A one-dimensional quantum charge pump transfers a quantized charge in each pumping cycle. This quantization is topologically robust being analogous to the quantum Hall effect. The charge transferred in a fraction of the pumping period is instead generally unquantized. We show, however, that with specific symmetries in parameter space the charge transferred at well-defined fractions of the pumping period is quantized as integer fractions of the Chern number. We illustrate this in a one-dimensional Harper-Hofstadter model and show that the fractional quantization of the topological charge pumping is independent of the specific boundary conditions taken into account. We further discuss the relevance of this phenomenon for cold atomic gases in optical superlattices.

Topological superconductors differ from topologically trivial ones due to the presence of topologically protected zero-energy modes. To date, experimental evidence of topological superconductivity in nanostructures has been mainly obtained by measuring the zero-bias conductance peak via tunneling spectroscopy. Here, we propose an alternative and complementary experimental recipe to detect topological phase transitions in these systems. We show in fact that, for a finite-sized system with broken time-reversal symmetry, discontinuities in the Josephson current-phase relation correspond to the presence of zero-energy modes and to a change in the fermion parity of the ground state. Such discontinuities can be experimentally revealed by a characteristic temperature dependence of the current, and can be related to a finite anomalous current at zero phase in systems with broken phase-inversion symmetry

We report the first experimental observation of the quenching of the superconducting state in current-voltage characteristics of an iron-based superconductor, namely, in FeSeTe thin films. Based on available theoretical models, our analysis suggests the presence of an intrinsic flux-flow electronic instability along with non-negligible extrinsic thermal effects. The coexistence and competition of these two mechanisms classify the observed instability as halfway between those of low-temperature and of high-temperature superconductors, where thermal effects are respectively largely negligible or predominant.

The capability to probe the dispersion of elementary spin, charge, orbital, and lattice excitations has positioned resonant inelastic s-ray scattering (RIXS) at the forefront of photon science. Here we develop the scattering theory for RIXS on superconductors, calculating its momentum-dependent scattering amplitude. Considering superconductors with different pairing symmetries we show that the low-energy scattering is strongly affected by the superconducting gap and coherence factors. This establishes RIXS as a tool to disentangle pairing symmetries and to probe the elementary excitations of unconventional superconductors.PACS numbers: 78.70. Ck, 74.20.Rp Introduction In the past decade, resonant inelastic x-ray scattering (RIXS) [1,2] has made remarkable progress as a spectroscopic technique, establishing itself as an experimental probe of elementary spin [3][4][5][6][7][8], orbital [9,10], and lattice excitations [11]. In quite a number of cases, theoretical considerations have preceded and stimulated these experimental advances, prominent examples being the theoretical demonstration of the presence of strong single-magnon scattering channels in cuprates [12,13] and iridates [14]. Being a photonin/photon-out spectroscopy, both the energy ω and the momentum change q of the scattered photon are measured. As the energy and momentum lost by the photon are transferred to intrinsic excitations of the material under study, direct information on the dispersion of those excitations becomes available. The resonant character of the technique is due to the energy of the incident photon being chosen such that it coincides, and hence resonates, with an x-ray absorption edge of the system [1,2]. This year the energy resolution of RIXS has reached ∼30 meV in the hard x-ray regime [7], will reach 50 meV in the soft x-ray regime by building on present instrumentation [15] and is designed to reach 11 meV at the Cu L-edges at the NSLS-II presently under construction [16]. This brings the RIXS energy resolution well into the regime of the energy gap of cuprate superconductors, which stretches out to 119 meV for mercury-based high T c systems [17]. Consequently the fundamental question arises of how the superconducting (SC) state leaves its fingerprints in RIXS spectra -in particular whether and how RIXS is sensitive to the phase and amplitude of the SC gap and to quasiparticle excitations.Probing the order parameter in unconventional superconductors is generally the first step for an investigation of the pairing mechanism and of the character of the SC state. Compared to the available spectroscopic methods, such as scanning-tunneling spectroscopy (STS), photoemission spectroscopy, optical spectroscopy or inelastic neutron scattering, RIXS uniquely combines the advantages of bulk-sensitivity and availability of momentum resolution while at the same time requiring only small sample volumes. Here we show how the sensitivity of the RIXS process to the dynamical structure factor (DSF) of the electron spin and density in the SC state...

Although orbital degrees of freedom are a factor of fundamental importance in strongly correlated transition metal compounds, orbital correlations and dynamics remain very difficult to access, in particular by neutron scattering. Via a direct calculation of scattering amplitudes we show that instead magnetic resonant inelastic x-ray scattering (RIXS) does reveal orbital correlations. In contrast to neutron scattering, the intensity of the magnetic excitations in RIXS depends very sensitively on the symmetry of the orbitals that spins occupy and on photon polarizations. We show in detail how this effect allows magnetic RIXS to distinguish between alternating orbital ordered and ferro-orbital (or orbital liquid) states.