The coupling between spin, charge, and lattice degrees of freedom plays an important role in a wide range of fundamental phenomena. Monolayer semiconducting transitional metal dichalcogenides have emerged as an outstanding platform for studying these coupling effects because they possess unique spin-valley locking physics for hosting rich excitonic species and the reduced screening for strong Coulomb interactions. Here, we report the observation of multiple valley phononsphonons with momentum vectors pointing to the corners of the hexagonal Brillouin zoneand the resulting exciton complexes in the monolayer semiconductor WSe2. From Landé g-factor and polarization analyses of photoluminescence peaks, we find that these valley phonons lead to efficient intervalley scattering of quasi particles in both exciton formation and relaxation. This leads to a series of photoluminescence peaks as valley phonon replicas of dark trions. Using identified valley phonons, we also uncovered an intervalley exciton near charge neutrality, and extract its short-range electron-hole exchange interaction to be about 10 meV. Our work not only identifies a number of previously unknown 2D excitonic species, but also shows that monolayer WSe2 is a prime candidate for studying interactions between spin, pseudospin, and zone-edge phonons.

We show that, for an exactly solvable quantum spin model, a discontinuity in the first derivative of the ground state concurrence appears in the absence of quantum phase transition. It is opposed to the popular belief that the non-analyticity property of entanglement (ground state concurrence) can be used to determine quantum phase transitions. We further point out that the analyticity property of the ground state concurrence in general can be more intricate than that of the ground state energy. Thus there is no one-to-one correspondence between quantum phase transitions and the non-analyticity property of the concurrence. Moreover, we show that the von Neumann entropy, as another measure of entanglement, can not reveal quantum phase transition in the present model. Therefore, in order to link with quantum phase transitions, some other measures of entanglement are needed. Quantum entanglement, as one of the most fascinating feature of quantum theory, has attracted much attention over the past decade, mostly because its nonlocal connotation [1] is regarded as a valuable resource in quantum communication and information processing [2]. Recently a great deal of effort has been devoted to the understanding of the connection between quantum entanglement and quantum phase transitions (QPTs) [3,4,5,6,7,8,9,10,11,12,13,14,15]. Quantum phase transitions [16] are transitions between qualitatively distinct phases of quantum many-body systems, driven by quantum fluctuations. In view of the connection between entanglement and quantum correlations [17], one anticipates that entanglement will furnish a dramatic signature of the quantum critical point. People hope that, by employing quantum entanglement, the global picture of the quantum many-body systems could be diagnosed, and one may obtain fresh insight into the quantum many-body problem. Hence, in addition to its intrinsic relevance with quantum information applications, entanglement may also play an interesting role in the context of statistical mechanics.The aforementioned studies are based on the analysis of particular many-body models. Recently a theorem of the relation between QPTs and bipartite entanglement is proposed [18]. The authors conclude that, under certain conditions, a discontinuity in or a divergence of the ground state concurrence [the first derivative of the ground state concurrence] is both necessary and sufficient to signal a first-order QPT (1QPT) [second-order QPT (2QPT)]. Most of the previous investigations for specific models support their conclusion. This may strengthen the belief that one can determine QPTs by using quantum entanglement.In this paper, the entanglement properties (the ground state concurrence and the von Neumann entropy) are calculated for an exactly solvable quantum spin model [19]. Contrary to conventional wisdom, we find that there exists a discontinuity in the first derivative of the concurrence, at which there is no quantum critical point. In fact, similar result had already been discovered in Ref. [7] for a quantum spin mode...

The fidelity approach to the Gaussian transitions in spin-one XXZ spin chains with three different values of Ising-like anisotropy lambda is analyzed by means of the density matrix renormalization group (DMRG) technique for systems of large sizes. We find that, despite the success in the cases of lambda=2.59 and 1, the fidelity susceptibility fails to detect the Gaussian transition for lambda=0.5. Thus our results demonstrate the limitation of the fidelity susceptibility in characterizing quantum phase transitions, which was proposed recently in general frameworks.Comment: 9 pages, 9 figure

Recently, the celebrated Rytova-Keldysh potential has been widely used to describe the Coulomb interaction of few-body complexes in monolayer transition-metal dichalcogenides. Using this potential to model charged excitons (trions), one finds a strong dependence of the binding energy on whether the monolayer is suspended in air, supported on SiO2, or encapsulated in hexagonal boronnitride. However, empirical values of the trion binding energies show weak dependence on the monolayer configuration. This deficiency indicates that the description of the Coulomb potential is still lacking in this important class of materials. We address this problem and derive a new potential form, which takes into account the three atomic sheets that compose a monolayer of transition-metal dichalcogenides. The new potential self-consistently supports (i) the non-hydrogenic Rydberg series of neutral excitons, and (ii) the weak dependence of the trion binding energy on the environment. Furthermore, we identify an important trion-lattice coupling due to the phonon cloud in the vicinity of charged complexes. Neutral excitons in their ground state, on the other hand, have weaker coupling to the lattice due to the confluence of their charge neutrality and small Bohr radius.

A generalized Středa formula is derived for the spin transport in spin-orbit coupled systems. As compared with the original Středa formula for charge transport, there is an extra contribution of the spin Hall conductance whenever the spin is not conserved. For recently studied systems with quantum spin Hall effect in which the z-component spin is conserved, this extra contribution vanishes and the quantized value of spin Hall conductivity can be reproduced in the present approach. However, as spin is not conserved in general, this extra contribution can not be neglected, and the quantization is not exact.PACS numbers: 72.25. Hg, 72.25.Mk, Intrinsic spin Hall effect (SHE) offers new possibility of designing semiconductor spintronic devices that do not require ferromagnetic elements or external magnetic fields. This effect has been theoretically predicted both in p-doped semiconductors with Luttinger type of spin-orbit (SO) coupling and in n-doped semiconductors with Rashba type of SO coupling.1,2,3 In the hole doped case, 1,2 the transverse spin current is generated by the Berry curvature correction to the group velocity of a Bloch wave packet, 4,5 which is similar to the case of the charge current in quantum Hall effect.6 Later it is pointed out that the intrinsic SHE can even exist in band insulators with SO coupling, which are called spin Hall insulators.7 These spin Hall insulators would allow spin currents to be generated without dissipation. This dissipationless character of the intrinsic SHE again finds analogy in the quantum Hall effect.Pioneered by the work of Kane and Mele, 8 several specific single-particle Hamiltonians (graphene 8,9,10 and semiconductors 11,12,13 ) giving rise to the quantum SHE (QSHE) have been proposed, in which the intrinsic spin Hall conductance can be quantized in units of e/2π. These models can be considered as multiple copies of the charge Hall effect with different values of the spin, arranged so that the time-reversal symmetry is unbroken and the spin current is nonzero in the presence of an applied electric field. The investigations on its stability with respect to interactions and disorders have just begun. 10,14,15Because there exists similarities between SHE and quantum Hall effect, one may wonder if some concepts used in quantum Hall effect can be generalized to SHE. It is well known that (integer) quantum Hall effect can be analyzed by the Středa formula.16 Středa showed that, if the Fermi level falls within the energy gap, the Hall conductance can be given by the charge-density response to a magnetic field (from orbital, rather than Zeeman coupling). This formula has been used to calculate the conductance of an electron gas in the presence of an additional periodic potential.17 It has also been generalized to three dimensional systems.18 Since the Středa formula is useful in quantum Hall effect, one may expect that similar formula for spin transport may be of some help in the study of SHE. Thus it is worthwhile to explore such a generalization. 19In the present work, w...