Charge ordering geometries in uniaxially strainedNbSe2

Abstract

Recent STM experiments reveal niobium diselenide to support domains of striped (1Q) charge order side-by-side with its better-known triangular (3Q) phase, suggesting that small variations in local strain may induce a quantum phase transition between the two. We use a theoretical model of the charge order in NbSe2, based on a strong momentum-and orbital-dependent electron-phonon coupling, to study the effect of uniaxial strain. We find that as little as 0.1% anisotropic shift in phonon energies breaks the threefold symmetry in favour of a 1Q state, in agreement with the experimental results. The altered symmetries change the transition into the ordered state from weakly-first-order in the 3Q case, to second order in the 1Q regime. Modeling the pseudogap phase of NbSe2 as the range of temperatures above the onset of long-range order in which phase coherence is destroyed by local phonon fluctuations, we find a shortening of the local ordering wavevector with increasing temperature, complementing recent X-ray diffraction observations within the lowtemperature phase.The stability of different charge density wave (CDW) geometries is a topic of much current interest. In the simplest case a '1Q' CDW selects a single preferential direction [1]. In two-dimensional materials, two perpendicular 1Q CDWs can coexist, creating a 2Q pattern. In the layered high-temperature superconductors such a checkerboard state is believed to compete with 1Q order [2-5]; recently the 1Q state was found to dominate the 2Q in YBCO [6]. The layered hexagonal structure of niobium diselenide (2H-NbSe 2 ) allows instead for a 3Q triangular CDW with three superposed 1Q patterns [7][8][9][10]. Recent surface studies via scanning tunnelling microscopy (STM) suggest a quantum phase transition between 3Q and 1Q states in NbSe 2 may be tuned by local strain, offering the possibility of studying the interplay between the two, as well as a direct comparison to the high-T c case [11,12].It was recently shown that the minimal model reproducing the full range of experimental observations on the 3Q ordered state in NbSe 2 includes a strong electronphonon coupling, dependent on both the momenta and the orbital characters of the electronic states scattered between [13]. Motivated by the recent STM observations, in this Letter we employ the same model in a free energy analysis to study the charge-ordered state upon application of uniaxial strain [12]. We find that while the 3Q state, which respects the threefold lattice symmetry, is the lowest-energy configuration in the unstrained case, little uniaxial strain is required to break the symmetry to 1Q, agreeing with suggestions that lattice defects may locally stabilize the 1Q state [12]. We find that the 1Q phase transitions are second-order, whereas the 3Q transitions are weakly-first-order. With increasing temperature we predict a shortening CDW wavevector in the locally-fluctuating, short-range-ordered, pseudogap regime above the CDW transition, analogous to the recently-observed non-monotonic evolution of the...

Thermodynamic anomaly above the superconducting critical temperature in the quasi-one-dimensional superconductorTa4Pd3Te16

“…The transition we see at 20 K could be the turning-on of these fluctuations. A sharp turn-on of CDW fluctuations has previously been proposed to account for a resistivity bump in the q2D transition metal oxide bronze P 4 W 10 O 38 [31,32] and has been predicted in the q2D transition metal dichalcogenide NbSe 2 [23,33]. Despite the fluctuating CDW order being along the b-direction chains it would not necessarily give a strong resistivity boost in this direction.…”

Charge order inNbSe2

“…It was suggested that the 1Q regions may be stabilized by local strain on the sample's surface. The fact that both 1Q and 3Q order can be observed sideby-side on the same sample suggests that the 3Q order is in fact close to a quantum critical point, and can be destroyed by relatively little strain 14,16 . To quantify this hypothesis, we now compare the free energy of the 3Q ordered state to that of the single Q pattern, as a function of externally-applied uniaxial strain.…”

“…Following the minima of the renormalized phonon dispersions in Fig. 21 as a function of temperature, gives an indication of the expected thermal evolution of the CDW vector Q CDW characterizing the local order in the fluctuating islands of the pseudogap phase 16 . The regions of stability surrounding defects are expected to grow continuously as temperature decreases, until at T CDW they overlap sufficiently for separate regions to become correlated.…”

“…In addition to the nature of the pseudogap phase, puzzling aspects of the NbSe 2 phenomenology include the question of why only one band develops a CDW gap; uncertainty over the size of the CDW gap, with estimates ranging from 0 meV 25 to 35 meV 29 ; and an observed asymmetry in the particle and hole states near the CDW gap 14 , leading to an offset of the gap with respect to E F 30 . The present authors recently outlined a model based on a strongly momentum-and orbital-dependent electron-phonon coupling to explain all of these unusual features of the NbSe 2 CDW state, as well as providing a quantitative explanation of how the wave vectors of the 3Q and 1Q CDW instabilities are selected 15,16 . The present paper extends the results of this previous work as well as providing details of the calculations involved.…”

“…In the absence of nesting, understanding the influence of electron-phonon coupling is paramount to understanding both the origin of charge order, and the competition between different geometries of CDW states. In two recent papers, the present authors outlined a model describing the charge-ordered phases of niobium diselenide 15,16 . The present paper extends these results and provides the calculational details of the model, showing how both the momentum and orbital dependence of the electron-phonon coupling co-operate to drive the onset of charge order in NbSe 2 , and how their interplay with the electronic structure directs the competition between single-Q and multi-Q CDWs.…”