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In a recent paper [R. Soto-Garrido and E. Muñoz, J. Phys. Condens. Matter 30, 195302 (2018)], we studied the electronic transport properties in Weyl semimetals (WSMs) submitted to the combined effects of torsional mechanical strain and magnetic field, showing that this configuration induces a node-polarization effect on the current that can be used to measure the torsion angle from transmission experiments. In this article, we extend our previous work to study thermoelectric transport in WSMs under torsional strain and an external magnetic field. Our analysis involves only the electronic contribution to the transport coefficients, and it is thus valid at low temperatures where the phonon contribution is negligible. We provide exact analytical expressions for the scattering cross section and the transmitted heat current, in order to calculate the thermal conductance and the Seebeck coefficient under this configuration. Our results suggest that thermoelectric transport coefficients in these materials can be engineered by appropriately tuning the magnitude of the magnetic field, torsional strain, and the applied bias or thermal gradient, leading to a potentially very high figure of merit. [ABSTRACT FROM AUTHOR]

This work proposes a new edge about the Chaotic Genetic Algorithm (CGA) and the importance of the entropy in the initial population. Inspired by chaos theory, the CGA uses chaotic maps to modify the stochastic parameters of Genetic Algorithm. The algorithm modifies the parameters of the initial population using chaotic series and then analyzes the entropy of such population. This strategy exhibits the relationship between entropy and performance optimization in complex search spaces. Our study includes the optimization of nine benchmark functions using eight different chaotic maps for each of the benchmark functions. The numerical experiment demonstrates a direct relation between entropy and performance of the algorithm. [ABSTRACT FROM AUTHOR]

We provide a quasi-one-dimensional model which can support a pair-density-wave (PDW) state, in which the superconducting (SC) order parameter modulates periodically in space, with gapless Bogoliubov quasiparticle excitations. The model consists of an array of strongly interacting one-dimensional systems, where the one-dimensional systems are coupled to each other by local interactions and tunneling of the electrons and Cooper pairs between them. Within the interchain mean-field theory, we find several SC states from the model, including a conventional uniform SC state, PDW SC state, and a coexisting phase of the uniform SC and PDW states. In this quasi-1D regime we can treat the strong correlation physics essentially exactly using bosonization methods and the crossover to the 2D system by means of interchain mean-field theory. The resulting critical temperatures of the SC phases generically exhibit a power-law scaling with the coupling constants of the array, instead of the essential singularity found in weak-coupling BCS-type theories. Electronic excitations with an open Fermi surface, which emerge from the electronic Luttinger liquid systems below their crossover temperature to the Fermi liquid, are then coupled to the SC order parameters via the proximity effect. From the Fermi surface thus coupled to the SC order parameters, we calculate the quasiparticle spectrum in detail. We show that the quasiparticle spectrum can be fully gapped or nodal in the uniform SC phase and also in the coexisting phase of the uniform SC and PDW parameters. In the pure PDW state, the excitation spectrum has a reconstructed Fermi surface in the form of Fermi pockets of Bogoliubov quasiparticles. [ABSTRACT FROM AUTHOR]

We show that the pair-density-wave (PDW) superconducting state emergent in extended Heisenberg- Hubbard models in two-leg ladders is topological in the presence of an Ising spin symmetry and supports a Majorana zero mode (MZM) at an open boundary and at a junction with a uniform 4-wave one-dimensional superconductor. Similarly to a conventional finite-momentum paired state, the order parameter of the PDW state is a charge-2e field with finite momentum. However, the order parameter here is a quartic electron operator and conventional mean-field theory cannot be applied to study this state. We use bosonization to show that the ID PDW state has a MZM at a boundary. This superconducting state is an exotic topological phase supporting Majorana fermions with finite-momentum pairing fields and charge-4

In conventional superconductors the Cooper pairs have a zero center-of-mass momentum. In this paper we present a theory of superconducting states where the Cooper pairs have a nonzero center-of-mass momentum, inhomogeneous superconducting states known as a pair-density-waves (PDWs) states. We show that in a system of spin-½ fermions in two dimensions in an electronic nematic spin-triplet phase where rotational symmetry is broken in both real- and spin-space PDW phases arise naturally in a theory that can be analyzed using controlled approximations. We show that several superfluid phases that may adse in this phase can be treated within a controlled BCS mean-field theory, with the strength of the spin-triplet nematic order parameter playing the role of the small parameter of this theory. We find that in a spin-triplet nematic phase, in addition to a triplet p-wave and spin-singlet d-wave (or s depending on the nematic phase) uniform superconducting states, it is also possible to have a d-wave (or s) PDW superconductor The PDW phases found here can be either unidirectional, bidirectional, or tridirectional depending on the spin-triplet nematic phase and which superconducting channel is dominant. In addition, a triple-helix state is found in a particular channel. We show that these PDW phases are present in the weak-coupling limit, in contrast to the usual Fulde-Ferrell-Larkin-Ovchinnikov phases, which require strong coupling physics in addition to a large magnetic field (and often both). [ABSTRACT FROM AUTHOR]

Herein, we study electronic and thermoelectric transport in a type I Weyl semimetal nanojunction, with a torsional dislocation defect, in the presence of an external magnetic field parallel to the dislocation axis. The defect is modeled in a cylindrical geometry, as a combination of a gauge field accounting for torsional strain and a delta-potential barrier for the lattice mismatch effect. In the Landauer formalism, we find that due to the combination of strain and magnetic field, the electric current exhibits chiral valley-polarization, and the conductance displays the signature of Landau levels. We also compute the thermal transport coefficients, where a high thermopower and a large figure of merit are predicted for the junction. [ABSTRACT FROM AUTHOR]

The pair density wave (PDW) superconducting state has been proposed to explain the layer-decoupling effect observed in the La2-x Bax CuO4 compound at x = 1/8 [E. Berg, E. Fradkin, E.-A. Kim, S. A. Kivelson, V. Oganesyan, J. M. Tranquada, and S. C. Zhang, Phys. Rev. Lett. 99, 127003 (2007)]. In this state the superconducting order parameter is spatially modulated, in contrast with the usual superconducting (SC) state where the order parameter is uniform. In this paper, we study the properties of the amplitude (Higgs) modes in a unidirectional PDW state. To this end we consider a phenomenological model of PDW-type states coupled to a Fermi surface of fermionic quasiparticles. In contrast to conventional superconductors that have a single Higgs mode, unidirectional PDW superconductors have two Higgs modes. While in the PDW state the Fermi surface largely remains gapless, we find that the damping of the PDW Higgs modes into fermionic quasiparticles requires exceeding an energy threshold. We show that this suppression of damping in the PDW state is due to kinematics. As a result, only one of the two Higgs modes is significantly damped. In addition, motivated by the experimental phase diagram, we discuss the mixing of Higgs modes in the coexistence regime of the PDW and uniform SC states. These results should be observable directly in a Raman spectroscopy, in momentum resolved electron energy-loss spectroscopy, and in resonant inelastic x-ray scattering, thus providing evidence of the PDW states. [ABSTRACT FROM AUTHOR]

We study the octahedron relation (also known as the A∞T-system), obeyed in particular by the partition function for dimer coverings of the Aztec Diamond graph. For a suitable class of doubly periodic initial conditions, we find exact solutions with a particularly simple factorized form. For these, we show that the density function that measures the average dimer occupation of a face of the Aztec graph, obeys a system of linear recursion relations with periodic coefficients. This allows us to explore the thermodynamic limit of the corresponding dimer models and to derive exact ‘arctic’ curves separating the various phases of the system. [ABSTRACT FROM AUTHOR]

Study of the strongly correlated states in van der Waals heterostructures is one of the central topics in modern condensed matter physics. Among these, the rhombohedral trilayer graphene (RTG) occupies a prominent place since it hosts a variety of interaction-driven phases, with the metallic ones yielding exotic superconducting orders upon doping. Motivated by these experimental findings, we show within the framework of the low-energy Dirac theory that the optical conductivity can distinguish different candidates for a paramagnetic metallic ground state in this system. In particular, this observable shows a single peak in the fully gapped valence-bond state. On the other hand, the bond-current state features two pronounced peaks in the optical conductivity as the probing frequency increases. Finally, the rotational symmetry breaking charge-density wave exhibits a minimal conductivity with the value independent of the amplitude of the order parameter, which corresponds precisely to the splitting of the two cubic nodal points at the two valleys into two triplets of the band touching points featuring linearly dispersing quasiparticles. These features represent the smoking gun signatures of different candidate order parameters for the paramagnetic metallic ground state, which should motivate further experimental studies of the RTG.

In a recent paper (Muñoz and Soto-Garrido 2017 J. Phys.: Condens. Matter 29 445302) we have studied the effects of mechanical strain and magnetic field on the electronic transport properties in graphene. In this article we extended our work to Weyl semimetals (WSM). We show that although the WSM are 3D materials, most of the analysis done for graphene (2D material) can be carried out. In particular, we studied the electronic transport through a cylindrical region submitted to torsional strain and external magnetic field. We provide exact analytical expressions for the scattering cross section and the transmitted electronic current. In addition, we show the node-polarization effect on the current and propose a recipe to measure the torsion angle from transmission experiments.

We consider the scattering of Dirac particles in graphene due to the superposition of an external magnetic field and mechanical strain. As a model for a graphene nanobubble, we find exact analytical solutions for single-particle states inside and outside a circular region submitted to the fields. Finally, we obtain analytical expressions for the scattering cross-section, as well as for the Landauer current through the circular region. Our results provide a fully-analytical treatment for electronic transport through a graphene nanobubble, showing that a combination of a physical magnetic field and strain leads to valley polarization and filtering of the electronic current. Moreover, our analytical model provides an explicit metrology principle to measure strain by performing conductance experiments under a controlled magnetic field imposed over the sample.