Conformality of Charge Density Wave

TL;DR

This paper introduces a conformal transformation framework to unify the understanding of 2D charge density wave phases in transition metal dichalcogenides, explaining experimental observations and revealing deep connections to quantum crystal physics.

Contribution

It proposes a novel conformal description of 2D CDW phases, explaining discommensurate structures through wavevector transformations and linking interference effects to conformality.

Findings

Discommensurate CDW phases explained by discrete conformal transformations.

Conformality arises from CDW-lattice commensurability and wave interference.

The theory accounts for various experimental CDW phases in MX$_2$ materials.

Abstract

New quantum phenomena are continuously being discovered in 2D systems. In particular, the charge density wave (CDW) has the aspect of a quantum crystal with a macroscopic wave function (order parameter), so unlike quantum liquids (superconductivity, quantum Hall liquids $^3$He, $^4$He), new ground states such as supersolid and Moir\'e solids can be expected. However, it is difficult to describe these states because of their quantum aspect, hence there is still no theory that can explain CDW phases in a unified way. The best way to describe a quantum crystal seems to be a conformal transformation that allows local deformation (wave properties) and preserves local angles (crystal properties). Here, we propose a unifying conformal description of 2D CDW phases in the typical 2D CDW material transition metal dichalcogenides (MX$_2$). We discover that the discommensurate CDW phases in MX$_2$ can be explained beautifully by a discrete conformal transformation of CDW wavevectors. This conformality is due to commensurability of CDW with the MX$_2$ lattice. In other words, interference of harmonic wavefunction induces conformality. Using this new conformal formulation, we explain experimental nearly-commensurate/stripe/T CDW phases in 1$T$-TaS$_2$ ($\sqrt{13}\times\sqrt{13}$ structure), 2$H$-TaSe$_2$ ($\sqrt{9}\times\sqrt{9}$ structure), and explain the origin of a new experimental nearly-commensurate phase in TaSe$_2$ thin-film ($\sqrt{7}\times\sqrt{7}$ structure). This theory is very simple in the sense that it includes only discommensuration and comprises physics as rich as quantum Hall liquids. This new description will broaden our perspective of quantum crystals.