Visualizing the charge density wave transition in $2H$-${\text{NbSe}}_2$ in real space

We report the direct observation in real space of the charge density wave (CDW) phase transition in pristine $2H$-${\text{NbSe}}_2$ using atomic-resolution scanning tunneling microscopy. We find that static CDW order is established in nanoscale regions in the vicinity of defects at temperatures that are several times the bulk transition temperature $T_{\mathrm{CDW}}$. On lowering the temperature, the correlation length of these patches increases steadily until CDW order is established in all of space, demonstrating the crucial role played by defects in the physics of the transition region. The nanoscale CDW order has an energy- and temperature-independent wavelength. Spectroscopic imaging measurements of the real-space phase of the CDW provide indirect evidence that an energy gap in ${\text{NbSe}}_2$ occurs at 0.7 eV below the Fermi energy in the CDW phase, suggesting that strong electron-lattice interactions, and not Fermi surface physics, are the dominant cause for CDW formation in ${\text{NbSe}}_2$.

Figure 1

(a) STM image ($V$ = −100 mV, $I$ = 20 pA) of the ${\text{NbSe}}_2$ surface above $T_{\mathrm{CDW}}$ = 33.7 K showing surface Se, crystalline, and a short-range atomic superstructure (CDW). (b)–(e) STM images at various temperatures and different locations below and above $T_{\mathrm{CDW}}$. The tunneling conditions were: at 22 K: $V$ = −44 mV, $I$ = 150 pA; at 57 K: $V$ = −200 mV, $I$ = 40 pA; at 82 K: $V$ = −90 mV, $I$ = 50 pA; at 96 K: $V$ = −230 mV, $I$ = 20 pA. (f) In-plane resistance and (g) temperature derivative of resistance of bulk samples plotted as a function of temperature. The temperatures at which the STM images are obtained are shown with color-coded arrows. On lowering the temperature below $T_{\mathrm{O}}$ ∼ 65 K, an additional contribution is seen in the resistivity (resulting in a decrease in $dR/dT$ from the constant value at higher temperatures).

Figure 2

(a) (Left) FT of a 15 nm STM image obtained at 22 K. The red peaks correspond to the atomic peaks, and the CDW wave vector is marked by a white arrow. The shaded area around the CDW peaks highlights the filter used to calculate the autocorrelations shown in Fig. 3. (Right) Subsets of FT images of large-area (>30 nm) STM maps at higher temperatures. The FT images are normalized to keep the atomic peak intensity constant. The tunneling conditions for each temperature were: at 22 K: $V$ = 25 mV, $I$ = 150 pA; at 38 K: $V$ = −100 mV, $I$ = 20 pA; at 72 K: $V$ = 160 mV, $I$ = 55 pA; at 96 K: $V$ = −230 mV, $I$ = 20 pA. (b) Line cuts of FT images along an atomic wave vector at different temperatures (curves offset for clarity) showing the drop-off in CDW peak intensity with increasing temperature.

Figure 3

(a)–(d) Autocorrelation functions and line cuts along the atomic directions from STM images at different temperatures (the same STM images were used for the analysis of Fig. 2). The images have been Fourier-filtered to remove the atomic peak. (e) A correlation length can be extracted from the falloff of the CDW intensity as a function of distance (dashed lines) at each temperature.

Figure 4

(a) $dI/dV$ maps taken at different energies (biases) at $T$ = 57 K over the same area of the ${\text{NbSe}}_2$ surface ($V$ = −1.4 V, $I$ = 700 pA). Short-range CDWs around the atomic defects are present as well as local effects of the defects themselves. (b) FT image of the $dI/dV$ map obtained at $V$ = 900 mV showing the atomic and CDW peaks but no other strong features at other wavelengths. (c) Line cut of FT images at different energies along the atomic peak direction. The CDW wave vector is seen to be independent of bias (energy).

Figure 5

(a) Fermi surface calculated with DFT. (b)–(e) Expected scattering pattern (JDOS) from the calculated DOS of ${\text{NbSe}}_2$ at different energies.

Figure 6

(a) Cross-correlation images between CDW band-pass filtered $dI/dV$ maps taken at different energies (biases) at $T$ = 57 K, and filtered $dI/dV$ map taken at $V$ = 1.4 V. The origin is indicated by a red dot. The CDW pattern changes from in phase (bright peak at the origin) to out of phase (origin is dark) between −0.65 and −1 V. The insets show the filtered $dI/dV$ data in the vicinity of one defect that also illustrates this effect. (b) Extracted phase of the CDW at different energies (biases) relative to the phase at 1.4 V. Error bars given by the resolution limit of the image in pixels/degree.

Figure 7

(a)–(d) Filtered topographic images showing CDW taken at different biases at $T$ = 57 K. An annular band-pass filter centered on the CDW peaks [shown in Fig. 2] has been used to suppress the atomic corrugation and enhance the CDW order. The CDW pattern (one of them shown enclosed in the black square) changes its phase between −1 V and −0.4 V in a consistent manner with the cross-correlation of the STS results presented in Fig. 6.

Figure 8

(a) Summary of the 1D tight-binding model results. The two different types of CDW lead to two different phase behaviors. A gap at ${\vec{K}}_{\mathrm{CDW}}$ for $E$ $\simeq$ −0.7 eV is to be expected from our experimental results. (b) Experimental average $dI/dV$ curves (in arbitrary units) for a CDW patch (blue) and for normal state (blue), taken at $T$ = 57 K. There are not obvious differences between these two spectra.

Figure 9

(a) Calculated DOS (Nb-like orbitals in red, Se-like orbitals in green) at different energies. At energies close to −0.6 eV, significant intensity is present at the CDW wave vectors (large nesting), whereas this is not true at other energies shown. (b) Calculated band structure projection onto Nb (red) and Se (green) orbitals along the CDW direction showing that conditions for a gap opening at the CDW Bragg point are in the vicinity of −0.6 eV (shaded blue area).