Quasiparticle-Like Resonances and Spectral Inhomogeneity on the Surface of Li0.9Mo6o17

Quasiparticle-Like Resonances and Spectral Inhomogeneity on the Surface of Li0.9Mo6O17

Samuel Detmer,1 Anjan Soumyanarayanan,2, 3 Michael M. Yee,1 Yang He,1 M. Greenblatt,4 Nigel E. Hussey,5 and Jennifer E. Hoﬀman1, 6, ∗ 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 2Institute of Materials Research and Engineering, A*STAR, Singapore 138634 3Department of Physics, National University of Singapore, Singapore 4Department of Chemistry and Chemical Biology, Rutgers University, 123 Bevier Rd., Piscataway, NJ 08854, USA 5School of Physics, University of Bristol, Beacon House, Queens Road, Bristol, BS8 1QU, UK 6School of Engineering & Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA (Dated: October 26, 2020) The marked deviation from Fermi liquid behavior for the quasi-one-dimensional (1D) purple bronze Li1−xMo6O17 (Li0.9Mo6O17) has generated much theoretical interest and has been observed by both bulk transport and surface-sensitive spectroscopic probes. Here we present spectroscopic scanning tunneling microscope (STM) images of 1D chains of molybdenum oxide units on the surface of Li0.9Mo6O17. We ﬁnd that the Coulomb suppression of tunneling around the Fermi energy is inhomogenous on the nanometer length scale, corresponding to inhomogeneity in the topography. Furthermore, we report that chains on the surface exhibit quasi-particle resonances at varying energies in their local density of states. These resonances break the particle-hole symmetry of the Tomonaga-Luttinger liquid model. We discuss the implications of this phenomenon for modeling the surface structure of Li0.9Mo6O17 as a quasi-1D quantum system.

I. INTRODUCTION havior in Li0.9Mo6O17 includes its anisotropic resistance [5], Coulomb suppression of density of states around the 1 Although Fermi-liquid theory satisfactorily de- Fermi energy [13], and violation of the Wiedemann-Franz scribes electron behavior in typical conducting solids, law due to spin-charge separation [6]. Recent theoreti- quasi-one-dimensional (1D) materials exhibit unique cal work has helped to explain the robustness of quasi- properties that are currently best understood within the one-dimensional behavior in Li0.9Mo6O17 at low energy framework of Luttinger liquid theory. Luttinger liquid [10, 12]. Nevertheless, the transition of Li0.9Mo6O17 theory provides the best low-energy effective description from a 1D to 3D interacting system at TC ≈ 1.9K for a diverse array of physical models [1] and has notably remains poorly understood. Experiments have refuted contributed to the study of the fractional quantum hall a charge-density wave explanation [14], and some have effect [2] and to the description of the normal states of proposed that Li0.9Mo6O17’s observed superconductivity high-temperature superconductors [3]. As rare alterna- arises through an unconventional spin-triplet mechanism tives to the predictions of Fermi-liquid theory, the unique [15, 16]. properties of Luttinger liquids continue to warrant ex- 3 Here we report STM evidence that the disordered tensive theoretical and experimental study in the recent surface of Li0.9Mo6O17 at low temperature is not fully de- literature. [4–12]. In particular, scanning tunnelling mi- scribed by the bulk Luttinger-liquid model, despite hav- croscopy (STM) has proven to be a powerful technique ing spatially-averaged properties that are consistent with for studying Luttinger liquids’ departure from the Fermi- the 1D theory. In fact, our study of a disordered b-c crys- liquid model. Recent STM experiments have confirmed tal surface of Li0.9Mo6O17 shows three ways in which its several unique 1D behaviors in Luttinger liquids, includ- energetic spectrum is spatially disordered: the width of ing a lack of quasiparticle resonances and a power-law the Coulomb gap, the value of the Luttinger-liquid alpha suppression of density of states near the Fermi energy. parameter, and the energies and intensities at which res- 2 Previous spectroscopic work has characterized the onance peaks appear in the local density of states. We purple bronze Li0.9Mo6O17 as a model 1D system for observed these resonance peaks frequently in the local studying Luttinger theory, but its 1D to 3D transition density of states (LDOS) spectra at various points on the at low temperature is still poorly understood. Elec- Li0.9Mo6O17 surface. The resonances appear to exhibit trons in Li0.9Mo6O17 are thought to be largely confined lifetime broadening, consistent with a Fermi-liquid the- to zigzag chains of molybdenum oxide octahedra (Fig- ory. We also observed that the value of α and the consis- ure 1a), giving rise to the material’s 1D properties. Ex- tency of the Coulomb gap varied dramatically from point perimental evidence confirming this one-dimensional be- to point on the surface, even in the absence of resonances. Inhomogeneities on the surface of Li0.9Mo6O17 have been mentioned elsewhere [13], but previous literature has not yet produced a detailed experimental study, nor have any ∗ jhoff[email protected] quasiparticle-like resonances on the surface been previ- 2

(b) ously noted. In fact, earlier STM studies have focused (a) 2 nm on spectra averaged over a Li0.9Mo6O17 surface [11, 13]. The inhomogeneities in LDOS spectra on Li0.9Mo6O17 that we observe are signiﬁcant for understanding the 1D to 3D transition of Li0.9Mo6O17 at low temperature as b well as the response of Luttinger-liquids to impurities and c boundary conditions. low high (c) b II. SURFACE CHARACTERIZATION

c 4 Data was collected using a home-built STM at a temperatures of 4K or 6K. We cleaved single crystals -1 of Li0.9Mo6O17 in cryogenic ultra-high vacuum in situ 5 nm 0.5 nm and inserted them directly into the STM. Measurements low high were performed with a mechanically cut Pt-Ir tip, which (d) was cleaned by field emission and characterized on gold. Spectroscopy was conducted using a lock-in technique at 1.115 kHz. Topographic and spectroscopic properties of the 1D chains were verified using several tips. 5 We characterized our surface as the b-c crystal plane b of Li0.9Mo6O17 using topographic maps. The lattice parameters were measured by Fourier analysis of 30 topo- c graphic scans, as shown in Figure 1. We found Bragg peaks for b = 0.98 ± 0.17 nm and c = 0.58 ± 0.06 nm, agreeing with the neutron scattering measurements for a the lattice parameters of Li0.9Mo6O17 within our uncer- c tainty [17]. We observe that our surface showed vari- b Li Mo O ous reconstructions and that chains are clearly visible despite the presence of nanometer scale disorder. There are four possible crystal planes which we could have ex- FIG. 1. Surface identification. (a) 30 nm topograph showing posed: Mo1, Mo2-Mo4, Mo3-Mo5, and Mo6 [11]. Based chains of molybdenum oxide clusters in LPB at T = 4.8 K. on the presence of alternating light and dark chains in the (b) 7 nm topograph of a different surface showing the inter- topographic scans which indicate the presence of two in- atomic spacing in more detail. (c) Fourier transform of the 30 equivalent types of Mo atoms, we expect to have revealed nm topograph in Figure 1A, with circled peaks corresponding either the Mo2-Mo4 or Mo3-Mo5 planes. The general to the lattice vectors. (d) Crystal structure of the b-c plane of LPB showing a lattice plane parallel to that in topographs spectral features that we observe on a 10nm scale are (a) and (b). Crystal structure coordinates are from [17] and consistent with the results of former experimental liter- image was produced with VESTA [18]. Setpoint parameters: ature. We obtained spectra from points on the surface sample bias, Vsample = −400 mV (a and b); junction resis- using the proportionality of the differential conductance tance, RJ = 40 GΩ (a) and −20 GΩ (b). of tunneling to the local density of states ρs(−eV ):

2 q 8mφ spectrum with previously reported results for dI 4πe −s 2 ≈ − e ~ ρ (0)ρ (−eV ) (1) Li Mo O , the spatially resolved results show dV t s 0.9 6 17 ~ significant spectral inhomogeneity. Specifically, the 6 The spatially-averaged spectrum of our samples shape and width of the Coulomb gap varies substantially agrees with a previous report [19] and is shown in Figure across the surface. We identified edges of the Coulomb 2. Consistent with earlier results, our average spectra gap as minima in the second derivative corresponding show band features around ±200 mV, as predicted by to kinks in the local density of states spectrum below DFT calculations [4]. Our spatially-averaged spectrum and above the Fermi energy for individual points in our also appears to show a Coulomb suppression of tunneling data set. The distance from the Fermi energy to the around the Fermi energy, which we henceforth refer to as gap edge on the hole side was not strongly correlated a Coulomb gap. Double-log scale plots of the data were with the distance from the Fermi energy to the gap edge used to extract the value of the Luttinger liquid param- on the particle side. Spectra with the same values of eter α from the spatially-averaged spectrum. We found positive or negative gap edge tended to occur in chains α ≈ 0.44, in agreement with earlier results for averaged that resembled the chains of atoms in the topography. spectra on Li0.9Mo6O17 within uncertainty [13, 19]. 8 Variation in the Coulomb gap width on both the pos- 7 Despite the agreement of the spatially-averaged itive and negative side of the Fermi energy is one example 3

-1.2 (a)(a) 2 nm (b) diﬀerent α values at diﬀerent points on the surface. 0.8 -1.6 III. RESONANCES 0.4 -2.0 9 The most interesting inhomogeneities that we ob-

Log(Conductance) -2.4 α ≈ 0.44 served on the surface of are the frequent resonance peaks

Conductance (arb. units) (arb. Conductance 0.0 in the LDOS. These resonances manifest in conductance -200 0 200 -80 -20 -5 5 20 80 maps as shown in Figure 3c-h and correlate to chain-like Sample Bias (mV) Sample Bias (mV) features in the topography. These resonance peaks have (c) (d) not been observed before in Li0.9Mo6O17 but are quite common on the surfaces that we studied. In the topog- 1.0 raphy shown in Figure 3, more than 50% of the roughly 1.0 83, 000 point spectra exhibited clearly identiﬁable resonances in their LDOS. Resonances can occur on both the particle and hole sides of the spectrum, but appear on the particle side with greater frequency. A consider- 0.5 able proportion of resonant spectra contain more than 0.6 one resonance peak, some containing up to three distinct resonance peaks on the same side of the Fermi energy.

Log(Conductance) Spectra exhibiting resonances are generally particle-hole 0.0

Conductance (arb. units) (arb. Conductance asymmetric. Most of the resonances appear in the energy range −100 mV to 100 mV. 10 Most of the resonances appear in chain-like pat- 0.2 terns that correspond to the topographical features on -0.5 the Li0.9Mo6O17 surface. The conductance maps in Fig- ure 3 demonstrate this chain-like behavior in the local -20 -200 0 200 -80 -5 5 20 80 density of states at fixed energies across the surface. The Sample Bias (mV) Sample Bias (mV) features in these conductance maps presumably show chains of atoms resonating at different energies. In ad- FIG. 2. Spatial inhomogeneity of spectra. (a) Average spec- dition to these chain resonances, we sometimes observe trum over the region shown in inset. Inset: 30 nm topograph additional peaks corresponding to unique resonances at of the a-b crystal plane of Li0.9Mo6O17. The Coulomb gap is delimited by dashed lines. A power law fit (α = 0.44) is each location along the chain. Thus, a given unit cell shown in red. (b) Log-log plot of average spectrum in 2a. (c) of Li0.9Mo6O17 that is observed in the topography may Waterfall plot showing variance in the size and shape of the contain both a large resonance peak that is common to Coulomb gap along the yellow line shown in the inset to 2a. all of its neighbors and some smaller resonances that are (d) Log-log plot of graph in 2c showing variance in the size unique to itself. and shape of the Coulomb gap along the red line shown in 11 The fact that resonances appear close together in Figure 2a. Setpoint Parameters for spectra in 2b, 2c, and 2d linear patterns allows them to be grouped together as (S) and for topograph in 2a (T): sample bias, Vsample = −400 chains. A custom code was used to select points that mV (S) and 100 mV (T); junction resistance, R = 1.6 GΩ J resonated at the same energy and then group them into (S) and 10 GΩ (T); and root mean square (RMS) lock-in ex- features. Over 400 groups of resonances were identified citation, Vrms = 6 mV (S). Temperature: T = 6 K (S) and 4.8 K (T). in this way. The output is shown overlaid on the topography in Figure 4a. Although the chains tend to form clusters that resonate at similar energies, there are also a number of cases where two chains resonating at dif- of the various types of spectral inhomogeneity apparent ferent energies are close to one another. We restricted in the waterfall plot shown in Figure 2, along with varia- our search for chains to those with resonances between tion in the value of the Luttinger liquid-alpha parameter. −120 mV and 120 mV, because most of the resonances The shape of the Coulomb gap is not consistent among identified occurred within those boundaries. the spectra shown and does not display the particle-hole 12 Identifying chains also allowed us to obtain an ap- symmetry expected for the Luttinger liquid model near proximate value for the spatial lengths of the resonance the Fermi energy. The Luttinger-liquid alpha parameter features. Figure 4c shows the frequency at which chains also varies across the Li0.9Mo6O17 surface. Log-log plots of a certain length resonate at a particular energy. Al- of point spectra, which are expected to be linear near though there may be a slight average trend toward longer the Fermi energy for a Luttinger liquid, display highly chains resonating at lower energies, noise in the data ren- nonlinear behavior (Figure 2d). Attempting to fit these ders it impossible to draw a statistically significant con- lines with a power-law exponent results in a variety of clusion. Details about the algorithms used to find chains 4

1.0 (a) (d) (b) (g) High 0.8 (c) (f) (e) (h) 0.6

0.4

0.2 Low

Conductance (arb. units) (arb. Conductance Avg. Spectrum 5 nm -300 -200 -100 0 100 200 300 Sample Bias (mV) 0.44 (c) -80 mV (e) -16 mV 0.20 (c) -80 mV (d) -44 mV 0.32

0.24 0.30 0.14 5 nm 55 nm 5 nm

0.38 (f) 12 mV 0.18 (g) 44 mV 0.32 (h) 104 mV

0.24 0.28 0.13 5 nm 5 nm 5 nm

FIG. 3. Characterization of resonances. (a) Sample of resonances peaks at various energies, corresponding to points labelled by the colored diamonds in Figure 3b. The spectral average over the entire surface is also displayed (bolded black line). (b) Topograph showing points where the resonances from Figure 3a are observed. (c)-(h): Conductance maps showing chain-like resonances at various energies. Setpoint parameters for spectra in 3a and 3c-3h (S) and for topograph in 3b (T): Vsample = −400 mV (S) and 100 mV (T); RJ = 1.6 GΩ (S) and 10 GΩ (T); Vrms = 6 mV (S). Temperature: T = 6 K (S) and 4.8 K (T). and compute their length are contained in the Supple- IV. DISCUSSION mental Material. 13 Surprisingly, the resonances that we observe tend 14 The new properties that we report for the to become broader at energies farther away from the Li Mo O surface, in particular the presence of quasi- Fermi energy, in both the particle and the hole direc- 0.9 6 17 particle scattering at low energy, show that the tradi- tions. The spectral resonances ﬁt well to a Lorentzian tional Luttinger liquid model is not adequate for fully lineshape, given by explaining the electronic properties of a disordered low- temperature Li Mo O surface. Certain properties of A 1 Γ 0.9 6 17 L(x) = 2 , (2) Li0.9Mo6O17 that resemble Tomonaga-Luttinger behav- 2 1 2 π (x − x0) + 2 Γ) ior did not completely break down even in our study, as a feature resembling a charge gap was still observed at most where A is the resonance amplitude and Γ the full-width sites. Nevertheless, TL parameters such as the gap width at half-maximum (FWHM). Using this formula, we cal- and α parameter did very across the surface, most likely culated full-widths at half-maxima for resonance features due to the presence of impurities and surface disorder. at each energy, averaged over points within a chain group- As has been noted by DFT calculations, the properties of ing. Figure 4b shows the result. We observe a clear in- Li0.9Mo6O17 are very sensitive to lithium stoichiometry crease in the width of resonances as the resonance energy [8]. The sensitivity of Li0.9Mo6O17 to exact stoichiometry moves away from the Fermi energy, also known as life- may cause the spectral behavior of Li0.9Mo6O17 chains time broadening. Lifetime broadening is typically associ- to change in the presence of surface reconstructions such ated with three-dimensional phenomena and is particu- as those observed on our Li0.9Mo6O17 surface. Variation larly reminiscent of Fermi-liquid quasiparticle signatures in the bulk concentration of Li atoms may lead to ef- in LDOS spectra. fects similar to those observed on the material’s surface, 5

(a) 80

50 ± Standard Error ± Standard

5 nm 30 Full Width Half Maximum (mV) of Resonance Peak 75 50 25 0 25 50 75 100 -100 -50 0 50 100 Resonance Energy (mV) Chain Resonance Energy (mV)

0.9 4.0 (Number of Chains) (Number e

Chain Length (nm) Chain Length 0.6 Log 2.0 0.3

0.0 0.0 -120 -80 -40 0 40 80 120 Chain Resonance Energy (mV)

FIG. 4. Chain analysis. (a) Chains identiﬁed by software (see Supplemental Information) are shown superposed on the surface topograph. The color of the chains corresponds to the sample bias at the chain resonance peak. (b) The average FWHM (full width at half maximum) of Lorentzian ﬁts to chain resonance peaks is shown in blue, as a function of chain resonance energy. The red lines denote one standard error above and below the mean. (c) A logarithmic heat map shows the number of chains of given length and resonance energy. The average chain length at each resonance energy is shown by the scatter plot of blue squares.

but spatial inhomogeneity in the spectral properties of model to describe Li0.9Mo6O17 chains on a disordered Li0.9Mo6O17 on its surface may also be consistent with surface. Quasiparticle resonances may arise from scat- the Luttinger model in the bulk. tering of fermionic bound states off of impurities, as has been proposed for similar chain-like resonances observed 15 On the other hand, quasiparticle-like resonances in YBa2Cu3O6+x [20]. An alternate explanation for these in Li0.9Mo6O17 do not fit the conventional Luttinger liq- resonances in terms of a modified Luttinger theory would uid model. Traditional quasiparticle resonances indicate need to account for resonances on both the particle and the presence of fermionic bound states, whereas Lut- hole sides of the spectrum, as well as for the compara- tinger liquids are expected to exhibit bosonic collective tively large width of resonance peaks that we observe. By excitations. Additionally, the quasiparticle resonances providing a picture of the formation of quasiparticle-like that we observed break the particle-hole symmetry of resonances in 1D systems, this research may help to elu- the Tomonaga-Luttinger liquid model. This suggests the cidate the elusive mechanism behind the 1D to 3D tran- need for a revision to the Tomonaga-Luttinger liquid 6 sition of Li0.9Mo6O17 at low energies and provide further insight into the properties of this unique material.

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