Rex Lundgren

Thermoelectric properties of Weyl and Dirac semimetals

We study the electronic contribution to the thermal conductivity and the thermopower of Weyl and Dirac semimetals using a semiclassical Boltzmann approach. We investigate the effect of various relaxation processes including disorder and interactions on the thermoelectric properties, and also consider doping away from the Weyl or Dirac point. We find that the thermal conductivity and thermopower have an interesting dependence on the chemical potential that is characteristic of the linear electronic dispersion, and that the electron-electron interactions modify the Lorenz number. For the interacting system, we also use the Kubo formalism to obtain the transport coefficients. We find exact agreement between the Kubo and Boltzmann approaches at high temperatures. We also consider the effect of electric and magnetic fields on the thermal conductivity in various orientations with respect to the temperature gradient. Notably, when the temperature gradient and magnetic field are parallel, we find a large contribution to the longitudinal thermal conductivity that is quadratic in the magnetic field strength, similar to the magnetic field dependence of the longitudinal electrical conductivity due to the presence of the chiral anomaly when no thermal gradient is present.

Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases

We study the entanglement spectrum (ES) and entropy between two coupled Tomonaga-Luttinger liquids (TLLs) on parallel periodic chains. This problem gives access to the entanglement properties of various interesting systems, such as spin ladders as well as two-dimensional topological phases. By expanding interchain interactions to quadratic order in bosonic fields, we are able to calculate the ES for both gapped and gapless systems using only methods for free theories. In certain gapless phases of coupled nonchiral TLLs, we interestingly find an ES with a dispersion relation proportional to the square root of the subsystem momentum, which we relate to a long-range interaction in the entanglement Hamiltonian. We numerically demonstrate the emergence of this unusual dispersion in a model of hard-core bosons on a ladder. In gapped phases of coupled nonchiral TLLs, which are relevant to spin ladders and topological insulators, we show that the ES consists of linearly dispersing modes, which resembles the spectrum of a single-chain TLL but is characterized by a modified TLL parameter. Based on a calculation for coupled chiral TLLs, we are also able to provide a very simple proof for the correspondence between the ES and the edge-state spectrum in quantum Hall systems consistent with previous numerical and analytical studies.

Electronic Cooling in Weyl and Dirac Semimetals

Energy transfer from electrons to phonons is an important consideration in any Weyl- or Dirac-semimetal-based application. In this work, we analytically calculate the cooling power of acoustic phonons, i.e., the energy relaxation rate of electrons which are interacting with acoustic phonons, for Weyl and Dirac semimetals in a variety of different situations. For cold Weyl or Dirac semimetals with the Fermi energy at the nodal points, we find that the electronic temperature

Topological insulators and quantum spin liquids

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Momentum-space entanglement in Heisenberg spin-half ladders

decays in time as a power law. In the heavily doped regime,

Universal entanglement spectra in critical spin chains

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Landau Theory of Helical Fermi Liquids.

decays linearly in time far from equilibrium. In a heavily doped system with short-range disorder we predict that the cooling power of acoustic phonons is drastically increased because of an enhanced energy transfer between electrons and phonons. When an external magnetic field is applied to an undoped system, the cooling power is linear in magnetic field strength and

Nematic Order on the Surface of a Three-dimensional Topological Insulator

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Momentum-Space Entanglement and Loschmidt Echo in Luttinger Liquids after a Quantum Quench.

has square-root decay in time, independent of magnetic-field strength over a range of values.

Bulk entanglement spectrum in gapped spin ladders

Abstract In this paper we review some connections recently discovered between topological insulators and certain classes of quantum spin liquids, focusing on two and three spatial dimensions. In two dimensions we show the integer quantum Hall effect plays a key role in relating topological insulators and chiral spin liquids described by fermionic excitations, and we describe a procedure for “generating” a certain class of topological states. In three dimensions we discuss interesting relationships between certain quantum spin liquids and interacting “exotic” variants of topological insulators. We focus attention on better understanding interactions in topological insulators, and the phases nearby in parameter space that might result from moderate to strong interactions in the presence of strong spin–orbit coupling. We stress that oxides with heavy transition metal ions, which often host a competition between electron interactions and spin–orbit coupling, are an excellent place to search for unusual topological phenomena and other unconventional phases.