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Register a new userLow-energy effective theory in the bulk for transport in a topological phase
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We construct a low-energy effective action for a two-dimensional non-relativistic topological (i.e. gapped) phase of matter in a continuum, which completely describes all of its bulk electrical, thermal, and stress-related properties in the limit of low frequencies, long distances, and zero temperature, without assuming either Lorentz or Galilean invariance. This is done by generalizing Luttingers approach to thermoelectric phenomena, via the introduction of a background vielbein (i.e. gravitational) field and spin connection a la Cartan, in addition to the electromagnetic vector potential, in the action for the microscopic degrees of freedom (the matter fields). Crucially, the geometry of spacetime is allowed to have timelike and spacelike torsion. These background fields make all natural invariances--- under U(1) gauge transformations, translations in both space and time, and spatial rotations---appear locally, and corresponding conserved currents and the stress tensor can be obtained, which obey natural continuity equations. On integrating out the matter fields, we derive the most general form of a local bulk induced action to first order in derivatives of the background fields, from which thermodynamic and transport properties can be obtained. We show that the gapped bulk cannot contribute to low-temperature thermoelectric transport other than the ordinary Hall conductivity; the other thermoelectric effects (if they occur) are thus purely edge effects. The coupling to reduced spacelike torsion is found to be absent in minimally-coupled models, and using a generalized Belinfante stress tensor, the stress response to time-dependent vielbeins (i.e. strains) is the Hall viscosity, which is robust against perturbations and related to the spin current as in earlier work.
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The bulk-edge correspondence (BEC) refers to a one-to-one relation between the bulk and edge properties ubiquitous in topologically nontrivial systems. Depending on the setup, BEC manifests in different forms and govern the spectral and transport properties of topological insulators and semimetals. Although the topological pump is theoretically old, BEC in the pump has been established just recently [1] motivated by the state-of-the-art experiments using cold atoms [2,3]. The center of mass (CM) of a system with boundaries shows a sequence of quantized jumps in the adiabatic limit associated with the edge states. Although the bulk is adiabatic, the edge is inevitably non-adiabatic in the experimental setup or in any numerical simulations. Still the pumped charge is quantized and carried by the bulk. Its quantization is guaranteed by a compensation between the bulk and edges. We show that in the presence of disorder the pumped charge continues to be quantized despite the appearance of non-quantized jumps.
Monolayer transition metal dichalcogenides in the distorted octahedral 1T$^prime$ phase exhibit a large bulk bandgap and gapless boundary states, which is an asset in the ongoing quest for topological electronics. In single-layer tungsten diselenide (WSe$_2$), the boundary states have been observed at well ordered interfaces between 1T$^prime$ and semiconducting (1H) phases. This paper proposes an effective 4-band theory for the boundary states in single-layer WSe$_2$,describing a Kramers pair of in-gap states as well as the behaviour at the spectrum termination points on the conduction and valence bands of the 1T$^prime$ phase. The spectrum termination points determine the temperature and chemical potential dependences of the ballistic conductance and thermopower at the phase boundary. Notably, the thermopower shows an ambipolar behaviour, changing the sign in the bandgap of the 1T$^prime$ - WSe$_2$ and reflecting its particle-hole asymmetry. The theory establishes a link between the bulk band structure and ballistic boundary transport in single-layer WSe$_2$ and is applicable to a range of related topological materials.
2+1 dimensional topological insulator described by the Kane-Mele model in the presence of Rashba spin-orbit interaction is considered. The effective action of the external fields coupled to electromagnetic and spin degrees of freedom is accomplished within this model. The Hamiltonian methods are adopted to provide the coefficients appearing in the action. It is demonstrated straightforwardly that the coefficients of the Chern-Simons terms are given by the first Chern number attained through the related non-Abelian Berry gauge field. The effective theory which we obtain is in accord with the existence of the spin Hall phase where the value of the spin Hall conductivity is very close to the quantized one.
Axions and axion-like particles (ALPs) are well-motivated low-energy relics of high-energy extensions of the Standard Model, which interact with the known particles through higher-dimensional operators suppressed by the mass scale $Lambda$ of the new-physics sector. Starting from the most general dimension-5 interactions, we discuss in detail the evolution of the ALP couplings from the new-physics scale to energies at and below the scale of electroweak symmetry breaking. We derive the relevant anomalous dimensions at two-loop order in gauge couplings and one-loop order in Yukawa interactions, carefully considering the treatment of a redundant operator involving an ALP coupling to the Higgs current. We account for one-loop (and partially two-loop) matching contributions at the weak scale, including in particular flavor-changing effects. The relations between different equivalent forms of the effective Lagrangian are discussed in detail. We also construct the effective chiral Lagrangian for an ALP interacting with photons and light pseudoscalar mesons, pointing out important differences with the corresponding Lagrangian for the QCD axion.
We determine analytically the phase diagram of the toric code model in a parallel magnetic field which displays three distinct regions. Our study relies on two high-order perturbative expansions in the strong- and weak-field limit, as well as a large-spin analysis. Calculations in the topological phase establish a quasiparticle picture for the anyonic excitations. We obtain two second-order transition lines that merge with a first-order line giving rise to a multicritical point as recently suggested by numerical simulations. We compute the values of the corresponding critical fields and exponents that drive the closure of the gap. We also give the one-particle dispersions of the anyonic quasiparticles inside the topological phase.
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