Linear Response Theory and Optical Conductivity of Floquet Topological Insulators

Motivated by the quest for experimentally accessible dynamical probes of Floquet topological insulators, we formulate the linear response theory of a periodically driven system. We illustrate the applications of this formalism by giving general expressions for optical conductivity of Floquet systems, including its homodyne and heterodyne components and beyond. We obtain the Floquet optical conductivity of specific driven models, including two-dimensional Dirac material such as the surface of a topological insulator, graphene, and the Haldane model irradiated with circularly or linearly polarized laser, as well as semiconductor quantum well driven by an ac potential. We obtain approximate analytical expressions and perform numerically exact calculations of the Floquet optical conductivity in different scenarios of the occupation of the Floquet bands, in particular, the diagonal Floquet distribution and the distribution obtained after a quench. We comment on experimental signatures and detection of Floquet topological phases using optical probes.Comment: 16 pages, 10 figure

Structure and implementation of novel task rules: A cross-sectional developmental study

This is the author accepted manuscript. The final version is available from SAGE Publications via the DOI in this record.Rule-based performance improves remarkably throughout childhood. The present study examined how children and adolescents structured tasks and implemented rules when novel task instructions were presented in a child-friendly version of a novel instruction-learning paradigm. Each mini-block started with the presentation of the new stimulus-response mappings for a GO task. Prior to implementing this mapping, responses were required to advance through screens during a preparatory (NEXT) phase. Children (4-11 years) and late adolescents (17-19 years) responded more slowly during the NEXT phase when the NEXT response was incompatible with the instructed stimulus-response mapping. This instructionbased interference effect was more pronounced in young children than in older children. We argue that these findings are most consistent with age-related differences in rule structuring. We discuss the implications of our findings for theories of rule-based performance, instruction-based learning, and development.This work was supported by an ERC starting grant to FV (No. 312445)

Quasiparticle interference patterns as a test for the nature of the pseudogap phase in the cuprate superconductors

Electrons, when scattered by static random disorder, form standing waves that can be imaged using scanning tunneling microscopy. Such interference patterns, observable by the recently developed technique of Fourier transform scanning tunneling spectroscopy (FT-STS), are shown to carry unique fingerprints characteristic of the electronic order present in a material. We exploit this feature of the FT-STS technique to propose a test for the nature of the enigmatic pseudogap phase in the high-$T_c$ cuprate superconductors. Through their sensitivity to the quasiparticle spectra and coherence factors, the FT-STS patterns in principle carry enough information to unambiguously determine the nature of the condensate responsible for the pseudogap phenomenon. We argue that the next generation of FT-STS experiments, currently underway, should be able to distinguish between the pseudogap dominated by the remnants of superconducting order from the pseudogap dominated by some competing order in the particle-hole channel. Using general arguments and detailed numerical calculations, we point to certain fundamental differences between the two scenarios and discuss the prospects for future experiments.Comment: 15 pages REVTeX + 9 ps figures. For related work and info visit http://www.physics.ubc.ca/~franz; version 2 to appear in IJMP

Duality and the vibrational modes of a Cooper-pair Wigner crystal

When quantum fluctuations in the phase of the superconducting order parameter destroy the off-diagonal long range order, duality arguments predict the formation of a Cooper pair crystal. This effect is thought to be responsible for the static checkerboard patterns observed recently in various underdoped cuprate superconductors by means of scanning tunneling spectroscopy. Breaking of the translational symmetry in such a Cooper pair Wigner crystal may, under certain conditions, lead to the emergence of low lying transverse vibrational modes which could then contribute to thermodynamic and transport properties at low temperatures. We investigate these vibrational modes using a continuum version of the standard vortex-boson duality, calculate the speed of sound in the Cooper pair Wigner crystal and deduce the associated specific heat and thermal conductivity. We then suggest that these modes could be responsible for the mysterious bosonic contribution to the thermal conductivity recently observed in strongly underdoped ultraclean single crystals of YBCO tuned across the superconductor-insulator transition.Comment: 14 pages; 3 figures; corrected the sample size value; version 3 to appear in PR

Magnetic field evolution of the quasiparticle interference in a d-wave superconductor

Quasiparticle interference in a d-wave superconductor with weak disorder produces distinctive peaks in the Fourier-transformed local density of states measured by scanning tunneling spectroscopy. We predict that amplitudes of these peaks can be enhanced or suppressed by applied magnetic field according to a very specific pattern governed by the symmetry of the superconducting order parameter. This calculated pattern agrees with the recent experimental measurement and suggests that the technique could be useful for probing the underlying normal state at high fields.Comment: 4 pages, 2 figures; version to appear in PRB/R

Quantum oscillations from Fermi arcs

When a metal is subjected to strong magnetic field B nearly all measurable quantities exhibit oscillations periodic in 1/B. Such quantum oscillations represent a canonical probe of the defining aspect of a metal, its Fermi surface (FS). In this study we establish a new mechanism for quantum oscillations which requires only finite segments of a FS to exist. Oscillations periodic in 1/B occur if the FS segments are terminated by a pairing gap. Our results reconcile the recent breakthrough experiments showing quantum oscillations in a cuprate superconductor YBCO, with a well-established result of many angle resolved photoemission (ARPES) studies which consistently indicate "Fermi arcs" -- truncated segments of a Fermi surface -- in the normal state of the cuprates.Comment: 8 pages, 5 figure

Quasi-particle interference and superconducting gap in a high-temperature superconductor Ca2-xNaxCuO2Cl2

High-transition-temperature (high-Tc) superconductivity is ubiquitous in the cuprates containing CuO2 planes but each cuprate has its own character. The study of the material dependence of the d-wave superconducting gap (SG) should provide important insights into the mechanism of high-Tc. However, because of the 'pseudogap' phenomenon, it is often unclear whether the energy gaps observed by spectroscopic techniques really represent the SG. Here, we report spectroscopic imaging scanning tunneling microscopy (SI-STM) studies of nearly-optimally-doped Ca2-xNaxCuO2Cl2 (Na-CCOC) with Tc = 25 ~ 28 K. They enable us to observe the quasi-particle interference (QPI) effect in this material, through which unambiguous new information on the SG is obtained. The analysis of QPI in Na-CCOC reveals that the SG dispersion near the gap node is almost identical to that of Bi2Sr2CaCu2Oy (Bi2212) at the same doping level, while Tc of Bi2212 is 3 times higher than that of Na-CCOC. We also find that SG in Na-CCOC is confined in narrower energy and momentum ranges than Bi2212. This explains at least in part the remarkable material dependence of TcComment: 13pages, 4fig