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Register a new userCoupled Wire Models of Interacting Dirac Nodal Superconductors
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Topological nodal superconductors possess gapless low energy excitations that are characterized by point or line nodal Fermi surfaces. In this work, using a coupled wire construction, we study topological nodal superconductors that have protected Dirac nodal points. In this construction, the low-energy electronic degrees of freedom are confined in a three dimensional array of wires, which emerge as pairing vortices of a microscopic superconducting system. The vortex array harbors an antiferromagnetic time-reversal and a mirror glide symmetry that protect the massless Dirac fermion in the single-body non-interacting limit. Within this model, we demonstrate exact-solvable many-body interactions that preserve the underlying symmetries and introduce a finite excitation energy gap. These gapping interactions support fractionalization and generically lead to non-trivial topological order. We also construct a special case of $N=16$ Dirac fermions where corresponding the gapping interaction leads to a trivial $E_8$ topological order that is closely related to the cancellation of the large gravitational anomaly.
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We propose and investigate a simple one-dimensional model for a single-channel quantum wire hosting electrons that interact repulsively and are subject to a significant spin-orbit interaction. We show that an external Zeeman magnetic field, applied at the right angle to the Rashba spin-orbit axis, drives the wire into a correlated spin-density wave state with gapped spin and gapless charge excitations. By computing the ground-state degeneracies of the model with either (anti-)periodic or open boundary conditions, we conclude that the correlated spin-density state realizes a gapless symmetry-protected topological phase, as the ground state is unique in the ring geometry while it is two-fold degenerate in the wire with open boundaries. Microscopically the two-fold degeneracy is found to be protected by the conservation of the magnetization parity. Open boundaries induce localized zero-energy (midgap) states which are described, at the special Luther-Emery point of the model, by Majorana fermions. We find that spin densities at the open ends of the wire exhibit unusual long-ranged correlations despite the fact that all correlations in the bulk of the wire decay in a power-law or exponential fashion. Our study exposes the crucial importance of the long-ranged string operator needed to implement the correct commutation relations between spin densities at different points in the wire. Along the way we rederive the low-energy theory of Galilean-invariant electron systems in terms of current operators.
Collective states of interacting non-Abelian anyons have recently been studied mostly in the context of certain fractional quantum Hall states, such as the Moore-Read state proposed to describe the physics of the quantum Hall plateau at filling fraction v = 5/2. In this manuscript, we further expand this line of research and present non-unitary generalizations of interacting anyon models. In particular, we introduce the notion of Yang-Lee anyons, discuss their relation to the so-called `Gaffnian quantum Hall wave function, and describe an elementary model for their interactions. A one-dimensional version of this model -- a non-unitary generalization of the original golden chain model -- can be fully understood in terms of an exact algebraic solution and numerical diagonalization. We discuss the gapless theories of these chain models for general su(2)_k anyonic theories and their Galois conjugates. We further introduce and solve a one-dimensional version of the Levin-Wen model for non-unitary Yang-Lee anyons.
We study the role of long-range electron-electron interactions in a system of two-dimensional anisotropic Dirac fermions, which naturally appear in uniaxially strained graphene, graphene in external potentials, some strongly anisotropic topological insulators, and engineered anisotropic graphene structures. We find that while for small interactions and anisotropy the system restores the conventional isotropic Dirac liquid behavior, strong enough anisotropy can lead to the formation of a quasi-one dimensional electronic phase with dominant charge order (anisotropic excitonic insulator).
We study the spectral density of electrons rho in an interacting quantum dot (QD) with a hybridization lambda to a non-interacting QD, which in turn is coupled to a non-interacting conduction band. The system corresponds to an impurity Anderson model in which the conduction band has a Lorentzian density of states of width Delta2. We solved the model using perturbation theory in the Coulomb repulsion U (PTU) up to second order and a slave-boson mean-field approximation (SBMFA). The PTU works surprisingly well near the exactly solvable limit Delta2 -> 0. For fixed U and large enough lambda or small enough Delta2, the Kondo peak in rho(omega) splits into two peaks. This splitting can be understood in terms of weakly interacting quasiparticles. Before the splitting takes place the universal properties of the model in the Kondo regime are lost. Using the SBMFA, simple analytical expressions for the occurrence of split peaks are obtained. For small or moderate Delta2, the side bands of rho(omega) have the form of narrow resonances, that were missed in previous studies using the numerical renormalization group. This technique also has shortcomings for describing properly the split Kondo peaks. As the temperature is increased, the intensity of the split Kondo peaks decreases, but it is not completely suppressed at high temperatures.
We describe a mechanism by which the longitudinal thermal conductivity $kappa_{xx}$, measured in an in-plane magnetic field, oscillates as a function of field angle in layered nodal superconductors. These oscillations occur when the spin-orbit splitting at the nodes is larger than the nodal scattering rate, and are complementary to vortex-induced oscillations identified previously. In sufficiently anisotropic materials, the spin-orbit mechanism may be dominant. As a particular application, we focus on the cuprate high-temperature superconductor YBa$_2$Cu$_3$O$_{6+x}$. This material belongs to the class of Rashba bilayers, in which individual CuO$_2$ layers lack inversion symmetry although the crystal itself is globally centrosymmetric. We show that spin-orbit coupling endows $kappa_{xx}/T$ with a characteristic dependence on magnetic field angle that should be easily detected experimentally, and argue that for underdoped samples the spin-orbit contribution is larger than the vortex contribution. A key advantage of the magneto-thermal conductivity is that it is a bulk probe of spin-orbit physics, and therefore not sensitive to inversion breaking at surfaces.
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