Unconventional spectral signature of Tc in a pure d-wave superconductor.

In conventional superconductors, the phase transition into a zero-resistance and perfectly diamagnetic state is accompanied by a jump in the specific heat and the opening of a spectral gap1. In the high-transition-temperature (high-Tc) cuprates, although the transport, magnetic and thermodynamic signatures of Tc have been known since the 1980s2, the spectroscopic singularity associated with the transition remains unknown. Here we resolve this long-standing puzzle with a high-precision angle-resolved photoemission spectroscopy (ARPES) study on overdoped (Bi,Pb)2Sr2CaCu2O8+δ (Bi2212). We first probe the momentum-resolved electronic specific heat via spectroscopy and reproduce the specific heat peak at Tc, completing the missing link for a holistic description of superconductivity. Then, by studying the full momentum, energy and temperature evolution of the spectra, we reveal that this thermodynamic anomaly arises from the singular growth of in-gap spectral intensity across Tc. Furthermore, we observe that the temperature evolution of in-gap intensity is highly anisotropic in the momentum space, and the gap itself obeys both the d-wave functional form and particle-hole symmetry. These findings support the scenario that the superconducting transition is driven by phase fluctuations. They also serve as an anchor point for understanding the Fermi arc and pseudogap phenomena in underdoped cuprates.

Concepts relating magnetic interactions, intertwined electronic orders, and strongly correlated superconductivity.

Unconventional superconductivity (SC) is said to occur when Cooper pair formation is dominated by repulsive electron-electron interactions, so that the symmetry of the pair wave function is other than an isotropic s-wave. The strong, on-site, repulsive electron-electron interactions that are the proximate cause of such SC are more typically drivers of commensurate magnetism. Indeed, it is the suppression of commensurate antiferromagnetism (AF) that usually allows this type of unconventional superconductivity to emerge. Importantly, however, intervening between these AF and SC phases, intertwined electronic ordered phases (IP) of an unexpected nature are frequently discovered. For this reason, it has been extremely difficult to distinguish the microscopic essence of the correlated superconductivity from the often spectacular phenomenology of the IPs. Here we introduce a model conceptual framework within which to understand the relationship between AF electron-electron interactions, IPs, and correlated SC. We demonstrate its effectiveness in simultaneously explaining the consequences of AF interactions for the copper-based, iron-based, and heavy-fermion superconductors, as well as for their quite distinct IPs.

Doping dependence of the anisotropic quasiparticle interference in NaFe(1-x)Co(x)As iron-based superconductors.

We use scanning tunneling microscopy to investigate the doping dependence of quasiparticle interference (QPI) in NaFe1-xCoxAs iron-based superconductors. The goal is to study the relation between nematic fluctuations and Cooper pairing. In the parent and underdoped compounds, where fourfold rotational symmetry is broken macroscopically, the QPI patterns reveal strong rotational anisotropy. At optimal doping, however, the QPI patterns are always fourfold symmetric. We argue this implies small nematic susceptibility and, hence, insignificant nematic fluctuation in optimally doped iron pnictides. Since TC is the highest this suggests nematic fluctuation is not a prerequistite for strong Cooper pairing.

Emergent normal fluid in the superconducting ground state of overdoped cuprates.

The microscopic mechanism for the disappearance of superconductivity in overdoped cuprates is still under heated debate. Here we use scanning tunneling spectroscopy to investigate the evolution of quasiparticle interference phenomenon in Bi2Sr2CuO6+δ over a wide range of hole densities. We find that when the system enters the overdoped regime, a peculiar quasiparticle interference wavevector with arc-like pattern starts to emerge even at zero bias, and its intensity grows with increasing doping level. Its energy dispersion is incompatible with the octet model for d-wave superconductivity, but is highly consistent with the scattering interference of gapless normal carriers. The gapless quasiparticles are mainly located near the antinodes and are independent of temperature, consistent with the disorder scattering mechanism. We propose that a branch of normal fluid emerges from the pair-breaking scattering between flat antinodal bands in the quantum ground state, which is the primary cause for the reduction of superfluid density and suppression of superconductivity in overdoped cuprates.

Anomalous normal-state gap in an electron-doped cuprate.

In the underdoped n-type cuprate Nd2-xCexCuO4, long-range antiferromagnetic order reconstructs the Fermi surface, resulting in a putative antiferromagnetic metal with small Fermi pockets. Using angle-resolved photoemission spectroscopy, we observe an anomalous energy gap, an order of magnitude smaller than the antiferromagnetic gap, in a wide portion of the underdoped regime and smoothly connecting to the superconducting gap at optimal doping. After considering all the known ordering tendencies in tandem with the phase diagram, we hypothesize that the normal-state gap in the underdoped n-type cuprates originates from Cooper pairing. The high temperature scale of the normal-state gap raises the prospect of engineering higher transition temperatures in the n-type cuprates comparable to those of the p-type cuprates.

Flat photonic surface bands pinned between Dirac points.

We point out that 2D photonic crystals (PhCs) can support surface bands that are pinned to Dirac points. These bands can be made very flat by optimizing the parameters of the system. Surface modes are found at the interface of two different cladding materials: one is a PhC with Dirac linear dispersion for the TE mode, and the other is a PhC that has a broad TE gap at the Dirac frequency.

Effects of interaction on quantum spin Hall insulators.

We study the S(z)-conserving quantum spin Hall insulator in the presence of Hubbard U from a field theory point of view. The main findings are the following. (1) For arbitrarily small U the edges possess power-law correlated antiferromagnetic XY local moments. Gapless charge excitations arise from the Goldstone-Wilczek mechanism. (2) Electron tunneling between opposite edges allows vortex instantons to proliferate when K, the XY stiffness constant, satisfies 4πK+(4πK)(-1)<4. When the preceding inequality is violated, the edge modes remain gapless despite the sample width being finite. (3) The phase transition from the topological insulator to the large U antiferromagnetic insulator is triggered by the condensation of magnetic excitons. (4) In the large U antiferromagnetic insulating phase the magnetic vortices carry charges proportional to the square magnitude of the antiferromagnetic order parameter.

Fermionic Magnons, non-Abelian spinons, and the spin quantum Hall effect from an exactly solvable spin-1/2 Kitaev model with SU(2) symmetry.

We introduce an exactly solvable SU(2)-invariant spin-1/2 model with exotic spin excitations. With time reversal symmetry (TRS), the ground state is a spin liquid with gapless or gapped spin-1 but fermionic excitations. When TRS is broken, the resulting spin liquid exhibits deconfined vortex excitations which carry spin-1/2 and obey non-Abelian statistics. We show that this SU(2) invariant non-Abelian spin liquid exhibits the spin quantum Hall effect with quantized spin Hall conductivity σ(xy)(s)=ℏ/2π, and that the spin response is effectively described by the SO(3) level-1 Chern-Simons theory at low energy. We further propose that a SU(2) level-2 Chern-Simons theory is the effective field theory describing the topological structure of the non-Abelian SU(2) invariant spin liquid.

Magic Doping and Robust Superconductivity in Monolayer FeSe on Titanates.

The enhanced superconductivity in monolayer FeSe on titanates opens a fascinating pathway toward the rational design of high-temperature superconductors. Utilizing the state-of-the-art oxide plus chalcogenide molecular beam epitaxy systems in situ connected to a synchrotron angle-resolved photoemission spectroscope, epitaxial LaTiO3 layers with varied atomic thicknesses are inserted between monolayer FeSe and SrTiO3, for systematic modulation of interfacial chemical potential. With the dramatic increase of electron accumulation at the LaTiO3/SrTiO3 surface, providing a substantial surge of work function mismatch across the FeSe/oxide interface, the charge transfer and the superconducting gap in the monolayer FeSe are found to remain markedly robust. This unexpected finding indicate the existence of an intrinsically anchored "magic" doping within the monolayer FeSe systems.

Surface states of topological insulators: the Dirac fermion in curved two-dimensional spaces.

The surface of a topological insulator is a closed two-dimensional manifold. The surface states are described by the Dirac Hamiltonian in curved two-dimensional spaces. For a slablike sample with a magnetic field perpendicular to its top and bottom surfaces, there are chiral states delocalized on the four side faces. These "chiral sheets" carry both charge and spin currents. In strong magnetic fields, the quantized charge Hall effect [sigma(xy) = (2n + 1)e2/h] will coexist with spin Hall effect.

Field-induced Kosterlitz-Thouless transition in the n=0 Landau level of graphene.

At the charge neutral point, graphene exhibits a very unusual high-resistance metallic state and a transition to a complete insulating phase in a strong magnetic field. We propose that the current carriers in this state are the charged vortices of the XY valley-pseudospin order parameter, a situation which is dual to a conventional thin superconducting film. We study energetics and the stability of this phase in the presence of disorder.

Localization of metal-induced gap states at the metal-insulator interface: origin of flux noise in SQUIDs and superconducting qubits.

The origin of magnetic flux noise in superconducting quantum interference devices with a power spectrum scaling as 1/f (f is frequency) has been a puzzle for over 20 years. This noise limits the decoherence time of superconducting qubits. A consensus has emerged that the noise arises from fluctuating spins of localized electrons with an areal density of 5x10(17) m(-2). We show that, in the presence of potential disorder at the metal-insulator interface, some of the metal-induced gap states become localized and produce local moments. A modest level of disorder yields the observed areal density.

Classification of topological trivial matter with non-trivial defects.

In this paper, we apply the K-theory to classify topological trivial fermionic phases which, nonetheless, host symmetry-protected non-trivial defects. An important implication of our work is that the existence of Majorana zero mode in the vortex core is neither a necessary nor a sufficient condition for the superconductor in question being topologically non-trivial.

Symmetry protected topological Luttinger liquids and the phase transition between them.

We show that a doped spin-1/2 ladder with antiferromagnetic intra-chain and ferromagnetic inter-chain coupling is a symmetry protected topologically non-trivial Luttinger liquid. Turning on a large easy-plane spin anisotropy drives the system to a topologically-trivial Luttinger liquid. Both phases have full spin gaps and exhibit power-law superconducting pair correlation. The Cooper pair symmetry is singlet dxy in the non-trivial phase and triplet Sz=0 in the trivial phase. The topologically non-trivial Luttinger liquid exhibits gapless spin excitations in the presence of a boundary, and it has no non-interacting or mean-field theory analog even when the fluctuating phase in the charge sector is pinned. As a function of the strength of spin anisotropy there is a topological phase transition upon which the spin gap closes. We speculate these Luttinger liquids are relevant to the superconductivity in metalized integer spin ladders or chains.

What makes the Tc of monolayer FeSe on SrTiO3 so high: a sign-problem-free quantum Monte Carlo study.

Monolayer FeSe films grown on SrTiO3 (STO) substrate show superconducting gap-opening temperatures ([Formula: see text]) which are almost an order of magnitude higher than those of the bulk FeSe and are highest among all known Fe-based superconductors. Angle-resolved photoemission spectroscopy observed "replica bands" suggesting the importance of the interaction between FeSe electrons and STO phonons. These facts rejuvenated the quest for [Formula: see text] enhancement mechanisms in iron-based, especially iron-chalcogenide, superconductors. Here, we perform the first numerically-exact sign-problem-free quantum Monte Carlo simulations to iron-based superconductors. We (1) study the electronic pairing mechanism intrinsic to heavily electron doped FeSe films, and (2) examine the effects of electron-phonon interaction between FeSe and STO as well as nematic fluctuations on [Formula: see text]. Armed with these results, we return to the question "what makes the [Formula: see text] of monolayer FeSe on SrTiO3 so high?" in the conclusion and discussions.

Spin-polarized surface resonances accompanying topological surface state formation.

Topological insulators host spin-polarized surface states born out of the energetic inversion of bulk bands driven by the spin-orbit interaction. Here we discover previously unidentified consequences of band-inversion on the surface electronic structure of the topological insulator Bi2Se3. By performing simultaneous spin, time, and angle-resolved photoemission spectroscopy, we map the spin-polarized unoccupied electronic structure and identify a surface resonance which is distinct from the topological surface state, yet shares a similar spin-orbital texture with opposite orientation. Its momentum dependence and spin texture imply an intimate connection with the topological surface state. Calculations show these two distinct states can emerge from trivial Rashba-like states that change topology through the spin-orbit-induced band inversion. This work thus provides a compelling view of the coevolution of surface states through a topological phase transition, enabled by the unique capability of directly measuring the spin-polarized unoccupied band structure.

Stimulated emission of Cooper pairs in a high-temperature cuprate superconductor.

The concept of stimulated emission of bosons has played an important role in modern science and technology, and constitutes the working principle for lasers. In a stimulated emission process, an incoming photon enhances the probability that an excited atomic state will transition to a lower energy state and generate a second photon of the same energy. It is expected, but not experimentally shown, that stimulated emission contributes significantly to the zero resistance current in a superconductor by enhancing the probability that scattered Cooper pairs will return to the macroscopically occupied condensate instead of entering any other state. Here, we use time- and angle-resolved photoemission spectroscopy to study the initial rise of the non-equilibrium quasiparticle population in a Bi2Sr2CaCu2O8+δ cuprate superconductor induced by an ultrashort laser pulse. Our finding reveals significantly slower buildup of quasiparticles in the superconducting state than in the normal state. The slower buildup only occurs when the pump pulse is too weak to deplete the superconducting condensate, and for cuts inside the Fermi arc region. We propose this is a manifestation of stimulated recombination of broken Cooper pairs, and signals an important momentum space dichotomy in the formation of Cooper pairs inside and outside the Fermi arc region.

Ultrafast quenching of electron-boson interaction and superconducting gap in a cuprate superconductor.

Ultrafast spectroscopy is an emerging technique with great promise in the study of quantum materials, as it makes it possible to track similarities and correlations that are not evident near equilibrium. Thus far, however, the way in which these processes modify the electron self-energy--a fundamental quantity describing many-body interactions in a material--has been little discussed. Here we use time- and angle-resolved photoemission to directly measure the ultrafast response of self-energy to near-infrared photoexcitation in high-temperature cuprate superconductor. Below the critical temperature of the superconductor, ultrafast excitations trigger a synchronous decrease of electron self-energy and superconducting gap, culminating in a saturation in the weakening of electron-boson coupling when the superconducting gap is fully quenched. In contrast, electron-boson coupling is unresponsive to ultrafast excitations above the critical temperature of the superconductor and in the metallic state of a related material. These findings open a new pathway for studying transient self-energy and correlation effects in solids.

Visualizing the microscopic coexistence of spin density wave and superconductivity in underdoped NaFe1₋xCoxAs.

Although the origin of high temperature superconductivity in the iron pnictides is still under debate, it is widely believed that magnetic interactions or fluctuations have a crucial role in triggering Cooper pairing. A key issue regarding the iron pnictide phase diagram is whether long-range magnetic order can coexist with superconductivity microscopically. Here we use scanning tunnelling microscopy to investigate the local electronic structure of underdoped NaFe1-xCoxAs near the spin density wave and superconducting phase boundary. Spatially resolved spectroscopy directly reveals both the spin density wave and superconducting gaps at the same atomic location, providing compelling evidence for the microscopic coexistence of the two phases. The strengths of the two orders are shown to anti-correlate with each other, indicating the competition between them. This work implies that Cooper pairing in the iron pnictides can occur when portions of the Fermi surface are already gapped by the spin density wave order.