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Register a new userInterplay between multiple charge-density waves and the relationship with superconductivity in Pd$_x$HoTe$_{3}$
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HoTe$_{3}$, a member of the rare-earth tritelluride ($R$Te$_{3}$) family, and its Pd-intercalated compounds, Pd$_x$HoTe$_{3}$, where superconductivity (SC) sets in as the charge-density wave (CDW) transition is suppressed by the intercalation of a small amount of Pd, are investigated using angle-resolved photoemission spectroscopy (ARPES) and electrical resistivity. Two incommensurate CDWs with perpendicular nesting vectors are observed in HoTe$_{3}$ at low temperatures. With a slight Pd intercalation ($x$ = 0.01), the large CDW gap decreases and the small one increases. The momentum dependence of the gaps along the inner Fermi surface (FS) evolves from orthorhombicity to near tetragonality, manifesting the competition between two CDW orders. At $x$ = 0.02, both CDW gaps decreases with the emergence of SC. Further increasing the content of Pd for $x$ = 0.04 will completely suppress the CDW instabilities and give rise to the maximal SC order. The evolution of the electronic structures and electron-phonon couplings (EPCs) of the multiple CDWs upon Pd intercalation are carefully scrutinized. We discuss the interplay between multiple CDW orders, and the competition between CDW and SC in detail.
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The electron-phonon (e-ph) interaction remains of great interest in condensed matter physics and plays a vital role in realizing superconductors, charge-density-waves (CDW), and polarons. We study the two-dimensional Holstein model for e-ph coupling using determinant quantum Monte Carlo across a wide range of its phase diagram as a function of temperature, electron density, dimensionless e-ph coupling strength, and the adiabatic ratio of the phonon frequency to the Fermi energy. We describe the behavior of the CDW correlations, the competition between superconducting and CDW orders and polaron formation, the optimal conditions for superconductivity, and the transition from the weak-coupling regime to the strong-coupling regime. Superconductivity is optimized at intermediate e-ph coupling strength and intermediate electron density, and the superconducting correlations increase monotonically with phonon frequency. The global maximum for superconductivity in the Holstein model occurs at large phonon frequency, the limit where an attractive Hubbard model effectively describes the physics.
By using variational wave functions and quantum Monte Carlo techniques, we investigate the interplay between electron-electron and electron-phonon interactions in the two-dimensional Hubbard-Holstein model. Here, the ground-state phase diagram is triggered by several energy scales, i.e., the electron hopping $t$, the on-site electron-electron interaction $U$, the phonon energy $omega_0$, and the electron-phonon coupling $g$. At half filling, the ground state is an antiferromagnetic insulator for $U gtrsim 2g^2/omega_0$, while it is a charge-density-wave (or bi-polaronic) insulator for $U lesssim 2g^2/omega_0$. In addition to these phases, we find a superconducting phase that intrudes between them. For $omega_0/t=1$, superconductivity emerges when both $U/t$ and $2g^2/tomega_0$ are small; then, by increasing the value of the phonon energy $omega_0$, it extends along the transition line between antiferromagnetic and charge-density-wave insulators. Away from half filling, phase separation occurs when doping the charge-density-wave insulator, while a uniform (superconducting) ground state is found when doping the superconducting phase. In the analysis of finite-size effects, it is extremely important to average over twisted boundary conditions, especially in the weak-coupling limit and in the doped case.
2$H$-TaSe$_2$ has been one of unique transition metal dichalcogenides exhibiting several phase transitions due to a delicate balance among competing electronic ground states. An unusual metallic state at high-$T$ is sequentially followed by an incommensurate charge density wave (ICDW) state at $approx$ 122 K and a commensurate charge density wave (CCDW) state at $approx$ 90 K, and superconductivity at $T_{rm{C}}sim$0.14 K. Upon systematic intercalation of Pd ions into TaSe$_2$, we find that CCDW order is destabilized more rapidly than ICDW to indicate a hidden quantum phase transition point at $x$$sim$0.09-0.10. Moreover, $T_{rm{C}}$ shows a dramatic enhancement up to 3.3 K at $x$ = 0.08, $sim$24 times of $T_{rm{C}}$ in 2$H$-TaSe$_2$, in proportional to the density of states $N(E_F)$. Investigations of upper critical fields $H_{c2}$ in single crystals reveal evidences of multiband superconductivity as temperature-dependent anisotropy factor $gamma_H$ = $H_{c2}^{ab}$/$H_{c2}^{c}$, quasi-linear increase of $H_{c2}^{c}(T)$, and an upward, positive-curvature in $H_{c2}^{ab}(T)$ near $T_{rm{C}}$. Furthermore, analysis of temperature-dependent electronic specific heat corroborates the presence of multiple superconducting gaps. Based on above findings and electronic phase diagram vs $x$, we propose that the increase of $N(E_F)$ and effective electron-phonon coupling in the vicinity of CDW quantum phase transition should be a key to the large enhancement of $T_{rm{C}}$ in Pd$_x$TaSe$_2$.
How superconductivity interacts with charge or nematic order is one of the great unresolved issues at the center of research in quantum materials. Ba$_{1-x}$Sr$_{x}$Ni$_{2}$As$_{2}$ (BSNA) is a charge ordered pnictide superconductor recently shown to exhibit a six-fold enhancement of superconductivity due to nematic fluctuations near a quantum phase transition (at $x_c=0.7$). The superconductivity is, however, anomalous, with the resistive transition for $0.4 < x< x_c$ occurring at a higher temperature than the specific heat anomaly. Using x-ray scattering, we discovered a new charge density wave (CDW) in BSNA in this composition range. The CDW is commensurate with a period of two lattice parameters, and is distinct from the two CDWs previously reported in this material. We argue that the anomalous transport behavior arises from heterogeneous superconductivity nucleating at antiphase domain walls in this CDW. We also present new data on the incommensurate CDW, previously identified as being unidirectional, showing that is a rotationally symmetric, 4$Q$ state with $C_4$ symmetry. Our study establishes BSNA as a rare material containing three distinct CDWs, and an exciting testbed for studying coupling between CDW, nematic, and SC orders.
One of the biggest puzzles concerning the cuprate high temperature superconductors is what determines the maximum transition temperature (Tc,max), which varies from less than 30 K to above 130 K in different compounds. Despite this dramatic variation, a robust trend is that within each family, the double-layer compound always has higher Tc,max than the single-layer counterpart. Here we use scanning tunneling microscopy to investigate the electronic structure of four cuprate parent compounds belonging to two different families. We find that within each family, the double layer compound has a much smaller charge transfer gap size ($Delta_{CT}$), indicating a clear anticorrelation between $Delta_{CT}$ and Tc,max. These results suggest that the charge transfer gap plays a key role in the superconducting physics of cuprates, which shed important new light on the high Tc mechanism from doped Mott insulator perspective.
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