Bounds for eigenvalue ratios of the Laplacian

For a bounded domain $\Omega$ with a piecewise smooth boundary in an $n$-dimensional Euclidean space $\mathbf{R}^{n}$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. First we give a general inequality for eigenvalues of the Laplacian. As an application, we study lower order eigenvalues of the Laplacian and derive the ratios of lower order eigenvalues of the Laplacian.Comment: 14 page

Local Density of States and Angle-Resolved Photoemission Spectral Function of an Inhomogeneous D-wave Superconductor

Nanoscale inhomogeneity seems to be a central feature of the d-wave superconductivity in the cuprates. Such a feature can strongly affect the local density of states (LDOS) and the spectral weight functions. Within the Bogoliubov-de Gennes formalism we examine various inhomogeneous configurations of the superconducting order parameter to see which ones better agree with the experimental data. Nanoscale large amplitude oscillations in the order parameter seem to fit the LDOS data for the underdoped cuprates. The one-particle spectral function for a general inhomogeneous configuration exhibits a coherent peak in the nodal direction. In contrast, the spectral function in the antinodal region is easily rendered incoherent by the inhomogeneity. This throws new light on the dichotomy between the nodal and antinodal quasiparticles in the underdoped cuprates.Comment: 5 pages, 9 pictures. Phys. Rev. B (in press

Mobility enhancement and highly efficient gating of monolayer MoS2 transistors with Polymer Electrolyte

We report electrical characterization of monolayer molybdenum disulfide (MoS2) devices using a thin layer of polymer electrolyte consisting of poly(ethylene oxide) (PEO) and lithium perchlorate (LiClO4) as both a contact-barrier reducer and channel mobility booster. We find that bare MoS2 devices (without polymer electrolyte) fabricated on Si/SiO2 have low channel mobility and large contact resistance, both of which severely limit the field-effect mobility of the devices. A thin layer of PEO/ LiClO4 deposited on top of the devices not only substantially reduces the contact resistance but also boost the channel mobility, leading up to three-orders-of-magnitude enhancement of the field-effect mobility of the device. When the polymer electrolyte is used as a gate medium, the MoS2 field-effect transistors exhibit excellent device characteristics such as a near ideal subthreshold swing and an on/off ratio of 106 as a result of the strong gate-channel coupling.Comment: 17 pages, 4 figures, accepted by J. Phys.

Emergent phases in a compass chain with multisite interactions

We study a dimerised spin chain with biaxial magnetic interacting ions in the presence of an externally induced three-site interactions out of equilibrium. In the general case, the three-site interactions play a role in renormalizing the effective uniform magnetic field. We find that the existence of zero-energy Majorana modes is intricately related to the sign of Pfaffian of the Bogoliubov-de Gennes Hamiltonian and the relevant $Z_2$ topological invariant. In contrast, we show that an exotic spin liquid phase can emerge in the compass limit through a Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition. Such a BKT transition is characterized by a large dynamic exponent $z=4$, and the spin-liquid phase is robust under a uniform magnetic field. We find the relative entropy and the quantum discord can signal the BKT transitions. We also uncover a few differences in deriving the correlation functions for the systems with broken reflection symmetry.Comment: 12 pages, 10 figure

Single deep ultraviolet light emission from boron nitride nanotube film

Light in deep ultraviolet DUV region has a wide range of applications and the demand for finding DUV light emitting materials at nanoscale is increasingly urgent as they are vital for building miniaturized optic and optoelectronic devices. We discover that boron nitride nanotubes BNNTs with a well-crystallized cylindrical multiwall structure and diameters smaller than 10 nm can have single DUV emission at 225 nm 5.51 eV. The measured BNNTs are grown on substrate in the form of a thin film. This study suggests that BNNTs may work as nanosized DUV light sources for various applications. © 20

The Quantum Geometric Phase between Orthogonal States

We show that the geometric phase between any two states, including orthogonal states, can be computed and measured using the notion of projective measurement, and we show that a topological number can be extracted in the geometric phase change in an infinitesimal loop near an orthogonal state. Also, the Pancharatnam phase change during the passage through an orthogonal state is shown to be either $\pi$ or zero (mod $2\pi$). All the off-diagonal geometric phases can be obtained from the projective geometric phase calculated with our generalized connection