The topological system with a twisting edge band: position-dependent Hall resistance

We study a $\nu=1$ topological system with one twisting edge-state band and one normal edge-state band. For the twisting edge-state band, Fermi energy goes through the band three times, thus, having three edge states on one side of the sample; while the normal edge band contributes only one edge state on the other side of the sample. In such a system, we show that it consists of both topologically protected and unprotected edge states, and as a consequence, its Hall resistance depends on the location where the Hall measurement is done even for a translationally invariant system. This unique property is absent in a normal topological insulator

Double-diamond NaAl via Pressure: Understanding Structure Through Jones Zone Activation

Under normal conditions, sodium forms a 1:1 stoichiometric compound with indium, and also with thallium, both in the double-diamond structure. But sodium does not combine with aluminum at all. Could NaAl exist? If so, under what conditions and in which structural types? Instead of beginning with a purely computational and first-principles structure search, we are led to apply the early Brillouin and higher (Jones) zone ideas of the physics determining structural selection. We begin with a brief recapitulation of the higher zone concept as applied to the stability of metals and intermetallic compounds. We then discuss the extension of this concept to problems where density becomes a primary variable, within the second-order band structure approximation. An analysis of the range of applicability of pressure-induced Jones zone activation is presented. The simple NaAl compound serves us as a numerical laboratory for the application of this concept. Higher zone arguments and chemical intuition lead quite naturally to the suggestion that 1:1 compound formation between sodium and aluminum should be favored under pressure and specifically in the double-diamond structure. This is confirmed computationally by density functional theoretic methods within the generalized gradient approximation

Entanglement of indistinguishable particles in condensed matter physics

The concept of entanglement in systems where the particles are indistinguishable has been the subject of much recent interest and controversy. In this paper we study the notion of entanglement of particles introduced by Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)] in several specific physical systems, including some that occur in condensed matter physics. The entanglement of particles is relevant when the identical particles are itinerant and so not distinguished by their position as in spin models. We show that entanglement of particles can behave differently to other approaches that have been used previously, such as entanglement of modes (occupation-number entanglement) and the entanglement in the two-spin reduced density matrix. We argue that the entanglement of particles is what could actually be measured in most experimental scenarios and thus its physical significance is clear. This suggests entanglement of particles may be useful in connecting theoretical and experimental studies of entanglement in condensed matter systems.Comment: 13 pages, 6 figures, comments welcome, published version (minor changes, added references

Multiband Transport in Bilayer Graphene at High Carrier Densities

We report a multiband transport study of bilayer graphene at high carrier densities. Employing a poly(ethylene)oxide-CsClO$_4$ solid polymer electrolyte gate we demonstrate the filling of the high energy subbands in bilayer graphene samples at carrier densities $|n|\geq2.4\times 10^{13}$ cm$^{-2}$. We observe a sudden increase of resistance and the onset of a second family of Shubnikov de Haas (SdH) oscillations as these high energy subbands are populated. From simultaneous Hall and magnetoresistance measurements together with SdH oscillations in the multiband conduction regime, we deduce the carrier densities and mobilities for the higher energy bands separately and find the mobilities to be at least a factor of two higher than those in the low energy bands

On the rigidity of a hard sphere glass near random close packing

We study theoretically and numerically the microscopic cause of the mechanical stability of hard sphere glasses near their maximum packing. We show that, after coarse-graining over time, the hard sphere interaction can be described by an effective potential which is exactly logarithmic at the random close packing $\phi_c$. This allows to define normal modes, and to apply recent results valid for elastic networks: mechanical stability is a non-local property of the packing geometry, and is characterized by some length scale $l^*$ which diverges at $\phi_c$ [1, 2]. We compute the scaling of the bulk and shear moduli near $\phi_c$, and speculate on the possible implications of these results for the glass transition.Comment: 7 pages, 4 figures. Figure 4 had a wrong unit in abscissa, which was correcte

Effects of compression on the vibrational modes of marginally jammed solids

Glasses have a large excess of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature is a necessary consequence of the weak connectivity of the solid, and that the frequency of modes in excess is very sensitive to the pressure. We analyze in particular two systems whose density D(w) of vibrational modes of angular frequency w display scaling behaviors with the packing fraction: (i) simulations of jammed packings of particles interacting through finite-range, purely repulsive potentials, comprised of weakly compressed spheres at zero temperature and (ii) a system with the same network of contacts, but where the force between any particles in contact (and therefore the total pressure) is set to zero. We account in the two cases for the observed a) convergence of D(w) toward a non-zero constant as w goes to 0, b) appearance of a low-frequency cutoff w*, and c) power-law increase of w* with compression. Differences between these two systems occur at lower frequency. The density of states of the modified system displays an abrupt plateau that appears at w*, below which we expect the system to behave as a normal, continuous, elastic body. In the unmodified system, the pressure lowers the frequency of the modes in excess. The requirement of stability despite the destabilizing effect of pressure yields a lower bound on the number of extra contact per particle dz: dz > p^(1/2), which generalizes the Maxwell criterion for rigidity when pressure is present. This scaling behavior is observed in the simulations. We finally discuss how the cooling procedure can affect the microscopic structure and the density of normal modes.Comment: 13 pages, 8 figure

The Initial and Final States of Electron and Energy Transfer Processes: Diabatization as Motivated by System-Solvent Interactions

For a system which undergoes electron or energy transfer in a polar solvent, we define the diabatic states to be the initial and final states of the system, before and after the nonequilibrium transfer process. We consider two models for the system-solvent interactions: A solvent which is linearly polarized in space and a solvent which responds linearly to the system. From these models, we derive two new schemes for obtaining diabatic states from ab initio calculations of the isolated system in the absence of solvent. These algorithms resemble standard approaches for orbital localization, namely, the Boys and Edmiston–Ruedenberg (ER) formalisms. We show that Boys localization is appropriate for describing electron transfer [ Subotnik et al., J. Chem. Phys. 129, 244101 (2008) ] while ER describes both electron and energy transfer. Neither the Boys nor the ER methods require definitions of donor or acceptor fragments and both are computationally inexpensive. We investigate one chemical example, the case of oligomethylphenyl-3, and we provide attachment/detachment plots whereby the ER diabatic states are seen to have localized electron-hole pairs

Exact Numerical Solution of the BCS Pairing Problem

We propose a new simulation computational method to solve the reduced BCS Hamiltonian based on spin analogy and submatrix diagonalization. Then we further apply this method to solve superconducting energy gap and the results are well consistent with those obtained by Bogoliubov transformation method. The exponential problem of 2^{N}-dimension matrix is reduced to the polynomial problem of N-dimension matrix. It is essential to validate this method on a real quantumComment: 7 pages, 3 figure

On the de Haas-van Alphen effect in inhomogeneous alloys

We show that Landau level broadening in alloys occurs naturally as a consequence of random variations in the local quasiparticle density, without the need to consider a relaxation time. This approach predicts Lorentzian-broadened Landau levels similar to those derived by Dingle using the relaxation-time approximation. However, rather than being determined by a finite relaxation time $\tau$, the Landau-level widths instead depend directly on the rate at which the de Haas-van Alphen frequency changes with alloy composition. The results are in good agreement with recent data from three very different alloy systems.Comment: 5 pages, no figure