Stripe and Short Range Order in the Charge Density Wave of 1T−CuxTiSe2

Abstract

We study the impact of Cu intercalation on the charge density wave (CDW) in 1T-Cu x TiSe 2 by scanning tunneling microscopy and spectroscopy. Cu atoms, identified through density functional theory modeling, are found to intercalate randomly on the octahedral site in the van der Waals gap and to dope delocalized electrons near the Fermi level. While the CDW modulation period does not depend on Cu content, we observe the formation of charge stripe domains at low Cu content (x < 0.02) and a breaking up of the commensurate order into 2 × 2 domains at higher Cu content. The latter shrink with increasing Cu concentration and tend to be phase shifted. These findings invalidate a proposed excitonic pairing as the primary CDW formation mechanism in this material. DOI: 10.1103/PhysRevLett.118.017002 Correlated electron systems are prone to develop distinct electronic ground states, such as superconductivity, charge density waves (CDWs), and spin ordered phases. The nature of the interplay between these ground states is the focus of intense research efforts. A CDW is a spatial modulation of the electron density associated with local lattice distortions. CDWs are found in a number of quasitwo-dimensional superconductors, including transition metal dichalcogenides [1], intercalated graphite [2], cuprates [3-5] and pnictides [6]. Of particular interest, largely driven by the puzzle of high temperature superconductivity, is whether charge order is competing, cooperating, or simply coexisting with superconductivity [7]. The layered transition metal dichalcogenide 1T-TiSe 2 offers an attractive playground to explore the interplay between these two electronic ground states, thus potentially contributing to resolving similar outstanding questions in cuprate superconductors and other strongly correlated materials.1T-TiSe 2 consists of a stack of van der Waals (vdW) coupled layers allowing in situ preparation of surfaces ideally suited for scanning probe investigations by cleaving. When cooled below T CDW ≃ 200 K, it undergoes a second-order phase transition into a commensurate 2 × 2 × 2 CDW superlattice [8,9]. There is currently no consensus on the origin of the CDW in this material. Two possible scenarios are being considered, one based on a purely electronic process characterized by an excitonic instability [8], while the other one involves a Jahn-Teller (JT) distortion [10]. More refined theories also propose a mixture of these two possible contributions, in the so called indirect JT transition [11][12][13].1T-TiSe 2 becomes superconducting when intercalating more than x ¼ 0.04 copper into the vdW gap, with a maximum critical temperature T c ¼ 4.1 K near x ¼ 0.08 [14]. Transport measurements [14,15] indicate the CDW is suppressed upon increasing the Cu content which would suggest a competition with superconductivity. A more recent report of an incommensurate CDW above the superconducting dome in pristine crystals under pressure [16] suggests a more complex scenario, where CDW fluctuations promote superconductivity. Traces of ...

Energy-dependent spatial texturing of charge order in 1T−CuxTiSe2

“…To understand this patchwork, we examine the spatial dependence of the tunneling spectra on a crystal with x = 0.02. On average, compared to pristine TiSe 2 , the spectral features shift towards higher binding energy, consistent with the electron band dopant character of Cu reported earlier [16,32]. A closer inspection of STS data over a 5.5 × 3.3 nm 2 area straddling a Cu-poor and a Cu-rich region ( Fig.…”

Extended Falicov-Kimball model: Exact solution for the ground state

“…In condensed-matter physics, correlations between electrons give rise to many intriguing phenomena ranging from simple band renormalization to complex phase diagrams with charge, spin, or orbital ordering as well as superconductivity [1][2][3][4][5][6][7][8][9][10][11]. The most popular model for the description of correlation effects in lattice systems is the Hubbard model (HM) [12], which captures essential physics related to the competition between electron localization (driven by the on-site U interaction) and electron itinerancy [13,14].…”

Extended Falicov-Kimball model: Exact solution for finite temperatures

“…Consequently, in the disordered phase with d = 0 and d 1 = 0 it does not change with temperature. Notice also that, in a general case of any value of ε, it is not possible to do determine expression for ρ(ε) analogous to (11). Fig.…”