Incommensurate Chiral CDW in $1T$-VSe$_2$

TL;DR

This study reveals the presence of incommensurate chiral charge-density waves in $1T$-VSe$_2$, characterized by lower rotational symmetry and a kagome lattice structure, confirmed through STM and optical measurements.

Contribution

The paper demonstrates the existence of chiral CDWs in $1T$-VSe$_2$ with unique symmetry properties and lattice arrangements, expanding understanding of chiral phenomena in layered materials.

Findings

CDW intensities differ along triple-q directions

CDW peaks form a kagome lattice

Chirality reflected in Friedel oscillations

Abstract

We have investigated the chiral charge-density wave (CDW) in $1T$-VSe$_2$ using scanning tunneling microscopy (STM) measurements and optical polarimetry measurements. With the STM mesurements, we revealed that the CDW intensities along each triple-$q$ directions are different. Thus the rotational symmetry of $1T$-VSe$_2$ is lower than that in typical two-dimentional triple-$q$ CDWs. We found that the CDW peaks form a kagome lattice rather than a triangular lattice. The Friedel oscillations have the chirality and the periodicity reflected properties of the background CDW. With the optical measurements in $1T$-VSe$_2$, we also observed a lower rotational symmetry with the polarization dependence of the transient reflectivity variation, which is consistent with the STM result on a microscopic scale. Both $1T$-TiSe$_2$ and $1T$-VSe$_2$ show chiral CDWs, which implies that such waves are usual for CDWs with the condition $H_\mathrm{CDW} \equiv q_{1}\cdot(q_{2} \times q_{3}) \neq0$.

Full text

Incommensurate Chiral CDW in 1T-VSe2

Y. Sugawara1

  

A. Nomura1

  

Y. Toda1

  

T. Kurosawa2

  

M. Oda2

  

T. Matsuura1

  

K. Ichimura1

  

S. Tanda1

1Department of Applied Physics, Hokkaido Univesity

2Department of Physics, Hokkaido University

I abstract

We have investigated the chiral charge-density wave (CDW) in 1T-VSe2 using scanning tunneling microscopy (STM) measurements and optical polarimetry measurements. With the STM mesurements, we revealed that the CDW intensities along each triple-$q$ directions are different. Thus the rotational symmetry of 1T-VSe2 is lower than that in typical two-dimentional triple-$q$ CDWs. We found that the CDW peaks form a kagome lattice rather than a triangular lattice. The Friedel oscillations have the chirality and the periodicity reflected properties of the background CDW. With the optical measurements in 1T-VSe2, we also observed a lower rotational symmetry with the polarization dependence of the transient reflectivity variation, which is consistent with the STM result on a microscopic scale. Both 1T-TiSe2 and 1T-VSe2 show chiral CDWs, which implies that such waves are usual for CDWs with the condition $H_{\mathrm{CDW}}\equiv q_{1}\cdot(q_{2}\times q_{3})\neq 0$.

II INTRODUCTION

The concept of chirality has recently been receiving a lot of attention in many fields, including chiral condensates and chiral density waves chiraldw in quantum chromodynamics, chiral spin texture texture and electrical magnetochiral anisotropy emcha1 ; emcha2 ; emcha3 in condensed matter physics, cholesteric liquid crystal and chiral helimagnetic order in application fields, and more. In relation to superconductors, chiral $p$-wave superconductivity pwave is also attracting attention. In particular, it is suggested that the pseudogap state in a high temperature superconductor is related to chiral order hightc1 ; hightc2 and this property must be understood if we are to clarify the high-$T\rm_{c}$ supercondutor mechanism. Thus chirality is related to many fields, from elementary particles to macroscopic phenomena.

In recent years, the chiral charge-density wave (CDW), which is a new class of two-dimensional triple-$q$ CDW, was discovered in 1T-TiSe2 ishi1 ; ishi2 . In transition metal dichalcogenides MX2 such as 1T-TaS2, which are well known as typical two-dimensional CDW materials MX2 , the intensities of CDW wave vectors $q_{1}$, $q_{2}$ and $q_{3}$ have the same magnitude. However in chiral CDWs, these values are different. Hence, the structure of the charge distribution has a clockwise or anticlockwise intensity anisotropy, so that the symmetry in a chiral CDW is less than in other MX2 CDWs. In other words, it is a system that is broken in terms of both inversion and rotational symmetry. This phenomenon has attracted a lot of attention as regards similarities between the high-$T\rm_{c}$ pseudogap state and charge-parity symmetry. A chiral CDW is believe to be a widespread phenomenon because it has also been observed in 2H-TaS2 2h , but its characteristics are as yet known. $H_{\mathrm{CDW}}$ is cited as the condition for CDW chirality and is defined as $H_{\mathrm{CDW}}\equiv q_{1}\cdot(q_{2}\times q_{3})$, where $q_{1}$, $q_{2}$ and $q_{3}$ are the CDW $q$ vectors or nesting vectors with $c^{*}$ components in triple-$q$ systems ishi1 . However, as yet there are no materials that fulfill the condition and can be confirmed to be a chiral CDW except for 1T-TiSe2. Therefore it is necessary to elucidate the condition of the chiral CDW.

We note that the new material 1T-VSe2 offers the potential for a chiral CDW. It is unique among MX2 CDW materials because an X-ray diffraction measurement xray confirmed that its CDW is commensurate in two-dimensional layers but incommensurate in the direction perpendicular to the layers. The CDW wave vector in the $c^{*}$ direction is 0.314$c^{*}$ above 85 K and 0.307$c^{*}$ below 85 K xray2 . These values are quite different from the commensurate value of 0.333$c^{*}$. This difference cannot be explained from the mechanism whereby most of the MX2 undergoes commensurate CDW in the interlayer direction by stacking to avoid the CDW peaks of each layer overlapping and thus benefit the Coulomb energy. Thus, with 1T-VSe2, CDWs may be commensurate both in the layer direction and the interlayer directions. The Fermi surface of 1T-VSe2 obtained by band calculations band and angle resolved photoemission spectroscopy arpes ; arpes2 suggests that its nesting vectors have $c^{*}$ components. So its CDW is three-dimensional although 1T-VSe2 is a two-dimensional layered material.

In this work, we investigated 1T-VSe2 as regards the chirality. We found the chirality in the 1T-VSe2 CDW by using scanning tunneling microscopy (STM) and optical polarimetry measurements. In the STM measurements, we found different intensity ratios for three CDW directions and the CDW peaks formed a kagome lattice. In optical polarimetry measurements, we found a lower two-fold symmetry in 1T-VSe2 than in a typical two-dimensional triple-$q$ CDW such as 1T-TaS2. By analyzing STM images, we found that Friedel oscillations on chiral CDWs reflect the chairality and periodicity of the underlying CDW.

III EXPERIMENTAL

The samples were grown by the chemical vapor transport method. The elements (vanadium rod and selenium flake) in evacuated silica tubes were heated at 750 for 5 days. We obtained single crystals of 1T-VSe2, which were platelets as large as 2  2  0.1 mm3.

In the STM measurements, the samples were cleaved in situ just before the STM tip approached the surface in an ultra high vacuum at 77 K and we obtained samples with clean surfaces. The STM images were obtained at 80 K and 8 K.

The pump-probe pulse method was employed with the sample surface using the micro-optics at 4 K. The pump and probe pulse polarization was varied to investigate the dominant direction of the deviation of the reflectivity $\Delta$R(t).

IV RESULTS AND DISCUSSION

Figure 1 shows an STM current image obtained at the $a$-$b$ plane of 1T-VSe2 at 80 K. The CDW transition temperature of 1T-VSe2 is 110 K vse3 , so this image shows the electronic property below the CDW transition temperature. The spots correspond to Se atoms and the brightness represents the magnitude of the local electron density. We can observe the periodic modulataion of the electron density over the entire image. It has a 4$a_{0}$  4$a_{0}$ periodicity indicated by the orange parallelogram in Fig. 1. This periodicity corresponds to the 4$a_{0}$ CDW superlattice, which is consistent with a report that employed X-ray diffraction measurementsxray2 . However, compared with a typical two-dimensional triple-$q$ CDW, such as 1T-TaS2, this CDW structure appears to be different because there is a difference in brightness that corresponds to the CDW intensity in each CDW direction.

To investigate that periodic structure, we analyzed a Fourier transformation (FT) image of the STM. Figure 2(a) shows an FT image of the entire field of Fig. 1. The bright spots surrounded by circles correspond to CDW vectors $q_{1}$, $q_{2}$ and $q_{3}$. The outer intensity peaks correspond to the Bragg peaks of the selenium lattice, and the inner peaks correspond to the CDW satellite peaks. Figure 2(b) shows line profiles of an FT image along the $q_{1}$, $q_{2}$ and $q_{3}$ wave vector. $I_{n}$ ($n$ = 1, 2, 3) represents the intensity of CDW satellite peaks along each wave vector. We found an obvious difference between the CDW intensities of CDW vectors $q_{1}$, $q_{2}$ and $q_{3}$; $I_{1}$ is the strongest and $I_{2}$ and $I_{3}$ are the second strongest and weakest, respectively. In typical two-dimensional CDWs $I_{1}$, $I_{2}$ and $I_{3}$ must be of equal value and the CDW structure is expected to have six-fold symmetry. However in 1T-VSe2 each $I_{n}$ is different, so the CDW of 1T-VSe2 has lower symmetry. We concluded that is a chiral CDW by analyzing an FT image and decided that the CDW structure is clockwise because the direction from $q_{1}$ to $q_{2}$ to $q_{3}$ in descending order of the magnitude of $I_{n}$ is clockwise in an FT image as reported elsewhere ishi2 .

Then we consider the CDW formation in real space from the result of an FT image. Figure 3 is an enlarged view of Fig. 1. The orange lines show the wave front of the strongest intensity CDW wave vector $q_{1}$ found in Fig. 2. The green and blue lines show the second strongest and weakest intensity CDW wave fronts of $q_{2}$ and $q_{3}$, respectively. We found that the CDW peaks form a kagome lattice rather than a triangular lattice. Previous papers on STM observations of 1T-VSe2 did not report on this matterstm ; stm2 ; stm3 . The kagome lattice, which has an intensity difference, has two-fold symmetry. This is unlike a conventional kagome lattice, which has three-fold symmetry and no mirror symmetry. As a result of the lower symmetry mentioned above, we conclude that the CDW on 1T-VSe2 is also a chiral CDW in real space.

Secondly, we measured the polarization dependence of the transient reflectivity of 1T-VSe2 by using the pump-probe method to investigate the macroscopic symmetry. With an optical measurement using a probe light whose penetration length is several tens of nanometers, we can measure the symmetry of more deeper samples than that with an STM. Figure 4 shows the polarization dependence of the transient reflectivity variation of 1T-VSe2 at 4 K. The heights of the peak intensities of each polarization angle in Fig. 4 (a) are plotted in Fig. 4 (b). The transient variation in optical reflectance $\Delta$R(t) was measured by changing the polarization angle $E\rm_{pol}$ of the incident probe laser pulse. In general, the peak intensity of transient signals corresponds to the number of electrons excited over the CDW gap pump1 ; pump2 . Figure 4 (b) shows that 1T-VSe2 exhibits two-fold symmetry despite the crystal structure being a triangular lattice. For this reason, this result reflects the CDW characteristics as two-fold symmetry. That is similar to the result with 1T-TiSe2 ishi1 and consistent with the result of the STM measurement on a microscopic scale. We also confirmed that the CDW in 1T-VSe2 is a chiral CDW with an optical polarimetry measurement.

Next, we analyzed the charge density modulation arround the charge impurities such as the lattice defects and add atoms observed in the STM measurements. Such modulations are called Friedel Oscillations (FOs). FOs are damped oscillations whose wave number is Fermi wave number $k\rm_{F}$, so an analysis of the FOs in CDW systems is important for the elucidation of CDW characteristics. Figures. 5 show the results analyzed the current images. The chirality of the underlying CDW is obtained by the process used in Fig. 2. Figure 5(a) is an STM image obtained in a clockwise CDW and Figure 5(b) shows an STM image obtained in a conuterclockwise CDW. We observe the dark FO around a bright spot whose charge density is rich has clockwise chirality in a clockwise CDW in Fig. 5(c), while the bright FO around a dark spot whose charge density is poor has counterclockwise chirality in the clockwise CDW in Fig. 5(d). Furthermore, we found that the bright FO around the dark spot has clockwise chirality in the counterclockwise CDW. That is, the chiralities of bright and dark FOs are the same and the opposite of the underlying CDW, respectively. We cannot observe any opposite chirality relationship between an underlying CDW and FOs in Fig 5(b). In the previous study of chiral CDWs in 1T-TiSe2, dark FOs around the bright spot also have the opposite chirality and bright FOs around the dark spot also have the same chirality as the underlying CDWishi2 . Thus the chirality of FOs in 1T-VSe2 is the same as those in 1T-TiSe2, but the periodicity of FOs in 1T-VSe2 is longer than those in 1T-TiSe2 because the CDW periodicities of 1T-VSe2 and 1T-TiSe2 are 4$a_{0}$ and 20, respectively. We found that the chirality of FOs reflects the underlying CDW chirality and periodicity.

Finally, we discuss the condition of the chiral CDW. Figure 6 shows the details of a CDW in the 1T-MSe2 group (M = Ta, Ti, V). These CDWs have the same characteristics as a CDW with commensurate in a layer but they are quite different in the $c$* direction. The CDW $c$* superlattice of 1T-TaSe2 is 3$c_{0}$, which originates from CDW stacking, and this structure does not relate to the direction of the nesting vectors. Most triple-$q$ CDW systems such as 1T-TaS2 have a similar structure to 1T-TaSe2. In 1T-TiSe2, the $c$* component is comensurate as with 1T-TaSe2, but it forms a 2$c_{0}$ superlattice originating from nesting vectors with a $c$/2 component. This 2$c_{0}$ superlattice stacks in the $c$ direction and forms a chiral CDW. Meanwhile, the 1T-VSe2 CDW is unique in triple-$q$ CDW systems as it is incommensurate along the $c$* direction because the $c$* component of its nesting vectors is an irrational number xray2 . We cannot consider 1T-VSe2 as composing the stacking unit, so the chiral CDW structure would appear directly below the transition temperature. In this respect, 1T-VSe2 is a more important chiral CDW material than 1T-TiSe2. A chiral CDW was discovered in both 1T-TiSe2 and 1T-VSe2 but there is little difference between them. Nevertheless, $H_{\mathrm{CDW}}\neq 0$ is probably a necessary condition of the chiral CDW.

V CONCLUSIONS

We discovered a chiral CDW in 1T-VSe2 by using STM measurements and optical polarimetry measurements and by analyzing of the FOs. We also discovered that the CDW peaks in 1T-VSe2 form a kagome lattice. 1T-VSe2 has a unique characteristic as an incommensurate CDW along the $c$* direction, which is different from other MX2 triple-$q$ CDWs, but it can be treated is the same way as 1T-TiSe2 in terms of $H_{\mathrm{CDW}}\equiv q_{1}\cdot(q_{2}\times q_{3})\neq 0$. These results strongly suggest that the chiral CDW is a general phenomenon that can occur in systems that fulfill the condition $H_{\mathrm{CDW}}\neq 0$.