Dimensionless ratios: characteristics of quantum liquids and their phase transitions

Dimensionless ratios of physical properties can characterize low-temperature phases in a wide variety of materials. As such, the Wilson ratio (WR), the Kadowaki-Woods ratio and the Wiedemann\--Franz law capture essential features of Fermi liquids in metals, heavy fermions, etc. Here we prove that the phases of many-body interacting multi-component quantum liquids in one dimension (1D) can be described by WRs based on the compressibility, susceptibility and specific heat associated with each component. These WRs arise due to additivity rules within subsystems reminiscent of the rules for multi-resistor networks in series and parallel --- a novel and useful characteristic of multi-component Tomonaga-Luttinger liquids (TLL) independent of microscopic details of the systems. Using experimentally realised multi-species cold atomic gases as examples, we prove that the Wilson ratios uniquely identify phases of TLL, while providing universal scaling relations at the boundaries between phases. Their values within a phase are solely determined by the stiffnesses and sound velocities of subsystems and identify the internal degrees of freedom of said phase such as its spin-degeneracy. This finding can be directly applied to a wide range of 1D many-body systems and reveals deep physical insights into recent experimental measurements of the universal thermodynamics in ultracold atoms and spins.Comment: 12 pages (main paper), (6 figures

Multiple Unpinned Dirac Points in Group-Va Single-layers with Phosphorene Structure

Emergent Dirac fermion states underlie many intriguing properties of graphene, and the search for them constitute one strong motivation to explore two-dimensional (2D) allotropes of other elements. Phosphorene, the ultrathin layers of black phosphorous, has been a subject of intense investigations recently, and it was found that other group-Va elements could also form 2D layers with similar puckered lattice structure. Here, by a close examination of their electronic band structure evolution, we discover two types of Dirac fermion states emerging in the low-energy spectrum. One pair of (type-I) Dirac points is sitting on high-symmetry lines, while two pairs of (type-II) Dirac points are located at generic $k$-points, with different anisotropic dispersions determined by the reduced symmetries at their locations. Such fully-unpinned (type-II) 2D Dirac points are discovered for the first time. In the absence of spin-orbit coupling, we find that each Dirac node is protected by the sublattice symmetry from gap opening, which is in turn ensured by any one of three point group symmetries. The spin-orbit coupling generally gaps the Dirac nodes, and for the type-I case, this drives the system into a quantum spin Hall insulator phase. We suggest possible ways to realize the unpinned Dirac points in strained phosphorene.Comment: 30 pages, 6 figure

Evidence for Half-Metallicity in n-type HgCr2Se4

High quality HgCr$_2$Se$_4$ single crystals have been investigated by magnetization, electron transport and Andreev reflection spectroscopy. In the ferromagnetic ground state, the saturation magnetic moment of each unit cell corresponds to an integer number of electron spins (3 $\mu_B$/Cr$^{3+}$), and the Hall effect measurements suggest n-type charge carriers. Spin polarizations as high as $97\%$ were obtained from fits of the differential conductance spectra of HgCr$_2$Se$_4$/Pb junctions with the modified Blonder-Tinkham-Klapwijk (BTK) theory. The temperature and bias-voltage dependencies of the sub-gap conductance are consistent with recent theoretical calculations based on spin active scatterings at a superconductor/half metal interface. Our results suggest that n-HgCr$_2$Se$_4$ is a half metal, in agreement with theoretical calculations that also predict undoped HgCr$_2$Se$_4$ is a magnetic Weyl semimetal.Comment: 6 pages, 4 figures, to appear in PR

Parallel field magnetoresistance in topological insulator thin films

We report that the finite thickness of three-dimensional topological insulator (TI) thin films produces an observable magnetoresistance (MR) in phase coherent transport in parallel magnetic fields. The MR data of Bi2Se3 and (Bi,Sb)2Te3 thin films are compared with existing theoretical models of parallel field magnetotransport. We conclude that the TI thin films bring parallel field transport into a unique regime in which the coupling of surface states to bulk and to opposite surfaces is indispensable for understanding the observed MR. The {\beta} parameter extracted from parallel field MR can in principle provide a figure of merit for searching TI compounds with more insulating bulk than existing materials.Comment: 6 pages, 4 figure