Roni Ilan

Nonequilibrium thermal transport and its relation to linear response

We study the real-time dynamics of spin chains driven out of thermal equilibrium by an initial temperature gradient T_L \neq T_R using density matrix renormalization group methods. We demonstrate that the nonequilibrium energy current saturates fast to a finite value if the linear-response thermal conductivity is infinite, i.e. if the Drude weight D is nonzero. Our data suggests that a nonintegrable dimerized chain might support such dissipationless transport (D>0). We show that the steady-state value J_E of the current for arbitrary T_L \neq T_R is of the functional form J_E=f(T_L)-f(T_R), i.e. it is completely determined by the linear conductance. We argue for this functional form, which is essentially a Stefan-Boltzmann law in this integrable model; for the XXX ferromagnet, f can be computed via thermodynamic Bethe ansatz in good agreement with the numerics. Inhomogeneous systems exhibiting different bulk parameters as well as Luttinger liquid boundary physics induced by single impurities are discussed briefly.

Inhomogeneous Weyl and Dirac Semimetals: Transport in Axial Magnetic Fields and Fermi Arc Surface States from Pseudo-Landau Levels

Author(s): Grushin, AG; Venderbos, JWF; Vishwanath, A; Ilan, R | Abstract: Topological Dirac and Weyl semimetals have an energy spectrum that hosts Weyl nodes appearing in pairs of opposite chirality. Topological stability is ensured when the nodes are separated in momentum space and unique spectral and transport properties follow. In this work, we study the effect of a spacedependent Weyl node separation, which we interpret as an emergent background axial-vector potential, on the electromagnetic response and the energy spectrum of Weyl and Dirac semimetals. This situation can arise in the solid state either from inhomogeneous strain or nonuniform magnetization and can also be engineered in cold atomic systems. Using a semiclassical approach, we show that the resulting axial magnetic field B5 is observable through an enhancement of the conductivity as s ~ B25 due to an underlying chiral pseudomagnetic effect. We then use two lattice models to analyze the effect of B5 on the spectral properties of topological semimetals.We describe the emergent pseudo-Landau-level structure for different spatial profiles of B5, revealing that (i) the celebrated surface states ofWeyl semimetals, the Fermi arcs, can be reinterpreted as n = 0 pseudo-Landau levels resulting from a B5 confined to the surface, (ii) as a consequence of position-momentum locking, a bulk B5 creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces, (iii) there are equilibrium bound currents proportional to B5 that average to zero over the sample, which are the analogs of bound currents in magnetic materials.We conclude by discussing how our findings can be probed experimentally.

Coulomb blockade as a probe for non-Abelian statistics in Read-Rezayi states.

We consider a quantum dot in the regime of the quantum Hall effect, particularly in Laughlin states and non-Abelian Read-Rezayi states. We find the location of the Coulomb blockade peaks in the conductance as a function of the area of the dot and the magnetic field. When the magnetic field is fixed and the area of the dot is varied, the peaks are equally spaced for the Laughlin states. In contrast, non-Abelian statistics is reflected in modulations of the spacing which depend on the magnetic field.

Detection of sub-MeV dark matter with three-dimensional Dirac materials

We propose the use of three-dimensional Dirac materials as targets for direct detection of sub-MeV dark matter. Dirac materials are characterized by a linear dispersion for low-energy electronic excitations, with a small band gap of O(meV) if lattice symmetries are broken. Dark matter at the keV scale carrying kinetic energy as small as a few meV can scatter and excite an electron across the gap. Alternatively, bosonic dark matter as light as a few meV can be absorbed by the electrons in the target. We develop the formalism for dark matter scattering and absorption in Dirac materials and calculate the experimental reach of these target materials. We find that Dirac materials can play a crucial role in detecting dark matter in the keV to MeV mass range that scatters with electrons via a kinetically mixed dark photon, as the dark photon does not develop an in-medium effective mass. The same target materials provide excellent sensitivity to absorption of light bosonic dark matter in the meV to hundreds of meV mass range, superior to all other existing proposals when the dark matter is a kinetically mixed dark photon.

Spin-Based Mach-Zehnder Interferometry in Topological Insulator p-n Junctions.

Transport in three-dimensional topological insulators relies on the existence of a spin-momentum locked surface state that encloses the insulating bulk. In this work we show how, in a topological insulator p-n junction, a magnetic field turns this surface state into an electronic Mach-Zehnder interferometer. Transmission of the junction can be tuned from zero to unity, resulting in virtually perfect visibility of the interference pattern, and the reflected and transmitted currents carry opposite spin polarization so that the junction also acts as a spin filter. Our setup therefore realizes a novel and highly tunable spintronic device where the effects of spin-momentum locking in topological insulator surface states can be probed directly in a transport experiment.

Experimental signatures of non-Abelian statistics in clustered quantum Hall states

We discuss transport experiments for various non-Abelian quantum Hall states, including the Read-Rezayi series and a paired spin-singlet state. We analyze the signatures of the unique characters of these states on Coulomb blockaded transport through large quantum dots. We show that the non-Abelian nature of the states manifests itself through modulations in the spacings between Coulomb blockade peaks as a function of the area of the dot. Even though the current flows only along the edge, these modulations vary with the number of quasiholes that are localized in the bulk of the dot. We discuss the effect of relaxation of edge states on the predicted Coulomb blockade patterns, and show that it may suppress the dependence on the number of bulk quasiholes. We predict the form of the lowest-order interference term in a Fabry-Perot interferometer for the spin-singlet state. The result indicates that this interference term is suppressed for certain values of the quantum numbers of the collective state of the bulk quasiholes, in agreement with previous findings for other clustered states belonging to the Read-Rezayi series.

Detecting Perfect Transmission in Josephson Junctions on the Surface of Three Dimensional Topological Insulators

We consider Josephson junctions on surfaces of three dimensional topological insulator nanowires. We find that in the presence of a parallel magnetic field, short junctions on nanowires show signatures of a perfectly transmitted mode capable of supporting Majorana fermions. Such signatures appear in the current-phase relation in the presence or absence of the fermion parity anomaly, and are most striking when considering the critical current as a function of flux , which exhibits a peak at . The peak sharpens in the presence of disorder at low but finite chemical potentials, and can be easily disentangled from weak-anti-localization effects. The peak also survives at small but finite temperatures, and represents a realistic and robust hallmark for perfect transmission and the emergence of Majorana physics inside the wire.

Inducing superconductivity in Weyl semimetal microstructures by selective ion sputtering

Novel ion beam–based method induces superconductivity in Weyl semimetal microstructures. By introducing a superconducting gap in Weyl or Dirac semimetals, the superconducting state inherits the nontrivial topology of their electronic structure. As a result, Weyl superconductors are expected to host exotic phenomena, such as nonzero-momentum pairing due to their chiral node structure, or zero-energy Majorana modes at the surface. These are of fundamental interest to improve our understanding of correlated topological systems, and, moreover, practical applications in phase-coherent devices and quantum applications have been proposed. Proximity-induced superconductivity promises to allow these experiments on nonsuperconducting Weyl semimetals. We show a new route to reliably fabricate superconducting microstructures from the nonsuperconducting Weyl semimetal NbAs under ion irradiation. The significant difference in the surface binding energy of Nb and As leads to a natural enrichment of Nb at the surface during ion milling, forming a superconducting surface layer (Tc ~ 3.5 K). Being formed from the target crystal itself, the ideal contact between the superconductor and the bulk may enable an effective gapping of the Weyl nodes in the bulk because of the proximity effect. Simple ion irradiation may thus serve as a powerful tool for the fabrication of topological quantum devices from monoarsenides, even on an industrial scale.

Scaling of electrical and thermal conductivities in an almost integrable chain

Many low-dimensional materials are well described by integrable one-dimensional models such as the Hubbard model of electrons or the Heisenberg model of spins. However, the small perturbations to these models required to describe real materials are expected to have singular effects on transport quantities: integrable models often support dissipationless transport, while weak non-integrable terms lead to finite conductivities. We use matrix-product-state methods to obtain quantitative values of spin/electrical and thermal conductivities in an almost integrable gapless chain (an XXZ spin chain with staggered fields, or equivalently a spinless fermion chain with staggered on-site potentials). The results at low temperatures validate a scaling theory based on bosonization.

Dynamical piezoelectric and magnetopiezoelectric effects in polar metals from Berry phases and orbital moments

The polarization of a material and its response to applied electric and magnetic fields are key solid-state properties with a long history in insulators, although a satisfactory theory required new concepts such as Berry-phase gauge fields. In metals, quantities such as static polarization and the magnetoelectric θ term cease to be well defined. In polar metals, there can be analogous dynamical current responses, which we study in a common theoretical framework. We find that current responses to dynamical strain in polar metals depend on both the first and second Chern forms, related to polarization and magnetoelectricity in insulators as well as the orbital magnetization on the Fermi surface. We provide realistic estimates that predict that the latter contribution will dominate, and we investigate the feasibility of experimental detection of this effect.