Many-body ground state localization and coexistence of localized and extended states in an interacting quasiperiodic system

We study the localization problem of one-dimensional interacting spinless fermions in an incommensurate optical lattice, which changes from an extended phase to a nonergoic many-body localized phase by increasing the strength of the incommensurate potential. We identify that there exists an intermediate regime before the system enters the many-body localized phase, in which both the localized and extended many-body states coexist, thus the system is divided into three different phases, which can be characterized by normalized participation ratios of the many-body eigenstates and distributions of natural orbitals of the corresponding one-particle density matrix. This is very different from its noninterating limit, in which all eigenstaes undergo a delocaliztion-localization transtion when the strength of the incommensurate potential exceeds a critical value.Comment: 5 pages, 6 figure

Raman fingerprint of semi-metal WTe2 from bulk to monolayer

Tungsten ditelluride (WTe2), a layered transition-metal dichalcogenide (TMD), has recently demonstrated an extremely large magnetoresistance effect, which is unique among TMDs. This fascinating feature seems to be correlated with its special electronic structure. Here, we report the observation of 6 Raman peaks corresponding to the A_2^4, A_1^9, A_1^8, A_1^6, A_1^5 and A_1^2 phonons, from the 33 Raman-active modes predicted for WTe2. This provides direct evidence to distinguish the space group of WTe2 from that of other TMDs. Moreover, the Raman evolution of WTe2 from bulk to monolayer is clearly revealed. It is interesting to find that the A_2^4 mode, centered at ~109.8 cm-1, is forbidden in a monolayer, which may be attributable to the transition of the point group from C2v (bulk) to C2h (monolayer). Our work characterizes all observed Raman peaks in the bulk and few-layer samples and provides a route to study the physical properties of two-dimensional WTe2.Comment: 19 pages, 4 figures and 2 table