Robust orbital diamagnetism in correlated Dirac fermions

We report on (resonant) x-ray diffraction experiments on the normal state properties of kagome-lattice superconductors KV3Sb5 and RbV3Sb5. We have confirmed previous reports indicating that the charge density wave (CDW) phase is characterized by a doubling of the unit cell in all three crystallographic directions. By monitoring the temperature dependence of Bragg peaks associated with the CDW phase, we ascertained that it develops gradually over several degrees, as opposed to CsV3Sb5, where the CDW peak intensity saturates promptly just below the CDW transition temperature. Analysis of symmetry modes indicates that this behavior arises due to lattice distortions linked to the formation of CDWs. These distortions occur abruptly in CsV3Sb5, while they progress more gradually in RbV3Sb5 and KV3Sb5. In contrast, the amplitude of the mode leading to the crystallographic symmetry breaking from P6/mmm to Fmmm appears to develop more gradually in CsV3Sb5 as well. Diffraction measurements close to the V K edge and the Sb L1 edge show no sensitivity to inversion- or time-symmetry breaking, which are claimed to be associated with the onset of the CDW phase. The azimuthal angle dependence of the resonant diffraction intensity observed at the Sb L1 edge is associated with the difference in the population of unoccupied states and the anisotropy of the electron density of certain Sb ions.

Vanadium ditelluride (VTe2) has been intensively explored to understand the charge density wave (CDW) phase and its connection to magnetic properties. Here, we conduct a systematic study to understand the fine structure of CDW via scanning tunneling microscopy (STM) combined with density functional theory (DFT) calculations. STM topograph at 79 K shows that a CDW phase in VTe2 has a stripe modulation with 3 × 1 periodicity, following the double zigzag chain of distorted Te lattices. Interestingly, the 3 × 1 CDW modulation undergoes contrast inversion between filled and empty state topographs. Atomistic features and contrast changes of CDW observed in STM are clearly reproduced in our DFT simulation images. Charge distribution calculation indicates that the spatial extension and density of Te 5p orbitals have strong variations with filled and empty states, explaining the fine structure of 3 × 1 CDW in VTe2. Our finding provides an inspiring insight to further research on the less explored electronic structure of VTe2.

We revisit a superconducting phase diagram and electronic structures across the charge density wave (CDW) phase transition of Cu-underdoped $1T\text{\ensuremath{-}}{\mathrm{Cu}}_{\ensuremath{\delta}}\mathrm{Ti}{\mathrm{Se}}_{2}$ ($\ensuremath{\delta}\ensuremath{\sim}0.03$) under hydrostatic pressure. Superconductivity appears right after the complete collapse of the long-range CDW at a critical pressure of ${P}_{\mathrm{c}}\ensuremath{\sim}2.48\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$, apart from the reported superconducting phase diagrams; it is found that the superconducting transition temperature shows a domelike pressure dependence covering a narrow pressure range with a maximum of ${{T}_{\mathrm{c}}}^{\mathrm{max}}\ensuremath{\sim}2.80\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ at 4.80 GPa. Accordingly, the residual resistivity ${\ensuremath{\rho}}_{0}$ and temperature exponent $n$ of normal-state resistivity (from \ensuremath{\sim}3.30 at ambient pressure to \ensuremath{\sim}2.38 at ${P}_{\mathrm{c}}$ and \ensuremath{\sim}4.0 at 6.50 GPa) reduce sizably while the quadratic temperature coefficient $A$ of normal-state resistivity is enhanced by one order in magnitude; these results indicate the importance of CDW quantum fluctuation in superconducting pairing; low-$T$ resistivity upwarps with a \ensuremath{-}ln$T$ dependence below a characteristic temperature ${T}^{*}$ which has a domelike shape in the pressure range of 2.82--4.80 GPa. Based on two-band analysis of Hall conductivity and Kohler-fitting of magnetotransport (MR), energy bands are dominated by electron-type carriers across the CDW phase transition for $P<{P}_{\mathrm{c}}$, and they reverse into hole-type for $P>{P}_{\mathrm{c}}$; interestingly, the mobility of carriers increases up to five times at ${P}_{\mathrm{c}}$, but carrier concentration shows a weak pressure dependence. The MR value increases with the pressure for $P<{P}_{\mathrm{c}}$ and then jump up to a saturated value after the collapse of the CDW. Our results show that the collapse of the CDW is accompanied by the reconstruction of the Fermi surface, and the enhancement in MR can be mainly attributed to the change of mobility. Possible mechanisms are discussed.

Two-dimensional materials are ideal candidates to host Charge Density Waves (CDWs) that exhibit paramagnetic limiting behavior, similar to the well-known case of superconductors. Here, we study how CDWs in two-dimensional systems can survive beyond the Pauli limit when they are subjected to a strong magnetic field by developing a generalized mean-field theory of CDWs under Zeeman fields that includes incommensurability, imperfect nesting, and temperature effects and the possibility of a competing or coexisting Spin Density Wave (SDW) order. Our numerical calculations yield rich phase diagrams with distinct high-field phases above the Pauli limiting field. For perfectly nested commensurate CDWs, a q-modulated CDW phase that is completely analogous to the superconducting Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase appears at high fields. In the more common case of imperfect nesting, the commensurate CDW ground state undergoes a series of magnetic-field-induced phase transitions first into a phase where commensurate CDW and SDW coexist and subsequently into another phase where CDW and SDW acquire a q-modulation that is, however, distinct from the pure FFLO CDW phase. The commensurate CDW + SDW phase occurs for fields comparable to but less than the Pauli limit and survives above it. Thus, this phase provides a plausible mechanism for the CDW to survive at high fields without the need for forming the more fragile FFLO phase. We suggest that the recently discovered 2D materials like the transition metal dichalcogenides offer a promising platform for observing such exotic field-induced CDW phenomena.

Modulating charge density wave states in 1T-TaS[formula omitted] by self-intercalation: A DFT study

Spin-triplet superconductivity induced by off-site Coulomb interaction in a triangular lattice

The 87 Rb NMR spin-lattice relaxation rate (SLRR) has been measured in the charge-density wave (CDW) phase of the quasi-one-dimensional conductor Rb 0.3 MoO 3 in a magnetic field of 2 T perpendicular to the conducting chains. The SLRR exhibits a peak at the critical temperature T c = 180 K, attributed to the critical fluctuations at the phase transition. Two more broad peaks are observed within the CDW phase: one peak at 150 K (0.8 T c ) and another one at 60 K (0.3 T c ). We discuss the 0.8-T c peak in terms of quantum coherence effects in analogy with the Hebel-Slichter peak in superconductors. The 60 K peak is attributed to the phase excitations of the CDW.

On the basis of extensive NMR measurements on a single crystal of Rbo.3MoO3 (blue bronze), we report several aspects of its charge density wave (CDW) and metallic phases that require a reinterpretation of some earlier results and indicate several aspects of the CDW fluctuations that will require further development of the theoretical models to describe them. From measurements of the spin-lattice relaxation rate (1/T1) of both 85Rb and 87Rb, it is clear that the dominant coupling responsible for 1/T1 is quadrupolar both above and below the CDW transition. This result contradicts the earlier interpretation that it was magnetic coupling to the conduction electrons above the transition. Also, there is no clear evidence of a coherence peak in 1/T1 below the transition. For most orientations of the external field relative to the crystalline axes, 1/T1 in the CDW phase is nearly constant across the spectrum of the central NMR transition, in contradiction to the prediction of the simple phason model for the fluctuations. Thus, there are additional fluctuation modes of the CDW that need to be included into the model for 1/T1.

The manipulation of charge density waves (CDWs) at the atomic scale offers a powerful approach to investigate their interplay with other quantum states. Monolayer NbTe 2 , which hosts coexisting 4×4 and 4×1 CDW phases, provides an ideal platform for such nanoscale exploration. Using scanning tunneling microscopy and spectroscopy (STM/S), we investigate the topography and electronic states of monolayer NbTe 2 near the boundaries between these CDW domains. We find a pronounced enhancement in both STM topography and the spectral weight of the valence band state (V 1 ) within the 4×4 CDW phase as its domain boundary is approached. This spatial evolution of topography and electronic states, accompanied by a downward band bending suggests a localized enhancement of the CDW order near the boundary. Based on the enhancement of the V 1 spectral weight, together with the large atomic spacing near the boundary, we suggest that a localized structural distortion may reinforce the CDW modulation and drive the accompanying electronic reconstruction. Our work highlights the critical role of nanoscale strain fields at structural interfaces in tailoring local electronic properties, offering a new dimension for understanding CDW phenomena in two-dimensional materials.

We reexamine the thermodynamic properties such as specific heat, thermal expansion, and elastic constants at the charge density wave (CDW) phase transition in several one- and two-dimensional materials. The amplitude of the specific heat anomaly at the CDW phase transition TCDW increases with increasing TCDW and a tendency to a lineal temperature dependence is verified. The Ehrenfest mean field theory relationships are approximately satisfied by several compounds such as the rare earth tritelluride compound TbTe3, transition metal dichalcogenide compound 2H-NbSe2, and quasi-one-dimensional conductor K0.3MoO3. In contrast inconsistency exists in the Ehrenfest relationships with the transition metal dichalcogenide compounds 2H-TaSe2 and TiSe2 having a different thermodynamic behavior at the transition temperature TCDW. It seems that elastic properties in the ordered phase of most of the compounds are related to the temperature dependence of the order parameter which follows a BCS behavior.

Advances in nanoscale material characterization on two-dimensional van der Waals layered materials primarily involve their optical and electronic properties. The thermal properties of these materials are harder to access due to the difficulty of thermal measurements at the nanoscale. In this work, we create a nanoscale magnetothermal device platform to access the basic out-of-plane magnetothermal transport properties of ultrathin van der Waals materials. Specifically, the Nernst effect in the charge density wave transition metal dichalcogenide 1T-TaS2 is examined on nano-thin flakes in a patterned device structure. It is revealed that near the commensurate charge density wave (CCDW) to nearly commensurate charge density wave (NCCDW) phase transition, the polarity of the Nernst effect changes. Since the Nernst effect is especially sensitive to changes in the Fermi surface, this suggests that large changes are occurring in the out-of-plane electronic structure of 1T-TaS2, which are otherwise unresolved in just in-plane electronic transport measurements. This may signal a coherent evolution of out-of-plane stacking in the CCDW → NCCDW transition.

In strongly anisotropic quasi-1D metallic systems the charge density wave (CDW) phase transition is given a generalised Ginzburg-Landau theory on the microscopic basis of the Gorkov-Dzyaloshinskii model. In the derivation of the free energy the interchain interaction is treated in MF approximation while the interchain interactions appear through the divergent (at T=0) CDW susceptibility chi 1DCDW of the 1D system. The exponent of chi 1DCDW is found to be the only decisive factor in determining the width of the Ginzburg critical region for a fixed interchain force range. The specific heat is also calculated and discussed.

In order to elucidate the origin of the interplay between charge density wave (CDW) and superconductivity in 1T-TaS2, we have synthesized powder samples of pure and C-intercalated 1T-CxTaS2 by means of a multi-anvil high-pressure synthesis method. We have found that single-phase samples are obtained in the 2-6 GPa range at 400 °C and for x=0-0.3. The structural, magnetic and transport properties of all samples have been investigated by means of neutron and x-ray diffraction, dc magnetization and dc electrical resistivity. For all x values including x=0, the data show that the CDW phase is suppressed concomitant to an abrupt onset of superconductivity, with Tc=3.2 K for x=0. The Tc value turns out to be weakly dependent on x, with a maximum Tc=3.8 K for x=0.2. This onset is accompanied by a crossover of magnetic behavior from paramagnetic Pauli-like to paramagnetic Curie-Weiss-like with effective moment  1.2 B/Ta, which suggests that a ionic picture is suitable for the superconducting phase, but not for the CDW phase. The analysis of the dependence of the a and c lattice parameters upon x as well as upon the synthesis conditions shows that the onset of superconductivity is mainly ascribed to unusual changes of the unit cell induced by the high-pressure synthesis. Specifically, the ex-situ lattice parameters exhibit a significantly larger c-axis parameter and a shrinking of the a-axis parameter stabilized by the high-pressure synthesis route. We argue that the above suppression of the CDW phase is induced by a broadening of the relevant 5d(t2g) band which stabilizes the metallic and superconducting phases. This scenario suggests that the strength of the electronic correlations are the main control parameter of the CDW-superconductivity competition in 1T-TaS2.

The first-order charge density wave (CDW) phase transition of ${\mathrm{Er}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Si}}_{5}$ is characterized by a crystal structure analysis, and electrical resistivity, magnetic susceptibility and specific heat measurements. The incommensurate CDW is accompanied by a strong lattice distortion, from which it is shown that the CDW resides on zigzag chains of iridium atoms. The CDW transition affects the magnitude of the local magnetic moments on ${\mathrm{Er}}^{3+}$, implying strong coupling between CDW and magnetism. This could account for the observation that magnetic order is suppressed down to at least 0.1 K in the high-quality single crystal presently studied. Any disorder in the crystallinity, as in ceramic material, broadens and suppresses the CDW transition, while magnetic order appears at 2.1 K.

Non-equilibrium dynamics of ultracold lattice bosons inside a cavity