Although Weyl fermions have proven elusive in high-energy physics, their existence as emergent quasiparticles has been predicted in certain crystalline solids in which either inversion or timereversal symmetry is broken [1][2][3][4]. Recently they have been observed in transition metal monopnictides (TMMPs) such as TaAs, a class of noncentrosymmetric materials that heretofore received only limited attention [5][6][7]. The question that arises now is whether these materials will exhibit novel, enhanced, or technologically applicable electronic properties. The TMMPs are polar metals, a rare subset of inversion-breaking crystals that would allow spontaneous polarization, were it not screened by conduction electrons [8][9][10]. Despite the absence of spontaneous polarization, polar metals can exhibit other signatures of inversion-symmetry breaking, most notably second-order nonlinear optical polarizability, χ (2) , leading to phenomena such as optical rectification and second-harmonic generation (SHG). Here we report measurements of SHG that reveal a giant, anisotropic χ (2) in the TMMPs TaAs, TaP, and NbAs. With the fundamental and second harmonic fields oriented parallel to the polar axis, the value of χ (2) is larger by almost one order of magnitude than its value in the archetypal electrooptic materials GaAs [11] and ZnTe [12], and in fact larger than reported in any crystal to date.The last decade has witnessed an explosion of research investigating the role of bandstructure topology, as characterized for example by the Berry curvature in momentum space, in the electronic response functions of crystalline solids [13]. While the best established example is the intrinsic anomalous Hall effect in time-reversal breaking systems [14], several nonlocal [15,16] and nonlinear effects related to Berry curvature generally [17,18]and in WSM's specifically [19,20] have been predicted in crystals that break inversion symmetry. Of these, the most relevant to this work is a theoretical formulation [21] of SHG in terms of the shift vector, which is a quantity related to the difference in Berry connection between two bands that participate in an optical transition. * Electronic address: liangwu@berkeley.edu † Electronic address: jworenstein@lbl.gov Fig. 1a and caption provide a schematic and description of the optical set-up for measurement of SHG in TMMP crystals . Figs. 1b,c show results from a (112) surface of TaAs. The SH intensity from this surface is very strong, allowing for polarization rotation scans with signal-to-noise ratio above 10 6 . In contrast, SHG from a TaAs (001) surface is barely detectable (at least six orders of magnitude lower than (112) surface). Below, we describe the use of the set-up shown in Fig. 1a to characterize the second-order optical susceptibility tensor, χ ijk , defined by the relation,As a first step, we determined the orientation of the high-symmetry axes in the (112) surface, which are the [1,-1,0] and [1,1,-1] directions. To do so, we simultaneously rotated the linear polarization of th...
In the underdoped copper-oxides, high-temperature superconductivity condenses from a nonconventional metallic ”pseudogap” phase that exhibits a variety of non-Fermi liquid properties. Recently, it has become clear that a charge density wave (CDW) phase exists within the pseudogap regime. This CDW coexists and competes with superconductivity (SC) below the transition temperature Tc, suggesting that these two orders are intimately related. Here we show that the condensation of the superfluid from this unconventional precursor is reflected in deviations from the predictions of BSC theory regarding the recombination rate of quasiparticles. We report a detailed investigation of the quasiparticle (QP) recombination lifetime, τqp, as a function of temperature and magnetic field in underdoped HgBa2CuO4+δ (Hg-1201) and YBa2Cu3O6+x (YBCO) single crystals by ultrafast time-resolved reflectivity. We find that τqp(T ) exhibits a local maximum in a small temperature window near Tc that is prominent in underdoped samples with coexisting charge order and vanishes with application of a small magnetic field. We explain this unusual, non-BCS behavior by positing that Tc marks a transition from phase-fluctuating SC/CDW composite order above to a SC/CDW condensate below. Our results suggest that the superfluid in underdoped cuprates is a condensate of coherently-mixed particle-particle and particle-hole pairs.
CeCoIn 5 is a heavy fermion superconductor with strong similarities to the high-T c cuprates, including quasi-two-dimensionality, proximity to antiferromagnetism and probable d-wave pairing arising from a non-Fermi-liquid normal state. Experiments allowing detailed comparisons of their electronic properties are of particular interest, but in most cases are difficult to realize, due to their very different transition temperatures. Here we use low-temperature microwave spectroscopy to study the charge dynamics of the CeCoIn 5 superconducting state. The similarities to cuprates, in particular to ultra-clean YBa 2 Cu 3 O y , are striking: the frequency and temperature dependence of the quasiparticle conductivity are instantly recognizable, a consequence of rapid suppression of quasiparticle scattering below T c ; and penetration-depth data, when properly treated, reveal a clean, linear temperature dependence of the quasiparticle contribution to superfluid density. The measurements also expose key differences, including prominent multiband effects and a temperature-dependent renormalization of the quasiparticle mass.
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