Doublonlike Excitations and Their Phononic Coupling in a Mott Charge-Density-Wave System

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Doublonlike Excitations and Their Phononic Coupling in a Mott Charge-Density-Wave System

C. J. Butler, M. Yoshida, T. Hanaguri, and Y. Iwasa

Phys. Rev. X 11, 011059 – Published 24 March 2021

Abstract

Electron-phonon-driven charge-density waves can in some circumstances allow electronic correlations to become predominant, driving a system into a Mott insulating state. New insight into both the Mott state and preceding charge-density wave may result from observations of the coupled dynamics of their underlying degrees of freedom. Here, tunneling injection of single electrons into the upper Hubbard band of the Mott charge-density-wave material $1 T − {TaS}_{2}$ reveals extraordinarily narrow electronic excitations which couple to amplitude mode phonons associated with the charge-density wave’s periodic lattice distortion. This gives a vivid microscopic view of the interplay between excitations of the Mott state and the lattice dynamics of its charge-density wave precursor.

Received 29 September 2020
Revised 1 February 2021
Accepted 9 February 2021

DOI:https://doi.org/10.1103/PhysRevX.11.011059

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Charge density waves Doublon Electron-phonon coupling Many-body localization Optical phonons

Transition metal dichalcogenides

Scanning tunneling spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

C. J. Butler ^1,*, M. Yoshida ¹, T. Hanaguri ^1,†, and Y. Iwasa^1,2

¹RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
²Quantum-Phase Electronics Center and Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

^*christopher.butler@riken.jp
^†hanaguri@riken.jp

Popular Summary

In some crystalline materials, electrons and ions can lower the overall system energy by forming matched static density-wave patterns. In tantalum disulfide, these modulations make the electrons’ motion so sluggish that they can no longer overcome their mutual repulsion to flow among each other freely. They are locked in place, forming a “Mott insulator,” a phase of electronic matter from which can emerge some of the most spectacular condensed-matter phenomena, including high-temperature superconductivity. To investigate how the electrons and ionic lattice coordinate to form this state, we induce an abrupt disturbance in one density wave to observe the dynamic response of the other, and we discover new electronic states that defy expectations.

In our experiments, we use a scanning tunneling microscope to observe the electronic density wave of tantalum disulfide, to inject electrons into the Mott state, and to observe spectroscopic markers of the response. Most interestingly, the extraordinary sharpness of these spectroscopic features hints at excitations that seemingly defy understanding in current theories of Mott insulators. The injection of electrons also upsets the balance of the ionic and electronic density waves, exciting a fundamental vibrational mode of the lattice, specifically the oscillation of the ionic density wave around the arriving electron.

This discovery of unexpected, discrete electronic states in a Mott insulator should spur a new theoretical push to understand their nature and will extend our microscopic understanding of systems in which electrons’ mutual repulsion and influence on the lattice are both strong.

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Vol. 11, Iss. 1 — January - March 2021

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Figure 1
Spectroscopically distinct surface terminations of the three-dimensional charge order in $1 T − {TaS}_{2}$ . (a) A typical constant-current topograph ( $V = 250 mV$ , $I = 250 pA$ ), acquired at a type 1 surface. (b) A depiction of the periodic lattice distortion forming SD clusters with 13 Ta atoms each (sulfur ions are neglected). A surface-projected supercell of the CDW distortion is shown with a black and white dashed line, corresponding to the cell shown in the inset of (a). (c) The alternating interlayer stacking of the SD clusters, showing the two inequivalent cleavage planes 1 and 2. (d) High-resolution $(d I / d V) (V)$ curves acquired at two types of surface. Recent STM investigations allow the identification of each spectrum with the type 1 and 2 surfaces formed by cleavage through the planes 1 and 2 in (c) [5]. The newly observed peaks at each surface are indicated with arrows. For ease of comparison, the curves are normalized by dividing by the current value at $+ 500 mV$ for each.
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Figure 2
Spectroscopic imaging at the UHB onset at type 1 and 2 surfaces. (a),(b) Constant-current topographs of each surface (setpoints $V = 0.25 V$ , $I = 1 nA$ , and $V = 0.11 V$ , $I = 0.44 nA$ , respectively). (c),(d) Spectroscopic line cuts taken along the white dashed lines shown in (a) and (b). Note that each energy range is chosen for suitability to each UHB onset energy. From here onward, this work focuses on the features observed at the type 2 surface.
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Figure 3
Analysis of $e$ -ph replica peaks at the type 2 surface. (a) Idealized line shapes described by Eq. (2) for various values of $D$ . The dashed lines show envelope functions for the relative peak intensities according to the Franck-Condon principle [Eq. (1)]. Plots are vertically offset for clarity. (b) Fitting, using Eq. (3), to the conductance spectrum of unoccupied states at the type 2 surface, acquired at the point shown in the inset. (c) Fitted energies for the peaks in (b), with a linear fit giving an average spacing of 8.8 meV. (d) Fitted peak intensities (total area under each Lorentzian curve), with further fitting using Eq. (1) yielding the Huang-Rhys parameter $D = 1.75$ . (e) Fitted Lorentzian broadening parameters for each peak.
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Figure 4
Insensitivity of Franck-Condon series to tip-sample separation. (a) Conductance curves collected at varying STM tip height. After stabilizing the tip at the height $z_{setpoint}$ (at $V = 0.11 V$ , $I = 0.44 nA$ ), the tip height was altered by an amount $z_{offset}$ before measuring the conductance spectrum. Here the curves are normalized for ease of comparison, using the value of $d I / d V$ at an energy 40 meV above that of the lowest-lying peak. (b) Results of the fitting with the function in Eq. (3). The parameters $E_{ph}$ , $D$ , and $Γ_{0}^{*}$ are insensitive to the tip height.
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Figure 5
Excitation of CDW amplitude mode by a transient doublonlike excitation. (a) A depiction of the excited amplitude mode in the SD cluster. (The Ta ionic displacements are greatly exaggerated.) (b) A qualitative plot of the SD cluster occupancy as a function of time, and the resulting local fluctuation of the order parameter.
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