Insight into the Charge Density Wave Gap from Contrast Inversion in Topographic STM Images

Charge density waves (CDWs) are understood in great detail in one dimension, but they remain largely enigmatic in two-dimensional systems. In particular, numerous aspects of the associated energy gap and the formation mechanism are not fully understood. Two long-standing riddles are the amplitude and position of the CDW gap with respect to the Fermi level ($E_F$) and the frequent absence of CDW contrast inversion (CI) between opposite bias scanning tunneling microscopy (STM) images. Here, we find compelling evidence that these two issues are intimately related. Combining density functional theory and STM to analyze the CDW pattern and modulation amplitude in $1T\text{−}{\mathrm{TiSe}}_2$, we find that CI takes place at an unexpected negative sample bias because the CDW gap opens away from $E_F$, deep inside the valence band. This bias becomes increasingly negative as the CDW gap shifts to higher binding energy with electron doping. This study shows the importance of CI in STM images to identify periodic modulations with a CDW and to gain valuable insight into the CDW gap, whose measurement is notoriously controversial.

Figure 1

Charge order contrast inversion revealed by STM on $1T\text{−}{\mathrm{TiSe}}_2$. Top row: $1.4\times 1.2{\mathrm{nm}}^2$ bias dependent STM micrographs of the same area showing contrast inversion below the Fermi energy between the two images recorded at $V_b=-300\mathrm{mV}$ and $V_b=-100\mathrm{mV}$. Set parameters of STM data are, from left to right, $V_b=-300\mathrm{mV}$ and $I_t=600\mathrm{pA}$, $V_b=-100\mathrm{mV}$ and $I_t=100\mathrm{pA}$, $V_b=100\mathrm{mV}$ and $I_t=200\mathrm{pA}$. The $Z$ range of the STM data from left to right is 4.3, 37.2, and 36.1 pm. Middle and bottom rows show the DFT simulations of the expected STM topographic contrast as a function of bias in electron doped and in pristine $1T\text{−}{\mathrm{TiSe}}_2$, respectively.

Figure 2

Doping dependence of the CDW contrast inversion. $10\times 10{\mathrm{nm}}^2$ STM topography of $1T\text{−}{\mathrm{TiSe}}_2$ at (a) $-300\mathrm{mV}$, (b) $-250\mathrm{mV}$, (c) $-200\mathrm{mV}$, (d) $-150\mathrm{mV}$, (e) $-100\mathrm{mV}$, and (f) $+100\mathrm{mV}$ sample bias. CI happens at an increasingly higher binding energy near defects $A$ to $D$, indicating their different doping nature (see text and Fig. S3 in Supplemental Material, Sec IV [16]). Set currents are (a) 600 pA; (b) 300 pA; (c),(d),(f) 200 pA; (e) 100 pA.

Figure 3

Charge order origin of the contrast inversion observed in bias dependent STM images of $1T\text{−}{\mathrm{TiSe}}_2$. (a) Negative sample bias image at $-250\mathrm{mV}$ showing the real space distribution of charge accumulation (set current is 300 pA, $z$ $\mathrm{range}=33\mathrm{pm}$). (b) Negative sample bias image at $-100\mathrm{mV}$ showing the real space distribution of charge depletion (set current is 100 pA, $z$ $\mathrm{range}=66\mathrm{pm}$). (c) Contrast inversion applied only to the CDW component of the image in (b). (d) Contrast inversion applied to all components of the image in (b). Image size is $6\times 6{\mathrm{nm}}^2$.

Figure 4

One-dimensional model description of the CDW contribution to the STM topography. (a) Spatial and energy dependent CDW local DOS with the CDW gap centered at $E_F$. (b) Corresponding topography traces with inverted contrast between opposite polarity traces, and (c) their bias dependent phases: contrast inversion happens at $E_F$. (d) Spatial and energy dependent CDW local DOS with the CDW gap shifted below $E_F$. (e) Corresponding topography traces at selected bias voltages and (f) their bias dependent phases: contrast inversion happens below $E_F$. The solid black line in panel (c) and (f) illustrate the BCS-like model DOS used in the modeling.