Topological Landscape of Competing Charge Density Waves in $2H\text{−}{\mathrm{NbSe}}_2$

Despite decades of studies of the charge density wave (CDW) of $2H\text{−}{\mathrm{NbSe}}_2$, the origin of its incommensurate CDW ground state has not been understood. We discover that the CDW of $2H\text{−}{\mathrm{NbSe}}_2$ is composed of two different, energetically competing, structures. The lateral heterostructures of two CDWs are entangled as topological excitations, which give rise to a CDW phase shift and the incommensuration without a conventional domain wall. A partially melted network of topological excitations and their vertices explain an unusual landscape of domains. The unconventional topological role of competing phases disclosed here can be widely applied to various incommensuration or phase coexistence phenomena in materials.

Figure 1

(a) STM topography of the coexisting domains in $2H\text{−}{\mathrm{NbSe}}_2$ at a sample bias of 100 mV. The blue dashed line separates two different domains. (b) Line profile along the black arrow in (a). Green arrows indicate the locations of bright topographic protrusions. (c) STM topography of HC CDW domains at 100 mV. Black dashed circles indicate the region of AC CDW dislocations as magnified in Fig. 4. The colors and numbers indicate particular HC CDW domains among nine translationally degenerate domains. These domains have to be connected properly in the ideal domain network shown in the insets. Different domains are identified by their relative translation as defined in the right inset within one CDW unit cell. The black arrows represent the directions of CDW translations among HC CDW domains.

Figure 2

Atomic structure models, simulated and experimental STM topographic images at two different biases of $+100$ and $-100\mathrm{mV}$ of the HC (upper) and AC (lower) CCDW structures. The large gray (small green) balls represent Nb (Se) atoms in the structure model and the solid lines indicate short bonds for CDW distortions. The blue dashed lines indicate ($3\times 3$) CCDW unit cells.

Figure 3

(a) STM topography of a HC-AC-HC heterostructure in $2H\text{−}{\mathrm{NbSe}}_2$ at 100 mV. The blue dashed lines represent boundaries between HC and AC structures. The black dashed lines indicate ($3\times 3$) CDW unit cells showing a CDW translation between HC structures. (b) Schematic atomic and CDW configurations of the HC-AC-HC heterostructure. The blue and red lines indicate CDW distortions of Nb atoms in the HC and AC structures, respectively. The green dots represent Se atoms and black circles indicate the bright protrusions in STM. ${\mathbf{a}}_1$ and ${\mathbf{a}}_2$ are pristine lattice vectors to define the CDW translation, which is indicated for the HC structure at the bottom. (c) Simulated STM topography of the fully relaxed HC-AC-HC heterostructure at 100 mV. The white lines are drawn to indicate a CDW translation between HC structures.

Figure 4

(a) Atomistic schematics of an ideal honeycomb structure of the HC CDW domains and discommensurations which are composed of type I and II vertices. The black dashed circle denotes the region of AC CDW dislocation and the black arrows the directions of CDW translations among the HC CDW domains. (b) STM topography of type I (left) and II (right) vertices where three AC CDW stripe domains merge. Black dashed circle indicates the region of AC CDW dislocations. Black solid lines represent the dislocations among the AC structures.