest value reported for this method. We investigate the efficacy of various quenching and annealing conditions, finding that quenching from temperatures above 560C is essential for superconductivity, whereas quenching from lower temperatures or not quenching at all is detrimental. A modified floating zone (FZ) method yielded large single crystals but little superconductivity. Even after annealing and quenching, FZ-grown samples had much less chance of being superconducting than MG-grown samples. From the low shielding fractions in FZ-grown samples and the quenching dependence, we suggest that a metastable secondary phase having a small volume fraction in most of the samples may be responsible for the superconductivity., Comment: 8 pages, 2 figures; to appear in Physical Review B

The chiral magnetic effect is the generation of electric current induced by chirality imbalance in the presence of magnetic field. It is a macroscopic manifestation of the quantum anomaly in relativistic field theory of chiral fermions (massless spin $1/2$ particles with a definite projection of spin on momentum) -- a dramatic phenomenon arising from a collective motion of particles and antiparticles in the Dirac sea. The recent discovery of Dirac semimetals with chiral quasi-particles opens a fascinating possibility to study this phenomenon in condensed matter experiments. Here we report on the first observation of chiral magnetic effect through the measurement of magneto-transport in zirconium pentatelluride, ZrTe_5. Our angle-resolved photoemission spectroscopy experiments show that this material's electronic structure is consistent with a 3D Dirac semimetal. We observe a large negative magnetoresistance when magnetic field is parallel with the current. The measured quadratic field dependence of the magnetoconductance is a clear indication of the chiral magnetic effect. The observed phenomenon stems from the effective transmutation of Dirac semimetal into a Weyl semimetal induced by the parallel electric and magnetic fields that represent a topologically nontrivial gauge field background., Comment: 15 pages, 5 figures

To achieve and utilize the most exotic electronic phenomena predicted for the surface states of 3D topological insulators (TI),it is necessary to open a "Dirac-mass gap" in their spectrum by breaking time-reversal symmetry. Use of magnetic dopant atoms to generate a ferromagnetic state is the most widely used approach. But it is unknown how the spatial arrangements of the magnetic dopant atoms influence the Dirac-mass gap at the atomic scale or, conversely, whether the ferromagnetic interactions between dopant atoms are influenced by the topological surface states. Here we image the locations of the magnetic (Cr) dopant atoms in the ferromagnetic TI Cr$_{0.08}$(Bi$_{0.1}$Sb$_{0.9}$)$_{1.92}$Te$_3$. Simultaneous visualization of the Dirac-mass gap $\Delta(r)$ reveals its intense disorder, which we demonstrate directly is related to fluctuations in $n(r)$, the Cr atom areal density in the termination layer. We find the relationship of surface-state Fermi wavevectors to the anisotropic structure of $\Delta(r)$ consistent with predictions for surface ferromagnetism mediated by those states. Moreover, despite the intense Dirac-mass disorder, the anticipated relationship $\Delta(r)\propto n(r)$ is confirmed throughout, and exhibits an electron-dopant interaction energy $J^*$=145$meV\cdot nm^2$. These observations reveal how magnetic dopant atoms actually generate the TI mass gap locally and that, to achieve the novel physics expected of time-reversal-symmetry breaking TI materials, control of the resulting Dirac-mass gap disorder will be essential.

We present neutron scattering measurements on low-energy phonons from a superconducting ($T_{c} = 2.7$~K) Sn$_{0.8}$In$_{0.2}$Te single crystal sample. The longitudinal acoustic phonon mode and one transverse acoustic branch have been mapped out around the (002) Bragg peak for temperatures of 1.7 K and 4.2 K. We observe a substantial energy width of the transverse phonons at energies comparable to twice the superconducting gap; however, there is no change in this width between the superconducting and normal states. We also confirm that the compound is well ordered, with no indications of structural instability., Comment: 5 pages, 4 figures

In three-dimensional topological insulators (3D TI) nanowires, transport occurs via gapless surface states where the spin is fixed perpendicular to the momentum[1-6]. Carriers encircling the surface thus acquire a \pi Berry phase, which is predicted to open up a gap in the lowest-energy 1D surface subband. Inserting a magnetic flux ({\Phi}) of h/2e through the nanowire should cancel the Berry phase and restore the gapless 1D mode[7-8]. However, this signature has been missing in transport experiments reported to date[9-11]. Here, we report measurements of mechanically-exfoliated 3D TI nanowires which exhibit Aharonov-Bohm oscillations consistent with topological surface transport. The use of low-doped, quasi-ballistic devices allows us to observe a minimum conductance at {\Phi} = 0 and a maximum conductance reaching e^2/h at {\Phi} = h/2e near the lowest subband (i.e. the Dirac point), as well as the carrier density dependence of the transport., Comment: 9 pages, 4 figures with additional Supplement

The temperature dependence of the in-plane optical conductivity has been determined for Fe$_{1.03}$Te above and below the magnetic and structural transition at $T_N\simeq 68$ K. The electron and hole pockets are treated as two separate electronic subsystems; a strong, broad Drude response that is largely temperature independent, and a much weaker, narrow Drude response with a strong temperature dependence. Spectral weight is transferred from high to low frequency below $T_N$, resulting in the dramatic increase of both the low-frequency conductivity and the related plasma frequency. The change in the plasma frequency is due to an increase in the carrier concentration resulting from the closing of the pseudogap on the electron pocket, as well as the likely decrease of the effective mass in the antiferromagnetic state., Comment: 5 pages, 4 figures with 1 table

The characteristics of topological insulators are manifested in both their surface and bulk properties, but the latter remain to be explored. Here we report bulk signatures of pressure-induced band inversion and topological phase transitions in Pb$_{1-x}$Sn$_x$Se ($x=$0.00, 0.15, and 0.23). The results of infrared measurements as a function of pressure indicate the closing and the reopening of the band gap as well as a maximum in the free carrier spectral weight. The enhanced density of states near the band gap in the topological phase give rise to a steep interband absorption edge. The change of density of states also yields a maximum in the pressure dependence of the Fermi level. Thus our conclusive results provide a consistent picture of pressure-induced topological phase transitions and highlight the bulk origin of the novel properties in topological insulators.

Indium substitution turns the topological crystalline insulator (TCI) Pb$_{0.5}$Sn$_{0.5}$Te into a possible topological superconductor. To investigate the effect of the indium concentration on the crystal structure and superconducting properties of (Pb$_{0.5}$Sn$_{0.5}$)$_{1-x}$In$_{x}$Te, we have grown high-quality single crystals using a modified floating-zone method, and have performed systematic studies for indium content in the range $0\leq x\leq 0.35$. We find that the single crystals retain the rock salt structure up to the solubility limit of indium ($x\sim0.30$). Experimental dependences of the superconducting transition temperature ($T_c$) and the upper critical magnetic field ($H_{c2}$) on the indium content $x$ have been measured. The maximum $T_c$ is determined to be 4.7 K at $x=0.30$, with $\mu_0H_{c2}(T=0)\approx 5$ T., Comment: 4 pages, 5 figures

We report neutron scattering measurements on low energy ($\hbar\omega \sim 5$~meV) magnetic excitations from a series of Fe$_{1+y-z}$(Ni/Cu)$_{z}$Te$_{1-x}$Se$_{x}$ samples which belong to the "11" Fe-chalcogenide family. Our results suggest a strong correlation between the magnetic excitations near (0.5,0.5,0) and the superconducting properties of the system. The low energy magnetic excitations are found to gradually move away from (0.5,0.5,0) to incommensurate positions when superconductivity is suppressed, either by heating or chemical doping, confirming previous observations., Comment: 5 pages, 5 figures

We report a fine tuned doping study of strongly overdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ single crystals using electronic Raman scattering. Combined with theoretical calculations, we show that the doping, at which the normal state pseudogap closes, coincides with a Lifshitz quantum phase transition where the active hole-like Fermi surface becomes electron-like. This conclusion suggests that the microscopic cause of the pseudogap is sensitive to the Fermi surface topology. Furthermore, we find that the superconducting transition temperature is unaffected by this transition, demonstrating that their origins are different on the overdoped side., Comment: 11 figures, 10 pages

Superconducting condensation energy $U_0^{int}$ has been determined by integrating the electronic entropy in various iron pnictide/chalcogenide superconducting systems. It is found that $U_0^{int}\propto T_c^n$ with $n$ = 3 to 4, which is in sharp contrast to the simple BCS prediction $U_0^{BCS}=1/2N_F\Delta_s^2$ with $N_F$ the quasiparticle density of states at the Fermi energy, $\Delta_s$ the superconducting gap. A similar correlation holds if we compute the condensation energy through $U_0^{cal}=3\gamma_n^{eff}\Delta_s^2/4\pi^2k_B^2$ with $\gamma_n^{eff}$ the effective normal state electronic specific heat coefficient. This indicates a general relationship $\gamma_n^{eff} \propto T_c^m$ with $m$ = 1 to 2, which is not predicted by the BCS scheme. A picture based on quantum criticality is proposed to explain this phenomenon., Comment: 5 pages, 5 figures