arXiv subjects

Piers Coleman

Publications and source records attributed to Piers Coleman.

At least 91 records · Page 5Linked to original sources

arXiv2014

End states in a 1-D topological Kondo insulator

To gain further insight into the properties of interacting topological insulators, we study a 1 dimensional model of topological Kondo insulators which can be regarded as the strongly interacting limit of the Tamm-Shockley model. Treating the model in a large $N$ expansion, we find a number of competing ground-state solutions, including topological insulating and valence bond ground-states. One of the effects to emerge in our treatment is a reconstruction of the Kondo screening process near the boundary of the material ("Kondo band bending"). Near the boundary for localization into a valence bond state, we find that the conduction character of the edge state grows substantially, leading to states that extend deeply into bulk. We speculate that such states are the one-dimensional analog of the light f-electron surface states which appear to develop in the putative topological Kondo insulator, SmB6.

cond-mat.str-el↗

arXiv2014

$^{3}$He-R: A Topological $s^{\pm}$ Superfluid with Triplet Pairing

We show that when spin and orbital angular momenta are entangled by spin-orbit coupling, this transforms a topological spin-triplet superfluid/superconductor state, such as $^{3}$He-B, into a topological $s^{\pm}$ state, with non-trivial gapless edge states. Similar to $^{3}$He-B, the $s^{\pm}$ state also minimizes on-site Coulomb repulsion for weak to moderate interactions. A topological phase transition into a $d$-wave state occurs for sufficiently strong spin-orbit coupling.

cond-mat.supr-con↗

arXiv2014

Hidden and Hastatic Orders in URu2Si2

The hidden order developing below 17.5K in the heavy fermion material URu2Si2 has eluded identification for over twenty five years. This paper will review the recent theory of ``hastatic order,'' a novel two-component order parameter capturing the hybridization between half-integer spin (Kramers) conduction electrons and the non-Kramers 5f^2 Ising local moments, as strongly indicated by the observation of Ising quasiparticles in de Haas-van Alphen measurements. Hastatic order differs from conventional magnetism as it is a spinor order that breaks both single and double time-reversal symmetry by mixing states of different Kramers parity. The broken time-reversal symmetry simply explains both the pseudo-Goldstone mode between the hidden order and antiferromagnetic phases and the nematic order seen in torque magnetometry. The spinorial nature of the hybridization also explains how the Kondo effect gives a phase transition, with the hybridization gap turning on at the hidden order transition as seen in scanning tunneling microscopy. Hastatic order also has a number of new predictions: a basal-plane magnetic moment of order .01μ_B, a gap to longitudinal spin fluctuations that vanishes continuously at the first order antiferromagnetic transition and a narrow resonant nematic feature in the scanning tunneling spectra.

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arXiv2014

Theory of the Electron Spin Resonance in the Heavy Fermion Metal β-YbAlB4

The heavy fermion metal β-YbAlB4 exhibits a bulk room temperature conduction electron ESR signal which evolves into an Ising-anisotropic f-electron signal exhibiting hyperfine features at low temperatures. We develop a theory for this phenomenon based on the development of resonant scattering off a periodic array of Kondo centers. We show that the hyperfine structure arises from the scattering off the Yb atoms with non zero nuclear spin, while the constancy of the ESR intensity is a consequence of the presence of CEF excitations of the order of the hybridization strength.

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arXiv2013

Emergent Criticality and Friedan Scaling in a 2D Frustrated Heisenberg Antiferromagnet

We study a two-dimensional frustrated Heisenberg antiferromagnet on the windmill lattice consisting of triangular and dual honeycomb lattice sites. In the classical ground state the spins on different sublattices are decoupled, but quantum and thermal fluctuations drive the system into a coplanar state via an "order from disorder" mechanism. We obtain the finite temperature phase diagram using renormalization group approaches. In the coplanar regime, the relative U$(1)$ phase between the spins on the two sublattices decouples from the remaining degrees of freedom, and is described by a six-state clock model with an emergent critical phase. At lower temperatures the system enters a $\mathbb{Z}_6$ broken phase with long-range phase correlations. We derive these results by two distinct renormalization group approaches to two-dimensional magnetism: by Wilson-Polyakov scaling and by Friedan's geometric approach to nonlinear sigma models where the scaling of the spin-stiffnesses is governed by the Ricci flow of a 4D metric tensor.

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arXiv2013

TAO pairing: a fully gapped pairing scenario for the Iron-Based Superconductors

Motivated by the fully gapped superconductivity in iron-based superconductors with uncompensated electron pockets, we propose a spin singlet, but orbital triplet analogue of the superfluid phase of He-3B. We show that orbital triplets with a nominal d-wave symmetry at the iron sites can transform as s-wave pairs under rotations about the selenium sites. Linear combinations of such d$_{xy}$ and d$_{x^{2}-y^{2}}$ triplets form a fully gapped, topological superconductor. Raman-active excitations are predicted to develop below the superconducting transition temperature.

cond-mat.supr-con↗

arXiv2013

Cubic Topological Kondo Insulators

Current theories of Kondo insulators employ the interaction of conduction electrons with localized Kramers doublets originating from a tetragonal crystalline environment, yet all Kondo insulators are cubic. Here we develop a theory of cubic topological Kondo insulators involving the interaction of spin quartets with a conduction sea. The spin quartets greatly increase the potential for strong topological insulators, entirely eliminating the weak-topological phases from the diagram. We show that the relevant topological behavior in cubic Kondo insulators can only reside at the lower symmetry X or M points in the Brillouin zone, leading to a three Dirac cones with heavy quasiparticles.

cond-mat.str-el↗

arXiv2012

Emergent Critical Phase and Ricci Flow in a 2D Frustrated Heisenberg Model

We introduce a two-dimensional frustrated Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. Classically the two sublattices decouple, and "order from disorder" drives them into a coplanar state. Applying Friedan's geometric approach to nonlinear sigma models, we show that the scaling of the spin-stiffnesses corresponds to the Ricci flow of a 4D metric tensor. At low temperatures, the relative phase between the spins on the two sublattices is described by a six-state clock model with an emergent critical phase.

cond-mat.str-el↗

arXiv2012

Origin of the Large Anisotropy in the χ_3 Anomaly in URu_2Si_2

Motivated by recent quantum oscillations experiments on URu_2Si_2, we discuss the microscopic origin of the large anisotropy observed many years ago in the anomaly of the nonlinear susceptibility in this same material. We show that the magnitude of this anomaly emerges naturally from hastatic order, a proposal for hidden order that is a two-component spinor arising from the hybridization of a non-Kramers Gamma_5 doublet with Kramers conduction electrons. A prediction is made for the angular anisotropy of the nonlinear susceptibility anomaly as a test of this proposed order parameter for URu_2Si_2.

cond-mat.str-el↗

arXiv2012

β-YbAlB4: a critical nodal metal

We propose a model for the intrinsic quantum criticality of β-YbAlB4, in which a vortex in momentum space gives rise to a new type of Fermi surface singularity. The unquenched angular momentum of the |J = 7/2,m_J = \pm5/2> Yb 4f-states generates a momentum-space line defect in the hybridization between 4f and conduction electrons, leading to a quasi-two dimensional Fermi surface with a k\perp4 dispersion and a singular density of states proportional to E^{-1/2}. We discuss the implications of this line-node in momentum space for our current understanding of quantum criticality and its interplay with topology.

cond-mat.str-el↗

arXiv2012

Hastatic Order in URu2Si2

The development of collective long-range order via phase transitions occurs by the spontaneous breaking of fundamental symmetries. Magnetism is a consequence of broken time-reversal symmetry while superfluidity results from broken gauge invariance. The broken symmetry that develops below 17.5K in the heavy fermion compound URu2Si2 has long eluded such identification. Here we show that the recent observation of Ising quasiparticles in URu2Si2 results from a spinor order parameter that breaks double time-reversal symmetry, mixing states of integer and half-integer spin. Such "hastatic order" hybridizes conduction electrons with Ising 5f^{2} states of the uranium atoms to produce Ising quasiparticles; it accounts for the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. Hastatic order predicts a tiny transverse moment in the conduction sea, a collosal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant energy-dependent nematicity in the tunneling density of states.

cond-mat.str-el↗

arXiv2012

Basal-Plane Nonlinear Susceptibility: A Direct Probe of the Single-Ion Physics in URu2Si2

The microscopic nature of the hidden order state in URu2Si2 is dependent on the low-energy configurations of the uranium ions, and there is currently no consensus on whether it is predominantly 5f^2 or 5f^3. Here we show that measurement of the basal-plane nonlinear susceptibility can resolve this issue; its sign at low-temperatures is a distinguishing factor. We calculate the linear and nonlinear susceptibilities for specific 5f^2 and 5f^3 crystal-field schemes that are consistent with current experiment. Because of its dual magnetic and orbital character, a Γ_5 magnetic non-Kramers doublet ground-state of the U ion can be identified by $χ_1^c(T) \propto χ_3^\perp(T)$ where we have determined the constant of proportionality for URu2Si2.

cond-mat.str-el↗

arXiv2012

Spin and holographic metals

In this paper we discuss two-dimensional holographic metals from a condensed matter physics perspective. We examine the spin structure of the Green's function of the holographic metal, demonstrating that the excitations of the holographic metal are "chiral", lacking the inversion symmetry of a conventional Fermi surface, with only one spin orientation for each point on the Fermi surface, aligned parallel to the momentum. While the presence of a Kramer's degeneracy across the Fermi surface permits the formation of a singlet superconductor, it also implies that ferromagnetic spin fluctuations are absent from the holographic metal, leading to a complete absence of Pauli paramgnetism. In addition, we show how the Green's function of the holographic metal can be regarded as a reflection coefficient in anti-de-Sitter space, relating the ingoing and outgoing waves created by a particle moving on the external surface.

cond-mat.str-el↗

arXiv2012

The symplectic-N t-J model and s$_\pm$ superconductors

The possible discovery of $s_\pm$ superconducting gaps in the moderately correlated iron-based superconductors has raised the question of how to properly treat $s_\pm$ gaps in strongly correlated superconductors. Unlike the d-wave cuprates, the Coulomb repulsion does not vanish by symmetry, and a careful treatment is essential. Thus far, only the weak correlation approaches have included this Coulomb pseudopotential, so here we introduce a symplectic N treatment of the t-J model that incorporates the strong Coulomb repulsion through the complete elimination of on-site pairing. Through a proper extension of time-reversal symmetry to the large N limit, symplectic-N is the first superconducting large N solution of the t-J model. For d-wave superconductors, the previous uncontrolled mean field solutions are reproduced, while for $s_\pm$ superconductors, the SU(2) constraint enforcing single occupancy acts as a pair chemical potential adjusting the location of the gap nodes. This adjustment can capture the wide variety of gaps proposed for the iron based superconductors: line and point nodes, as well as two different, but related full gaps on different Fermi surfaces.

cond-mat.supr-con↗

arXiv2011

Local Quantum Criticality of an Iron-Pnictide Tetrahedron

Motivated by the close correlation between transition temperature ($T_c$) and the tetrahedral bond angle of the As-Fe-As layer observed in the iron-based superconductors, we study the interplay between spin and orbital physics of an isolated iron-arsenide tetrahedron embedded in a metallic environment. Whereas the spin Kondo effect is suppressed to low temperatures by Hund's coupling, the orbital degrees of freedom are expected to quantum mechanically quench at high temperatures, giving rise to an overscreened, non-Fermi liquid ground-state. Translated into a dense environment, this critical state may play an important role in the superconductivity of these materials.

cond-mat.str-el↗

arXiv2011

A theory of Topological Kondo Insulators

We examine how the properties of the Kondo insulators change when the symmetry of the underlying crystal field multiplets is taken into account. We employ the Anderson lattice model and consider its low-energy physics. We show that in a large class of crystal field configurations, Kondo insulators can develop a topological non-trivial ground-state. Such topological Kondo insulators are adiabatically connected to non-interacting insulators with unphysically large spin-orbit coupling, and as such may be regarded as interaction-driven topological insulators. We analyze the entanglement entropy of the Anderson lattice model of Kondo insulators by evaluating its entanglement spectrum. Our results for the entanglement spectrum are consistent with the surface state calculations. Lastly, we discuss the construction of the maximally localized Wannier wave functions for generic Kondo insulators.

cond-mat.str-el↗

arXiv2011

Quasiparticle interference in an iron-based superconductor

We develop a model for the effect of a magnetic field on quasiparticle interference in an iron-based superconductor. Recently, scanning tunneling experiments have been performed on Fe(Se,Te) to determine the relative sign of the superconducting gap from the magnetic-field dependence of quasiparticle scattering amplitudes. Using a simple two-band BCS model, we study three different cases of scattering in a spin-split spectrum. The dominant effect of a magnetic field in iron-based superconductors is caused by the Pauli limiting of conduction electrons. Thereby time reversal odd scattering is induced which enhances the sign-preserving and depresses the sign-reversing peaks in the quasiparticle interference patterns.

cond-mat.supr-con↗

arXiv2011

Composite pairing in a mixed valent two channel Anderson model

Using a two-channel Anderson model, we develop a theory of composite pairing in the 115 family of heavy fermion superconductors that incorporates the effects of f-electron valence fluctuations. Our calculations introduce "symplectic Hubbard operators": an extension of the slave boson Hubbard operators that preserves both spin rotation and time-reversal symmetry in a large N expansion, permitting a unified treatment of anisotropic singlet pairing and valence fluctuations. We find that the development of composite pairing in the presence of valence fluctuations manifests itself as a phase-coherent mixing of the empty and doubly occupied configurations of the mixed valent ion. This effect redistributes the f-electron charge within the unit cell. Our theory predicts a sharp superconducting shift in the nuclear quadrupole resonance frequency associated with this redistribution. We calculate the magnitude and sign of the predicted shift expected in CeCoIn_5.

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