Strong-coupling charge density wave in a one-dimensional topological metal

Philip Hofmann, Miguel M. Ugeda, Anton Tamtögl, Adrian Ruckhofer, Wolfgang E. Ernst, Giorgio Benedek, Antonio J. Martínez-Galera, Anna Stróżecka, José M. Gómez-Rodríguez, Emile Rienks, Maria Fuglsang Jensen, José I. Pascual, and Justin W. Wells

Phys. Rev. B 99, 035438 – Published 25 January 2019

Abstract

Scanning tunneling microscopy, low-energy electron diffraction, and helium atom scattering show a transition to a dimerizationlike reconstruction in the one-dimensional atomic chains on Bi(114) at low temperatures. One-dimensional metals are generally unstable against such a Peierls-like distortion, but neither the shape nor the spin texture of the Bi(114) Fermi contour favors the transition: Although the Fermi contour is one dimensional and thus perfectly nested, the very short nesting vector $2 k_{F}$ is inconsistent with the periodicity of the distortion. Moreover, the nesting occurs between two Fermi contour branches of opposite spin, which is also expected to prevent the formation of a Peierls phase. Indeed, angle-resolved photoemission spectroscopy does not reveal any change in the electronic structure near the Fermi energy around the phase transition. On the other hand, distinct changes at higher binding energies are found to accompany the structural phase transition. This suggests that the transition of a strong-coupling type and that it is driven by phonon entropy rather than electronic entropy. This picture is supported by the observed short correlation length of the pairing distortion, the second-order-like character of the phase transition, and pronounced differences between the surface phonon spectra of the high- and low-temperature phases.

Received 12 July 2017

DOI:https://doi.org/10.1103/PhysRevB.99.035438

Physics Subject Headings (PhySH)

Charge density waves Rashba coupling Topological insulators

1-dimensional systems Peierls transition

Angle-resolved photoemission spectroscopy Low-energy electron diffraction Scanning tunneling microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Philip Hofmann^1,*, Miguel M. Ugeda^2,3, Anton Tamtögl⁴, Adrian Ruckhofer⁴, Wolfgang E. Ernst⁴, Giorgio Benedek^2,5, Antonio J. Martínez-Galera⁶, Anna Stróżecka⁷, José M. Gómez-Rodríguez^6,8,9, Emile Rienks¹, Maria Fuglsang Jensen¹, José I. Pascual^10,3, and Justin W. Wells¹¹

¹Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), Aarhus University, 8000 Aarhus C, Denmark
²Donostia International Physics Center, DIPC, 20018 San Sebastian-Donostia, Spain
³Ikerbasque, Basque Foundation for Science, 48011 Bilbao, Spain
⁴Institute of Experimental Physics, Graz University of Technology, 8010 Graz, Austria
⁵Dipartimento di Scienza dei Materiali, Universitá di Milano-Bicocca, Via Roberto Cozzi 55, 20125 Milano, Italy
⁶Department Física de la Materia Condensada, Universidad Autónoma de Madrid, Madrid 28049, Spain
⁷Institut für Experimentalphysik, Freie Universität Berlin, 14195 Berlin, Germany
⁸Instituto Nicolas Cabrera, Universidad Autónoma de Madrid, 28049 Madrid, Spain
⁹Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain
¹⁰CIC nanoGUNE, 20018 San Sebastián-Donostia, Spain
¹¹Department of Physics, Center for Quantum Spintronics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway

^*philip@phys.au.dk

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Vol. 99, Iss. 3 — 15 January 2019

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Images

Figure 1
(a) Conventional one-dimensional electronic state at half-filling. The black dispersion is spin degenerate. This system is sensitive to a Peierls-type instability due to the perfect nesting and the fact that the nesting vector's length corresponds to a real-space periodicity of $2 a$ . (b) Situation on Bi(114). The spin degeneracy of the bands is lifted, and although perfect nesting is still present, it takes place for a very short nesting vector and between states of opposite spin (indicated by the color of the bands and the arrows), thus protecting against a Peierls-type instability.
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Figure 2
Dimerization distortion of the quasi-one-dimensional lattice structure of Bi(114). (a) STM image taken at 5 K showing dimer formation in some of the protruding atomic rows (red dashed frames) with frequently appearing defects, such as trimers (blue dashed frame). (b) STM images at higher temperatures and (c) profiles along the protruding atomic rows, measured at the indicated temperatures. At 195 K, the dimerization is lifted and only observed in the immediate vicinity of defects. Tunneling parameters: (a) $U = 0.2 V$ and $I = 0.1 nA$ and (b) $U = 0.2, 1.0, - 0.1, 0.25 V$ and $I = 0.1$ , 4.0, 2.0, 4.0 nA. All STM data were processed with the wsxm software [36].
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Figure 3
(a) and (b) LEED patterns collected above and below, respectively, the temperature of the phase transition observed by STM. The arrow in (b) shows the additional streaks induced by the periodicity doubling along the atomic chains. The electron kinetic energy is 27.2 eV.
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Figure 4
(a) Scattered He intensities (logarithmic scale) versus parallel momentum transfer $k_{x}$ (crystal azimuth aligned along $\bar{Γ} - \bar{X}$ ) for various sample temperatures $T$ . A small vertical offset between the individual scans was added for better visibility. The vertical dotted lines illustrate the position of the CDW superlattice peaks due to the doubled periodicity. (b) Normalized square root of the CDW superlattice peak's integrated intensity (peak at $k_{x} = - 2.15 Å^{- 1}$ ), which is proportional to the CDW order parameter. The lines represents fits to Eq. (1) for different choices of the critical exponent $β$ . (c) Peak area of the CDW superlattice peak when integrated over energy in the energy-resolved TOF measurements.
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Figure 5
(a) and (b) Photoemission intensity in the low-temperature phase at $T = 60 K$ in a 20-meV window around the Fermi energy and a binding energy of 170 meV, respectively. The sketched continuation of the Fermi surface illustrates that the observed linelike intensity is composed of two unresolved spin-polarized Fermi-level crossings [13], see also Fig. 1. The photon energy is $h ν = 70 eV$ . The dashed line shows the direction of the data in (c) and (e). (c) and (d) Photoemission intensity close to and below the CDW transition (at $T = 200$ and 62 K), respectively, along the dashed black line in (a). (e) Momentum distribution curves at the Fermi energy along the dashed line in (a) as a function of temperature. (f) Energy distribution curves along the crossing point of the dashed line in (a) and the Fermi surface at $k_{x} = 0$ , i.e., through the center of the images in (c) and (d). $h ν = 17 eV$ in (c)–(f).
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Figure 6
Comparison of several TOF spectra for the cooled sample and the sample at room temperature, transformed to energy transfer spectra $Δ E = E_{f} - E_{i}$ . Energy loss ( $Δ E < 0$ ) corresponds to the creation of a phonon with phonon energy $Δ E = ℏ ω$ , and energy gain ( $Δ E > 0$ ) corresponds to the annihilation of a phonon. RW and L stand for the Rayleigh wave and longitudinal phonon modes, respectively.
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