Discovery of a strain-stabilised charge density wave in LiFeAs

Discovery of a strain-stabilised charge density wave in LiFeAs

Abstract

In many high temperature superconductors, small orthorhombic distortions of the lattice structure result in surprisingly large symmetry breaking of the electronic states and macroscopic properties, an effect often referred to as nematicity. This nematicity has been studied extensively on materials with an orthorhombic crystal structure, where the lattice symmetry is already reduced from four-fold () to two-fold (). In order to directly study the impact of symmetry breaking lattice distortions on the electronic states, we image at the atomic scale the influence of strain-tuned lattice distortions on the correlated electronic states in the iron-based superconductor LiFeAs, a material which in its ground state is tetragonal, with symmetry. Our experiments uncover a new strain-stabilised nematic phase which exhibits a unidirectional charge density wave (CDW) in LiFeAs, an electronic state which not only breaks rotational symmetry but also reduces translational symmetry through a characteristic long-range stripe-like modulation of the electronic density of states. We follow the evolution of the superconducting gap from the unstrained material with symmetry through the new nematic phase with symmetry and CDW order to a state where superconductivity is completely suppressed.

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The impact of the lattice anisotropy on the electronic properties of iron-based superconductors in the orthorhombic phase has been studied in great detail, revealing a strong anisotropy of electronic transport 1 and a significant nematic susceptibility even above the orthorhombic phase transition 2; 3; 4; 5.

Here, we use atomic scale imaging and spectroscopy using low temperature scanning tunnelling microscopy (STM) with in-situ strain tuning to directly image at the atomic scale the impact of uniaxial strain on the correlated electronic states of the iron-based superconductor LiFeAs. Combining strain tuning with STM is highly non-trivial due to the need to prepare atomically clean and flat surfaces in-situ for a sample mounted in a strain device. LiFeAs is ideally suited as it does not exhibit any evidence for nematic order and has a tetragonal crystal structure, hence uniaxial strain will directly affect the crystal lattice and hence the electronic states.

The superconductivity in iron pnictides is widely believed to be mediated by spin-fluctuation pairing of charge carriers between the hole pocket near the point and electron pockets near the zone corner6; 7. In this scenario, uniaxial strain (see Fig. 1a) is expected to impact on the near nesting (indicated by arrows in Fig. 1b), rendering the pairing strength anisotropic for strain along , with direct consequences for the order parameter 8. For strain along the direction, the consequences are expected to be less dramatic.

To achieve in-situ strain tuning, we have designed a sample holder which enables control of the expansion of a piezo stack to which the sample is mounted, through application of a voltage 9, see inset in Fig. 1c. We have studied the effect of uniaxial strain along both the and directions by mounting samples with different alignments in the device. Upon cooling the sample holder down, the strain in the sample is governed by the anisotropic thermal contraction of the piezo stack 10, while the voltage tuning enables a variable additional strain to be applied to the sample. Tunnelling spectra obtained in the same clean spot in the topography shown in Fig. 1c for a sample strained along at different levels of strain are shown in Fig. 1d. All the spectra are characterised by a clear superconducting gap with two pairs of coherence peaks, one near and another at . The size of the large gap is significantly smaller than the one observed for unstrained LiFeAs at the same temperature () 11; 12; 13; 14. Upon application of a voltage to the piezo stack, the field of view moves along the direction of the additional strain (see Supplementary Fig. 1) and a small but systematic change in the size of the superconducting gap, measured at the same defect-free position, is seen (Fig. 1e). As the strain voltage (and ) along increases, the size of the superconducting gap, extracted from the energies of the outer coherence peaks, is slightly suppressed. The data reveal a direct correlation between the size of the superconducting gap and the uniaxial strain applied to the sample, demonstrating that we achieve tunability of the superconductivity in LiFeAs.

Strain along the direction has a much larger impact on the spectra and on superconductivity: in Fig. 1f, we show how the tunnelling spectra vary with uniaxial strain along , from an unstrained sample (bottom curve) to a sample in which superconductivity is completely suppressed (top curve).

For intermediate levels of strain (corresponding to Curve V in Fig. 1f), we find that the material enters into a nematic phase which exhibits a long-range spatial modulation of the charge density. Figure 2a shows a topographic STM image of this phase revealing stripe-like patterns. The appearance of the charge modulation exhibits a phase shift between positive and negative bias voltages (Fig. 2a,b), a key signature for a CDW. For comparison, STM images of unstrained LiFeAs are shown in Fig. 2c, exhibiting no trace of this modulation, consistent with previous studies 11; 13; 12; 14. The stripes in the modulated phase run along the crystallographic direction of LiFeAs, parallel to the direction of the applied strain. They have a spatial periodicity of (Supplementary Note 2, Supplementary Fig. 2), corresponding to a wave vector of , independent of the applied strain. A closer inspection reveals that the stripes exhibit topological defects (Supplementary Fig. 3).

To assess whether the modulation of the charge density is associated with a characteristic energy scale, and its influence on superconductivity, we have acquired a spectroscopic map to study the electronic states across the modulation. Figs. 2d,e show the topography and a differential conductance map map. The map exhibits a strong modulation of the height of the superconducting coherence peaks, which can be more clearly seen from spectra taken on top of the charge modulation and between the maxima in Fig. 2f. Most notably, the spectra show an additional feature at which is modulated with opposite phase compared to the coherence peaks. In addition, a weak feature can be seen at . To extract the characteristic energy scale of the charge modulation, we analyse the amplitude of the modulation in the ratio of the differential to the total conductivity , a quantity which is free from the influence of the tip-sample distance on the overall spectra and can be taken as a representative for the density of states 15; 16. In Fig. 2g we show the variance of the stripe modulation in as a function of bias voltage, as well as its wave vector. The variance exhibits a clear maximum at and , at slightly smaller energies than the maxima in seen in fig. 2f. The wave vector stays practically constant within the energy range investigated here, confirming that it stems from a static charge modulation rather than quasi-particle interference, which would lead to a dispersion of the modulation. From the contrast inversion seen in topographic images and the characteristic energy scale of the modulation we observe in the differential conductance (or ), we attribute the modulated phase to the formation of a CDW, with formation of a partial gap between and .

In this CDW phase, the shape of the superconducting gap differs significantly from the one found in unstrained LiFeAs, as can be seen from the spectra in Fig. 2f. Spectra taken in the CDW phase are characterised by a pair of superconducting coherence peaks at . The gap size is substantially reduced compared to unstrained LiFeAs12.

In order to assess how the modulation of the charge density affects the superconducting state we have studied the vortex lattice and vortex core bound states in this phase. Figure 3a,b show the topography and map of the zero-bias conductance of strained LiFeAs in a magnetic field. The topographic appearance of the modulation (Fig. 3a) is unaffected by the magnetic field, whereas the vortex cores appear distorted by the stripe modulation, and their whole appearance becomes modulated and elongated in the direction perpendicular to the stripes. For comparison, we show the vortex lattice of unstrained LiFeAs in Fig. 3c. Most intriguingly, the charge modulation changes the vortex core bound state: while in unstrained LiFeAs, the vortex cores exhibit a bound state peak centred at 13, in the modulated phase the cores exhibit a bound state peak at (Fig. 3d). The particle-hole asymmetry of the vortex core bound states has been ascribed previously to vortices being close to the quantum limit, where the coherence length is of the order of the Fermi length, 17; 18; 13; 19. The change of the dominant bound state energy from the occupied states in unstrained LiFeAs to the unoccupied states in the strained sample indicates that either the superconducting gap on the small hole pocket at the -point (labelled in Fig. 1b) is strongly suppressed, or that the pocket is reconstructed by the modulated phase. This is also consistent with the reduced size of the superconducting gap, as the largest gap has been reported for the -band at the point for unstrained LiFeAs20.

Temperature dependent measurements show that the superconducting transition temperature is suppressed to about in the modulated phase (see Fig. 4a), consistent with the reduced size of the superconducting gap. The modulated phase persists into the normal state (Supplementary Fig. 4), demonstrating that it emerges from the normal state and superconductivity forms on top of it.

The picture which emerges from our measurements is summarised in the phase diagram in Fig. 4b. Starting from the unstrained material, superconductivity is initially suppressed slightly with increasing strain. At intermediate strain, the material enters into the CDW phase. Images of coexistence between areas showing the modulated phase and areas with no modulation suggest that this is a first order phase transition. At the transition to the modulated phase, the size of the superconducting gap is reduced rather abruptly, with spectra of areas of the sample which are in the modulated phase showing a significantly smaller gap than areas which have not undergone the transition. The modulated phase itself is hardly influenced by additional strain, and retains the same periodicity. The intensity with which we observe the modulation is reduced with increasing strain until it is completely suppressed (Supplementary Fig. 6). Superconductivity is suppressed (at the temperature of our measurements) at the same level of strain where the modulation of the charge density disappears. At higher levels of strain we see no trace of the stripe-like modulation or of superconductivity.

Several mechanisms could lead to the formation of a unidirectional modulation of the density of states. The magnetic order observed in several iron pnictides 21, as well as the spin fluctuations, are unlikely candidates as they occur at a completely different wave vector at (or near) . A peculiarity in the spin excitations in LiFeAs is that the wave vector of the spin resonance mode is incommensurate, with an incommensurability of 22, resulting in a splitting in the maxima by about the same wave vector as the modulation reported here. This indicates an instability in the susceptibility towards the modulated order we see here.

Nematic orders in iron pnictides normally break the rotational symmetry but not translational symmetry: they do not by themselves lead to an additional periodicity 23; 24; 25; 26, but rather a strong anisotropy of the electronic structure. However, nesting in a nematic phase might lead to a modulation of the charge density and hence a nematic electronic state as observed here. Formation of such a CDW could be additionally stabilised by a lattice instability due to a softening of a phonon mode. Calculations suggest that the phonon dispersion does exhibit a minimum at the zone face 27.

Our results report the discovery of a strain-induced transition into a charge density wave phase for a material which in its ground states does not show any evidence for nematicity, charge order or magnetic order. They provide surprising new evidence for the importance of the coupling between the strongly correlated electronic states and lattice degrees of freedom. We introduce strain STM as a new tool to stabilise and visualise novel superconducting phases and the interplay between electronic correlation effects and lattice distortions at the atomic scale.

Materials and Methods

STM measurements

The STM experiments were performed using two home-built low temperature STMs which operate at a base temperature of 28; 9. Pt-Ir tips were used, and conditioned by field emission with a Au sample. Differential conductance (dI/dV) maps and single point spectra were obtained using a standard lock-in technique, with frequency of the bias modulation set at 409.2 Hz. To obtain fresh and clean surfaces for STM measurements, 0.5% Zn- (Co-) doped LiFeAs samples were cleaved in-situ at in cryogenic vacuum. The results reported here have been obtained from a total of 20 cleaves for unstrained LiFeAs and 11 cleaves of four different samples for strained LiFeAs with sample thickness ranging from to .

Piezoelectric device

Motivated by previous nematic susceptibility measurements by Chu et al. 3, we have constructed a sample holder which allows for the application of in-situ tunable strain to single crystal samples. As shown in Fig. 1c in the main text, the sample holder comprises a brass main body, and a piezoelectric actuator which is mounted side-ways atop the main body. By applying a positive (negative) voltage across the leads of the piezoelectric actuator, it expands (contracts) along the longitudinal direction and contracts (expands) along the transverse direction. Samples were glued onto the side-wall of the piezoelectric stack facing towards the STM tip using Epotek H20E conductive epoxy. The orientation of the crystal relative to the piezoelectric stack determines the direction in which the strain is applied. Samples were cleaved by glueing a rod on top of the sample, which was knocked off at an in-situ cleaving stage 28. To extend the range of strain achieved at the surface of the material, we have studied multiple cleaves of the same sample, as the strain detected at the surface depends on the sample thickness. For the sample strained along , the main direction of the strain was within of the direction, for the the alignment was better than . Anisotropic thermal contraction/expansion of the piezo stack leads to a strain at the interface between stack and the LiFeAs sample of about , which provides an upper boundary for the levels of strain achieved here. Strain levels achieved by voltage tuning were up to at the interface.

Sample growth

LiFeAs samples were grown using a self-flux technique 12. Samples studied here contained minute amounts of engineered defects such as Zn and Co (on the order of ), which do not affect the spectra of clean areas of the surface or the occurrence of the modulated phase 29.

Acknowledgements: CT, CMY and PW acknowledge funding from EPSRC through EP/L505079/1 and EP/I031014/1. Research at UBC was supported by the Natural Science and Engineering Research Council of Canada, the Canadian Institute for Advanced Research, and the Stewart Blusson Quantum Matter Institute. We acknowledge valuable discussions with Cliff Hicks, Andreas Kreisel, Andreas Rost, Steve Simon and Matt Watson. Underpinning data will be made available at DOI:10.17630/c47ff360-09d4-4620-9ebf-bbb8792fb808
Correspondence: Correspondence and requests for materials should be addressed to P.W. (email: wahl@st-andrews.ac.uk).

Figure 1: Tuning superconductivity in LiFeAs by uniaxial strain. a, Ball model of the unit cell of LiFeAs under positive uniaxial strain along the direction. Dashed open circles represent the atomic positions in the unstrained unit cell, red and blue arrows indicate strain direction along and . b, Fermi surface of unstrained LiFeAs. Arrows indicate nesting vectors between hole bands at the zone centre and electron bands at the zone corner. c, Topographic image of LiFeAs strained along . (setpoint conditions , , ). A blue arrow indicates the strain direction. Inset, sample holder for in-situ strain tuning (without sample). An arrow indicates the direction of strain. d, dI/dV spectra obtained at the position marked with a cross in c with strain along at different voltages applied to the piezo stack, showing the superconducting gap (, , , spectra are normalised at ). Red dashed vertical lines indicate the positions of the coherence peaks for the spectrum obtained at , black dashed vertical lines for unstrained LiFeAs. e, Plot of gap size versus extracted from d (for details see Supplementary Note 1). The number near each data point indicates the order in which the spectra were taken. For unstrained LiFeAs, at , outside the range of the graph. f, dI/dV spectra on samples strained along . Spectra from bottom to top are shown in order of increasing strain. The bottom curve is for an unstrained crystal. All spectra are normalised at and vertically offset for clarity. Vertical lines indicate the energy of the coherence peaks for the unstrained crystal. Horizontal lines in d,f indicate zero conductance for each of the spectra.
Figure 2: Modulated phase of LiFeAs strained along . a-b, Topographic image taken from the same position on the modulated phase at of (a) and (b) respectively [, ]. A red arrow indicates the direction of the strain along . Crosses mark the positions of the same point defect. Dash lines highlight the phase shift of the stripe-like modulation between two images. c, Topographic image of unstrained LiFeAs (, , ). Inset, Atomically resolved image of unstrained LiFeAs (, , ). d, Topography of the modulated phase (, , ). e, Differential conductance as a function of position and bias voltage across the stripes, along the solid line in d. f, Averaged dI/dV spectra recorded from the positions on- (solid) and off- (dashed) the stripes (averaged over areas indicated in d). Arrows mark the bias positions of the peaks where the contrast of the charge modulation is strongest. A spectrum obtained on unstrained LiFeAs (dashed grey line, , , ) is included for comparison. The spectra were normalized at . Spectroscopy setpoints: (e) , , (f) , for the solid and dashed black spectra. Unless stated otherwise, all data in a-b, d-f have been recorded at . g, (Top panel) Spatial variance of the calculated normalized conductance as a function of bias voltage, extracted from e. Dashed vertical lines mark the positions of the charge modulation peaks. (Bottom panel) Wave-vector of the spatial modulation of as a function of bias voltage, extracted from e. A red line shows the average wave vector of . In the grey shaded region, inside the superconducting gap, becomes unreliable because the current becomes very small.
Figure 3: Vortices in the modulated phase. a, Topographic image of the modulated phase taken in the presence of 9 T out-of-plane field at (, ). A red arrow indicates the direction of the strain. b, Corresponding dI/dV map recorded at zero bias. Vortices are seen as areas of high zero bias conductance (red). c, dI/dV map taken at bias voltage of on an unstrained sample in the presence of an out-of-plane field of at . d, Averaged dI/dV spectra extracted from the centres of the vortices formed on the modulated phase (black) and those on the surface of an unstrained LiFeAs crystal (mid-blue), respectively. An averaged spectrum taken from a defect-free region on unstrained LiFeAs at , (light-blue) is included for reference. Spectra are vertically offset for clarity. Dashed horizontal lines indicate the positions of zero conductance for each spectrum. For b-c, , .
Figure 4: Phase diagram of LiFeAs as a function of uniaxial strain. a, dI/dV spectra acquired on LiFeAs in the modulated phase at different temperatures (all spectra normalised at , Dashed horizontal lines are zero conductance for each spectrum, , ). b, Phase diagram of LiFeAs as a function of uniaxial strain along , with the superconducting gap size (squares) and the characteristic energy of the CDW (triangles) as a function of strain. STM images showing coexistence between SC1 and CM/SC2 (see inset) indicate a first order phase transition to the modulated phase. Roman numerals and colours of squares and triangles refer to spectra in Fig. 1f. Round points corresponding to spectra in a are positioned at , using determined from the temperature dependence in a. Inset: topographic image of an area showing coexistence of SC1 and SC2/CM phases. Scale bar: .

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Footnotes

  1. thanks: These authors contributed equally.
  2. thanks: These authors contributed equally.

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