Shockley model description of surface states in topological insulators

We show that the surface states in topological insulators can be understood based on a well-known Shockley model, a one-dimensional tight-binding model with two atoms per elementary cell, connected via alternating tunneling amplitudes. We generalize the one-dimensional model to the three-dimensional case corresponding to the sequence of layers connected via the amplitudes, which depend on the in-plane momentum p = (p_x,p_y). The Hamiltonian of the model is described a (2 x 2) Hamiltonian with the off-diagonal element t(k,p) depending also on the out-of-plane momentum k. We show that the complex function t(k,p) defines the properties of the surface states. The surface states exist for the in-plane momenta p, where the winding number of the function t(k,p) is non-zero as k is changed from 0 to 2pi. The sign of the winding number defines the sublattice on which the surface states are localized. The equation t(k,p)=0 defines a vortex line in the three-dimensional momentum space. The projection of the vortex line on the two-dimensional momentum p space encircles the domain where the surface states exist. We illustrate how our approach works for a well-known TI model on a diamond lattice. We find that different configurations of the vortex lines are responsible for the "weak" and "strong" topological insulator phases. The phase transition occurs when the vortex lines reconnect from spiral to circular form. We discuss the Shockley model description of Bi_2Se_3 and the applicability of the continuous approximation for the description of the topological edge states. We conclude that the tight-binding model gives a better description of the surface states.Comment: 18 pages, 17 figures; version 3: Sections I-IV revised, Section VII added, Refs. [33]-[35] added; Corresponds to the published versio

Topological insulating phases in mono and bilayer graphene

We analyze the influence of different quadratic interactions giving rise to time reversal invariant topological insulating phases in mono and bilayer graphene. We make use of the effective action formalism to determine the dependence of the Chern Simons coefficient on the different interactions

Dispersion Instability in Strongly Interacting Electron Liquids

We show that the low-density strongly interacting electron liquid, interacting via the long-range Coulomb interaction, could develop a dispersion instability at a critical density associated with the approximate flattening of the quasiparticle energy dispersion. At the critical density the quasiparticle effective mass diverges at the Fermi surface, but the signature of this Fermi surface instability manifests itself away from the Fermi momentum at higher densities. For densities below the critical density the system is unstable since the quasiparticle velocity becomes negative. We show that one physical mechanism underlying the dispersion instability is the emission of soft plasmons by the quasiparticles. The dispersion instability occurs both in two and three dimensional electron liquids. We discuss the implications of the dispersion instability for experiments at low electron densities.Comment: Accepted version for publicatio

Sign reversals of the quantum Hall effect and helicoidal magnetic-field-induced spin-density waves in quasi-one-dimensional organic conductors

We study the effect of umklapp scattering on the magnetic-field-induced spin-density-wave phases, which are experimentally observed in the quasi-one-dimensional organic conductors of the Bechgaard salts family. Within the framework of the quantized nesting model, we show that umklapp processes may naturally explain sign reversals of the quantum Hall effect (QHE) observed in these conductors. Moreover, umklapp scattering can change the polarization of the spin-density wave (SDW) from linear (sinusoidal SDW) to circular (helicoidal SDW). The QHE vanishes in the helicoidal phases, but a magnetoelectric effect appears. These two characteristic properties may be utilized to detect the magnetic-field-induced helicoidal SDW phases experimentally.Comment: 4 pages, latex, 3 figure

Edge electron states for quasi-one-dimensional organic conductors in the magnetic-field-induced spin-density-wave phases

We develop a microscopic picture of the electron states localized at the edges perpendicular to the chains in the Bechgaard salts in the quantum Hall regime. In a magnetic-field-induced spin-density-wave state (FISDW) characterized by an integer N, there exist N branches of chiral gapless edge excitations. Localization length is much longer and velocity much lower for these states than for the edge states parallel to the chains. We calculate the contribution of these states to the specific heat and propose a time-of-flight experiment to probe the propagating edge modes directly.Comment: 4 pages, 2 figures. V.2: Minor changes to the final version published in PR

Effect of umklapp scattering on the magnetic-field-induced spin-density waves in quasi-one-dimensional organic conductors

We study the effect of umklapp scattering on the magnetic-field-induced spin-density-wave (FISDW) phases which are experimentally observed in the quasi-one-dimensional organic conductors of the Bechgaard salts family. Within the framework of the quantized nesting model, we show that the transition temperature is determined by a modified Stoner criterion which includes the effect of umklapp scattering. We determine the SDW polarization (linear or circular) by analyzing the Ginzburg-Landau expansion of the free energy. We also study how umklapp processes modify the quantum Hall effect (QHE) and the spectrum of the FISDW phases. We find that umklapp scattering stabilizes phases which exhibit a sign reversal of the QHE, as experimentally observed in the Bechgaard salts. These ``negative'' phases are characterized by the simultaneous existence of two SDWs with comparable amplitudes. As the umklapp scattering strength increases, they may become helicoidal (circularly polarized SDWs). The QHE vanishes in the helicoidal phases, but a magnetoelectric effect appears. These two characteristic properties may be utilized to detect the magnetic-field-induced helicoidal SDW phases experimentally.Comment: Revtex, 27 pages, 9 figure

Theory of Thermodynamic Magnetic Oscillations in Quasi-One-Dimensional Conductors

The second order correction to free energy due to the interaction between electrons is calculated for a quasi-one-dimensional conductor exposed to a magnetic field perpendicular to the chains. It is found that specific heat, magnetization and torque oscillate when the magnetic field is rotated in the plane perpendicular to the chains or when the magnitude of magnetic filed is changed. This new mechanism of thermodynamic magnetic oscillations in metals, which is not related to the presence of any closed electron orbits, is applied to explain behavior of the organic conductor (TMTSF)$_2$ClO$_4$.Comment: 11 pages + 5 figures (included

Collective modes in a system with two spin-density waves: the `Ribault' phase of quasi-one-dimensional organic conductors

We study the long-wavelength collective modes in the magnetic-field-induced spin-density-wave (FISDW) phases experimentally observed in organic conductors of the Bechgaard salts family, focusing on phases that exhibit a sign reversal of the quantum Hall effect (Ribault anomaly). We have recently proposed that two SDW's coexist in the Ribault phase, as a result of Umklapp processes. When the latter are strong enough, the two SDW's become circularly polarized (helicoidal SDW's). In this paper, we study the collective modes which result from the presence of two SDW's. We find two Goldstone modes, an out-of-phase sliding mode and an in-phase spin-wave mode, and two gapped modes. The sliding Goldstone mode carries only a fraction of the total optical spectral weight, which is determined by the ratio of the amplitude of the two SDW's. In the helicoidal phase, all the spectral weight is pushed up above the SDW gap. We also point out similarities with phase modes in two-band or bilayer superconductors. We expect our conclusions to hold for generic two-SDW systems.Comment: Revised version, 25 pages, RevTex, 7 figure

Current facilitation by plasmon resonances between parallel wires of finite length

The current voltage (IV) characteristics for perpendicular transport through two sequentially coupled wires of finite length is calculated analytically. The transport within a Coulomb blockade step is assisted by plasmon resonances that appear as steps in the IV characteristics with positions and heights depending on inter- and intrawire interactions. In particular, due to the interwire interactions, the peak positions shift to lower voltages in comparison to the noninteracting wires which reflects the facilitation of current by interactions. The interwire interactions are also found to enhance the thermally activated current.Comment: 5 pages, 1figur