Intervalley scattering by atomic defects in monolayer transition metal dichalcogenides (TMDs; M X2) presents a serious obstacle for applications exploiting their unique valley-contrasting properties. Here, we show that the symmetry of the atomic defects can give rise to an unconventional protection mechanism against intervalley scattering in monolayer TMDs. The predicted defectdependent selection rules for intervalley scattering can be verified via Fourier transform scanning tunneling spectroscopy (FT-STS), and provide a unique identification of, e.g., atomic vacancy defects (M vs X). Our findings put the absence of the intervalley FT-STS peak in recent experiments in a different perspective.Introduction.-Two-dimensional (2D) monolayers of transition metal dichalcogenides (TMDs; M X 2 ) are promising candidates for spin-and valleytronics applications [1]. Their hallmarks include unique valleycontrasting properties and strong spin-valley coupling [1, 2] exemplified by, e.g., valley-selective optical pumping [3][4][5], a valley-dependent Zeeman effect [6][7][8][9], and the valley Hall effect [10]. Such means to control the valley degree of freedom are instrumental for valleytronics applications.Another prerequisite for a successful realization of valleytronics is a sufficiently long valley lifetime [11,12]; atomic defects are a common limiting factor which can provide the required momentum for intervalley scattering due to their short-range nature. However, as illustrated in Fig. 1(a), the spin-orbit (SO) induced spin-valley coupling in the K, K valleys of 2D TMDs partially protects the valley degree of freedom against relaxation via intervalley scattering by nonmagnetic defects [2]. Due to the small spin-orbit splitting in the conduction band valleys [13,14], only the valence-band valleys fully benefit from this protection. Identification of additional protection mechanisms in the conduction band would hence be advantageous for valleytronics in 2D TMDs.In this work, we demonstrate that besides the spinvalley coupling, the symmetry and position of atomic defects give rise to unconventional selection rules for intervalley quasiparticle scattering in 2D TMDs. As illustrated in Fig. 1(b), we find that for defects with threefold rotational symmetry (C 3 ), e.g., atomic vacancies, intervalley K ↔ K scattering in the conduction band is forbidden for defects centered on the X site while it is allowed for M centered defects. In the valence band, intervalley scattering is forbidden in both cases. Analogous selection rules for the intervalley coupling due to confinement potentials in 2D TMD based quantum dots have previously been noted [15].Our findings can be readily verified with scanning tunneling spectroscopy (STS) which has provided valuable insight to the electronic properties of 2D TMDs [16][17][18][19][20]. In particular, Fourier transform STS (FT-STS) is a powerful method for investigating atomic defects and their scattering properties in 2D materials [21,22]. The measured STS map is a probe of the local density ...

Recently, a test for a sign-changing gap function in a candidate multiband unconventional superconductor involving quasiparticle interference data was proposed. The test was based on the antisymmetric, Fourier transformed conductance maps integrated over a range of momenta q corresponding to interband processes, which was argued to display a particular resonant form, provided the gaps changed sign between the Fermi surface sheets connected by q. The calculation was performed for a single impurity, however, raising the question of how robust this measure is as a test of sign-changing pairing in a realistic system with many impurities. Here we reproduce the results of the previous work within a model with two distinct Fermi surface sheets, and show explicitly that the previous result, while exact for a single nonmagnetic scatterer and also in the limit of a dense set of random impurities, can be difficult to implement for a few dilute impurities. In this case, however, appropriate isolation of a single impurity is sufficient to recover the expected result, allowing a robust statement about the gap signs to be made.

We investigate the properties of the coexistence phase of itinerant antiferromagnetism and nodal d-wave superconductivity (Q-phase) discovered in heavy fermion CeCoIn5 under applied magnetic field. We solve the minimal model that includes d-wave superconductivity and underlying magnetic correlations in real space to elucidate the structure of the Q-phase in the presence of an externally applied magnetic field. We further focus on the role of magnetic impurities, and show that they nucleate the Q-phase at lower magnetic fields. Our most crucial finding is that, even at zero applied field, dilute magnetic impurities cooperate via RKKY-like exchange interactions to generate a longrange ordered coexistence state identical to the Q-phase. This result is in agreement with recent neutron scattering measurements [S. Raymond et al., J. Phys. Soc. Jpn. 83, 013707 (2014)].

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Experimental evidence suggests that FeSe is close to a magnetic instability, and recent scanning tunneling microscopy (STM) measurements on FeSe multilayer films have revealed stripe order locally pinned near defect sites. Motivated by these findings, we perform a theoretical study of locally induced magnetic order near nonmagnetic impurities in a model relevant for FeSe. We find that relatively weak repulsive impurities indeed are capable of generating short-range magnetism, and explain the driving mechanism for the local order by resonant eg-orbital states. In addition, we investigate the importance of orbital-selective self-energy effects relevant for Hund's metals, and show how the structure of the induced magnetization cloud gets modified by orbital selectivity. Finally, we make concrete connection to STM measurements of iron-based superconductors by symmetry arguments of the induced magnetic order, and the basic properties of the Fe Wannier functions relevant for tunneling spectroscopy. arXiv:1811.01788v1 [cond-mat.supr-con] 5 Nov 2018The Hamiltonian H = H 0 + H imp + H M F int defines the "bare" version of our model, where effects of orbital se-