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Electron-phonon coupling in the spin-split valence band of single layer WS$_2$

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 Added by Philip Hofmann
 Publication date 2017
  fields Physics
and research's language is English




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The absence of inversion symmetry leads to a strong spin-orbit splitting of the upper valence band of semiconducting single layer transition metal dichalchogenides such as MoS$_2$ or WS$_2$. This permits a direct comparison of the electron-phonon coupling strength in states that only differ by their spin. Here, the electron-phonon coupling in the valence band maximum of single-layer WS$_2$ is studied by first principles calculations and angle-resolved photoemission. The coupling strength is found to be drastically different for the two spin-split branches, with calculated values of $lambda_K=$0.0021 and 0.40 for the upper and lower spin-split valence band of the free-standing layer, respectively. This difference is somewhat reduced when including scattering processes involving the Au(111) substrate present in the experiment and the experimental results confirm the strongly branch-dependent coupling strength.



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Understanding the physics of strongly correlated electronic systems has been a central issue in condensed matter physics for decades. In transition metal oxides, strong correlations characteristic of narrow $d$ bands is at the origin of such remarkable properties as the Mott gap opening, enhanced effective mass, and anomalous vibronic coupling, to mention a few. SrVO$_3$, with V$^{4+}$ in a $3d^1$ electronic configuration is the simplest example of a 3D correlated metallic electronic system. Here, we focus on the observation of a (roughly) quadratic temperature dependence of the inverse electron mobility of this seemingly simple system, which is an intriguing property shared by other metallic oxides. The systematic analysis of electronic transport in SrVO$_3$ thin films discloses the limitations of the simplest picture of e-e correlations in a Fermi liquid; instead, we show that the quasi-2D topology of the Fermi surface and a strong electron-phonon coupling, contributing to dress carriers with a phonon cloud, play a pivotal role on the reported electron spectroscopic, optical, thermodynamic and transport data. The picture that emerges is not restricted to SrVO$_3$ but can be shared with other $3d$ and $4d$ metallic oxides.
The dynamics of S=1/2 quantum spins on a 2D square lattice lie at the heart of the mystery of the cuprates cite{Hayden2004,Vignolle2007,Li2010,LeTacon2011,Coldea2001,Headings2010,Braicovich2010}. In bulk cuprates such as LCO{}, the presence of a weak interlayer coupling stabilizes 3D N{e}el order up to high temperatures. In a truly 2D system however, thermal spin fluctuations melt long range order at any finite temperature cite{Mermin1966}. Further, quantum spin fluctuations transfer magnetic spectral weight out of a well-defined magnon excitation into a magnetic continuum, the nature of which remains controversial cite{Sandvik2001,Ho2001,Christensen2007,Headings2010}. Here, we measure the spin response of emph{isolated one-unit-cell thick layers} of LCO{}. We show that coherent magnons persist even in a single layer of LCO{} despite the loss of magnetic order, with no evidence for resonating valence bond (RVB)-like spin correlations cite{Anderson1987,Hsu1990,Christensen2007}. Thus these excitations are well described by linear spin wave theory (LSWT). We also observe a high-energy magnetic continuum in the isotropic magnetic response. This high-energy continuum is not well described by 2 magnon LSWT, or indeed any existing theories.
The electron-phonon coupling strength in the spin-split valence band maximum of single-layer MoS$_2$ is studied using angle-resolved photoemission spectroscopy and density functional theory-based calculations. Values of the electron-phonon coupling parameter $lambda$ are obtained by measuring the linewidth of the spin-split bands as a function of temperature and fitting the data points using a Debye model. The experimental values of $lambda$ for the upper and lower spin-split bands at K are found to be 0.05 and 0.32, respectively, in excellent agreement with the calculated values for a free-standing single-layer MoS$_2$. The results are discussed in the context of spin and phase-space restricted scattering channels, as reported earlier for single-layer WS$_2$ on Au(111). The fact that the absolute valence band maximum in single-layer MoS$_2$ at K is almost degenerate with the local valence band maximum at $Gamma$ can potentially be used to tune the strength of the electron-phonon interaction in this material.
Fe$^{3+}$ $S = 5/2$ ions form saw-tooth like chains along the $a$ axis of the oxo-selenite Fe$_2$O(SeO$_3$)$_2$ and an onset of long-range magnetic order is observed for temperatures below $T_C = 105$ K. This order leads to distinct fingerprints in phonon mode linewidths and energies as resolved by Raman scattering. In addition, new excitations with small linewidths emerge below $T = 150$ K, and are assigned to two-magnon scattering processes with the participation of flat-band and high energy magnon branches. From this a set of exchange coupling constants is estimated. The specific ratio of the saw-tooth spine-spine and spine-vertex interactions may explain the instability of the dimer quantum ground state against an incommensurate 3D magnetic order.
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