NbSe₃ is a multiband Peierls system that is known to undergo two CDW transitions, one at T₁ = 145 K and another at T₂ = 59 K. Its Fermi surface (which decribes the location of the conduction electrons in reciprocal space) as calculated by density functional theory (DFT) consists of five electron bands. In this system, the presence of CDWs is signaled by the so-called "nesting" of its lattice distortion vectors in reciprocal space (i.e., for each CDW, vectors span a pair of bands in the Fermi surface).

Schematic of the Fermi surface of NbSe₃ calculated with DFT. Five bands are seen in a cross section along the chain direction (1D axis) and K_⊥. "Nesting" vectors connect bands 2 and 3 (red) and 1 and 4 (blue).

Single-crystal NbSe₃ "whiskers" were grown via vapor transport and cleaved into fine fibers in ultrahigh vacuum. High-resolution ARPES data at T = 15 K were obtained from the tiny samples using the microfocused synchrotron beam at ALS Beamline 10.0.1. At low temperature, energy gaps are expected to occur in the Fermi surface where the lattice distortion vectors q₁ and q₂ are nested. However, the NbSe₃ spectra obtained do not display well-defined gaps; instead, pseudogap behavior is observed, with the photoemission intensity continuously decreasing toward the Fermi energy E_F. Extrinsic defect scattering is an unlikely cause of this since many other spectral features are rather sharp. The researchers therefore concluded that the pseudogaps are intrinsic properties of the CDW phase. Photoemission intensity in the gap region can be generated by quantum fluctuations. Also, an imperfectly nested Fermi surface with permanently metallic sections may cause additional interactions that contribute to the gap spectral function. Effective gap values of Δ₁* = 110 ± 20 meV and Δ ₂* = 45 ± 10 meV were obtained for the q₁ and q₂ CDWs, respectively.

Riding the Charge-Density Wave

Cars caught in stop-and-go traffic on a one-lane road can be described as "strongly interacting" components of a one-dimensional system. They are strongly interacting because, being restricted to one lane, the motion of each car is tied to the motion of its nearest neighbors, and traffic will tend to bunch up into "car density waves" rather than flow homogeneously (as on a four-lane freeway where there is room to pass).

In the 1930s, physicist Rudolf Peierls theorized that electrons confined to a one-dimensional metal crystal at low temperature would interact strongly with one another and with the crystal lattice to form charge-density waves. In the 1970s, the existence of CDWs was detected in a variety of quasi-one-dimensional metals whose structure consists of weakly coupled molecular chains. More recently, the occurrence of CDWs in one-dimensional metals has been the object of intense research. In addition to serving as a conveniently observable model system for complex dynamical theories, CDW materials exhibit many exotic properties (e.g., nonlinear conduction, gigantic dielectric constants, and the ability to "remember" previous inputs) that may one day find practical applications as memory devices, tunable capacitors, or extremely sensitive optical detectors.

Spectral functions from ARPES line scans at k_|| = 0 and at k_F for the effective gaps Δ₁* and Δ₂*. Gap spectra are identified by "nesting" conditions in reciprocal space. They are inherently broad and are complemented with second derivatives –d²I/dE².

Nominally metallic bands are encountered at the boundaries of the Brillouin zone, where the bands do not match a CDW nesting condition. Here, a low-energy shoulder near E_F is also observed. It displays a much-reduced dispersion that is equivalent to a particularly heavy electron mass. Such an effect has been known to occur from "dressing" of the electron with phonons. In the present data, the shallow slope indicates an enhanced electron mass over an energy window of about 90 meV, coinciding with a value for the energy gap of 2Δ₂*. The effect disappears above T₂ = 59 K, supporting a connection to the q₂ CDW phase. The effect may be caused by the reduced phase space available for electron scattering that results from the gapped regions. However, a theoretical description of the effect is outstanding to date.

Left: Modified electron band dispersion along the Y-C direction in the Brillouin zone, where nominally metallic bands are expected (intensity displayed as –d²I/dE²). The branch with shallow slope is representative of an enhanced electron mass over an energy window of ~90 meV. Right: Above T₂ , the effect is no longer detected.

In conclusion, this study elucidates the nature of the energy gaps in the multiband environment encountered in many quasi-1D systems, where the energy gaps deviate from simple gap behavior. Nondistorted parts of the electron bands do not show a conventional Fermi edge, and the electronic dispersion exhibits the signature of electron mass enhancement on the energy scale of the full gap, 2Δ₂*. Thus, both gapped and permanently metallic parts of the Fermi surface seem to mutually influence each other.

Research conducted by J. Schaefer, M. Sing, and R. Claessen (Universität Augsburg); E. Rotenberg (Berkeley Lab); X.J. Zhou (Berkeley Lab and Stanford University); R.E. Thorne (Cornell University); and S.D. Kevan (University of Oregon).

Research funding: Deutsche Forschungsgemeinschaft (German Research Foundation) and the Bavaria California Technology Center (BaCaTeC). Operation of the ALS is supported by the U.S. Department of Energy, Office of Basic Energy Sciences.

Publication about this research: J. Schaefer, M. Sing, R. Claessen, E. Rotenberg, X.J. Zhou, R.E. Thorne, S.D. Kevan, "Unusual Spectral Behavior of Charge-Density Waves with Imperfect Nesting in a Quasi-One-Dimensional Metal," Phys. Rev. Lett. 91, 066401 (2003).