Experimental Evidence for a Bragg Glass Density Wave Phase in a Transition-Metal Dichalcogenide

Abstract

Analysis of the spatial dependence of current-voltage characteristics obtained from scanning tunneling microscopy experiments indicates that the charge density wave (CDW) occurring in NbSe2 is subject to locally strong pinning by a non-negligible density of defects, but that on the length scales accessible in this experiment the material is in a "Bragg glass" phase where dislocations and antidislocations occur in bound pairs and free dislocations are not observed. A Landau theory-based analysis is presented showing how a strong local modulation may produce only a weak long range effect on the CDW phase. The effect of disorder on the properties of condensed matter systems is important both in terms of fundamental physics and of technological applications. In charge density wave (CDW) systems, randomly positioned impurities provide a random field which couples linearly to the order parameter [1]. Theory dating back to the 1970s indicates that if the impurity potential is strong enough, the random field destroys the charge density wave completely, leading to a phase with exponentially decaying correlations and a correlation length of the order of the mean distance between impurities [2, 3]. Subsequent work revised this picture, showing that in spatial dimensions d = 3, weak impurity pinning may lead instead to a topologically ordered "Bragg glass" phase with powerlaw density correlations [4][5][6][7][8][9][10][11][12].While the physics of random field systems has been of intense theoretical interest, experimental information has mainly come from transport and scattering measurements which average over large sample volumes [1,[13][14][15][16][17]. An important exception is the flux lattice decoration experiments which provided important early support to the Bragg glass picture for vortices in superconductors [18,19]. The development of stable scanning tunneling spectroscopy (STS) techniques which provide atomic-resolution imaging of local electronic density over wide fields of view has opened up new avenues for investigation of fundamental electronic physics, in particular providing real-space information on the effects of disorder on electronically ordered states [20,21]. In this paper, we present an analysis of scanning tunneling spectroscopy measurements carried out on NbSe 2 , a representative charge density wave system. The analysis motivates a Landau theory which provides insights into the effects of strong pinning in charge density wave systems.NbSe 2 is a quasi-two dimensional material. Its unit cell consists of two blocks of Se-Nb-Se layers; the Nb atoms in each layer form a triangular lattice and the electrical conductivity is strongly anisotropic, being much larger for in-plane currents than for currents flowing perpendicular to the layers [22]. Scattering measurements [23] indicate that a second order phase transition occurs at

Effect of dilute strongly pinning impurities on charge density waves

“…However, analysis of the STM data suggests that the impurities in NbSe 2 are strong pinning centers. 1 In this situation, conventional theories 11-13 predict short-range order with a correlation length L c of the order of the average interimpurity distance l and with a proliferation of topological defects, 8,9 in apparent contradiction to the experimental result. The NbSe 2 sample studied in Ref.…”

“…Recent scanning tunnelling microscopy (STM) data 1 suggests that the charge density wave (CDW) in NbSe 2 is a topologically ordered Bragg glass at least on the length scales (∼ 30 unit cells) accessible in the experiment. Such a glass phase with a power law density correlation was predicted theoretically [2][3][4][5][6][7][8][9][10] for three dimensional systems with a high density of weak pinning centers.…”

“…The NbSe 2 sample studied in Ref. 1 was found to have a CDW coherence length ξ 0 ≈ 1 nm and l ≈ 5 nm, so the pinning centers are dilute (note that ξ 0 is used here to denote the "BCS" coherence length, which sets the length scale of CDW amplitude fluctuations and is the ultraviolet cutoff for a Ginzburg-Landau like theory of phase fluctuations). This dilute-pinning limit has not been extensively studied in the literature.…”

Charge density wave in layeredLa1−xCexSb2

“…Condensation of CDW by disorder has been examined in Refs. [35,36,[44][45][46][47][48][49]. Pinning of the CDW bears some similarities to pinning of the vortex lattice in superconductors [50][51][52], and is discussed using the Fukuyama-Lee-Rice theory [53,54].…”

“…However, dynamic, or fluctuating, CDWs can be pinned by disorder [36,[44][45][46]. Condensation of CDW by disorder has been examined in Refs.…”