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The transition metal dichalcogenide 1$T$-TiSe$_2$ is a quasi-two-dimensional layered material undergoing a commensurate 2 $times$ 2 $times$ 2 charge density wave (CDW) transition with a weak periodic lattice distortion (PLD) below $approx$ 200 K. Scanning tunneling microscopy (STM) combined with intentionally introduced interstitial Ti atoms allows to go beyond the usual spatial resolution of STM and to intimately probe the three-dimensional character of the PLD. Furthermore, the inversion-symmetric, achiral nature of the CDW in the $z$-direction is revealed, contradicting the claimed existence of helical CDW stacking and associated chiral order. This study paves the way to a simultaneous real-space probing of both charge and structural reconstructions in CDW compounds.
A charge density wave (CDW) of a nonzero ordering vector $mathbf{q}$ couple electronic states at $mathbf{k}$ and $mathbf{k}+mathbf{q}$ statically, giving rise to a reduced Brillouin zone (RBZ) due to the band folding effect. Its structure, in terms o
A semi-relativistic density-functional theory that includes spin-orbit couplings and Zeeman fields on equal footing with the electromagnetic potentials, is an appealing framework to develop a unified first-principles computational approach for non-co
In Ti-intercalated self-doped $1T$-TiSe$_2$ crystals, the charge density wave (CDW) superstructure induces two nonequivalent sites for Ti dopants. Recently, it has been shown that increasing Ti doping dramatically influences the CDW by breaking it in
The semimetallic or semiconducting nature of the transition metal dichalcogenide 1$T$-TiSe$_2$ remains under debate after many decades mainly due to the fluctuating nature of its 2 $times$ 2 $times$ 2 charge-density-wave (CDW) phase at room-temperatu
In this paper we shall prove a subconvexity bound for $GL(2) times GL(2)$ $L$-function in $t$-aspect by using a $GL(1)$ circle method.