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We revisit charge density wave (CDW) behavior in the archetypalquasi-one-dimensional (quasi-1D) material NbSe$_3$ by high-resolutionangle-resolved photoemission spectroscopy measurements utilizing a microfocusedlaser with a photon energy of 6.3 eV. We present a detailed view of theelectronic structure of this complex multiband system and unambiguously resolveCDW gaps at the Fermi level ($E_F$). By employing a tight-binding model, weargue that these gaps are the result of interband coupling between electronicstates that reside predominantly on distinct 1D chains within the material. Twosuch localized states are found to couple to an electronic state that extendsacross multiple 1D chains, highlighting the importance of a higher-dimensionalinteraction in stabilizing the CDW ordering in this material. In addition, thetemperature evolution of intrachain gaps caused by the CDW periodicities farbelow $E_F$ deviate from the behavior expected for a Peierls-type mechanismdriven by nesting; the upper and lower bands of the renormalized CDWdispersions maintain a fixed peak-to-peak distance while the gaps are graduallyremoved at higher temperatures. This points toward a gradual loss of long-rangephase coherence as the dominant effect in reducing the CDW order parameter,which may correspond to the loss of coherence between the coupled chains.Furthermore, one of the gaps is observed above the bulk and surface CDWtransition temperatures, implying the persistence of short-range incoherent CDWorder. The influence of such higher-dimensional interactions likely plays animportant role in a range of low-dimensional systems.

physical review. b./physical review. b

Role of a higher dimensional interaction in stabilizing charge density  waves in quasi-1D NbSe$_3$ revealed by angle-resolved photoemission  spectroscopy