G. Lemut

Bio: G. Lemut is an academic researcher from Leiden University. The author has contributed to research in topics: Magnetic field & Topological insulator. The author has an hindex of 3, co-authored 10 publications receiving 20 citations.

Localization landscape for Dirac fermions

Abstract: In the theory of Anderson localization, a landscape function predicts where wave functions localize in a disordered medium, without requiring the solution of an eigenvalue problem. It is known how to construct the localization landscape for the scalar wave equation in a random potential, or equivalently for the Schr\"odinger equation of spinless electrons. Here, we generalize the concept to the Dirac equation, which includes the effects of spin-orbit coupling and allows us to study quantum localization in graphene or in topological insulators and superconductors. The landscape function $u(\mathbit{r})$ is defined on a lattice as a solution of the differential equation $\stackrel{⎴}{H}u(\mathbit{r})=1$, where $\stackrel{⎴}{H}$ is the Ostrowski comparison matrix of the Dirac Hamiltonian. Random Hamiltonians with the same (positive-definite) comparison matrix have localized states at the same positions, defining an equivalence class for Anderson localization. This provides for a mapping between the Hermitian and non-Hermitian Anderson model.

Effect of charge renormalization on the electric and thermoelectric transport along the vortex lattice of a Weyl superconductor

Abstract: Building on the discovery that a Weyl superconductor in a magnetic field supports chiral Landau-level motion along the vortex lines, we investigate its transport properties out of equilibrium. We show that the vortex lattice carries an electric current I = 1/2(Q(eff)(2)/h)(Phi/Phi(0))V between two normal-metal contacts at voltage difference V, with Phi the magnetic flux through the system, Phi(0) the superconducting flux quantum, and Q(eff) < e the renormalized charge of the Weyl fermions in the superconducting Landau level. Because the charge renormalization is energy dependent, a nonzero thermoelectric coefficient appears even in the absence of energy-dependent scattering processes.

Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice

Abstract: The spatial discretization of the single-cone Dirac Hamiltonian on the surface of a topological insulator or superconductor needs a special "staggered" grid, to avoid the appearance of a spurious second cone in the Brillouin zone. We adapt the Stacey discretization from lattice gauge theory to produce a generalized eigenvalue problem, of the form ${\mathcal H}\psi=E {\mathcal P}\psi$, with Hermitian tight-binding operators ${\mathcal H}$, ${\mathcal P}$, a locally conserved particle current, and preserved chiral and symplectic symmetries. This permits the study of the spectral statistics of Dirac fermions in each of the four symmetry classes A, AII, AIII, and D.

Magnetic breakdown spectrum of a Kramers-Weyl semimetal

Abstract: We calculate the Landau levels of a Kramers-Weyl semimetal thin slab in a perpendicular magnetic field $B$. The coupling of Fermi arcs on opposite surfaces broadens the Landau levels with a band width that oscillates periodically in $1/B$. We interpret the spectrum in terms of a one-dimensional superlattice induced by magnetic breakdown at Weyl points. The band width oscillations may be observed as $1/B$-periodic magnetoconductance oscillations, at weaker fields and higher temperatures than the Shubnikov-de Haas oscillations due to Landau level quantization. No such spectrum appears in a generic Weyl semimetal, the Kramers degeneracy at time-reversally invariant momenta is essential.

Deconfinement of Majorana Vortex Modes Produces a Superconducting Landau Level

Abstract: A spatially oscillating pair potential $\mathrm{\ensuremath{\Delta}}(\mathbit{r})={\mathrm{\ensuremath{\Delta}}}_{0}{e}^{2i\mathbit{K}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{r}}$ with momentum $Kg{\mathrm{\ensuremath{\Delta}}}_{0}/\ensuremath{\hbar}v$ drives a deconfinement transition of the Majorana bound states in the vortex cores of a Fu-Kane heterostructure (a 3D topological insulator with Fermi velocity $v$, on a superconducting substrate with gap ${\mathrm{\ensuremath{\Delta}}}_{0}$, in a perpendicular magnetic field). In the deconfined phase at zero chemical potential the Majorana fermions form a dispersionless Landau level, protected by chiral symmetry against broadening due to vortex scattering. The coherent superposition of electrons and holes in the Majorana Landau level is detectable as a local density of states oscillation with wave vector $\sqrt{{K}^{2}\ensuremath{-}({\mathrm{\ensuremath{\Delta}}}_{0}/\ensuremath{\hbar}v{)}^{2}}$. The striped pattern also provides a means to measure the chirality of the Majorana fermions.

Topological Quantum Properties of Chiral Crystals

Abstract: Chiral crystals are materials with a lattice structure that has a well-defined handedness due to the lack of inversion, mirror or other roto-inversion symmetries. Although it has been shown that the presence of crystalline symmetries can protect topological band crossings, the topological electronic properties of chiral crystals remain largely uncharacterized. Here we show that Kramers–Weyl fermions are a universal topological electronic property of all non-magnetic chiral crystals with spin–orbit coupling and are guaranteed by structural chirality, lattice translation and time-reversal symmetry. Unlike conventional Weyl fermions, they appear at time-reversal-invariant momenta. We identify representative chiral materials in 33 of the 65 chiral space groups in which Kramers–Weyl fermions are relevant to the low-energy physics. We determine that all point-like nodal degeneracies in non-magnetic chiral crystals with relevant spin–orbit coupling carry non-trivial Chern numbers. Kramers–Weyl materials can exhibit a monopole-like electron spin texture and topologically non-trivial bulk Fermi surfaces over an unusually large energy window.Kramers–Weyl fermions are identified in chiral crystals, and their phenomenology is drawn out.

Axionic band topology in inversion-symmetric Weyl-charge-density waves

Abstract: In recent theoretical and experimental investigations, researchers have linked the low-energy field theory of a Weyl semimetal gapped with a charge-density wave (CDW) to high-energy theories with axion electrodynamics. However, it remains an open question whether a lattice regularization of the dynamical Weyl-CDW is in fact a single-particle axion insulator (AXI). In this Rapid Communication, we use analytic and numerical methods to study both lattice-commensurate and incommensurate minimal (magnetic) Weyl-CDW phases in the mean-field state. We observe that, as previously predicted from field theory, the two inversion (I)-symmetric Weyl-CDWs with ϕ=0,π differ by a topological axion angle δθϕ=π. However, we crucially discover that neither of the minimal Weyl-CDW phases at ϕ=0,π is individually an AXI; they are instead quantum anomalous Hall (QAH) and “obstructed” QAH insulators that differ by a fractional translation in the modulated cell, analogous to the two phases of the Su-Schrieffer-Heeger model of polyacetylene. Using symmetry indicators of band topology and non-Abelian Berry phase, we demonstrate that our results generalize to multiband systems with only two Weyl fermions, establishing that minimal Weyl-CDWs unavoidably carry nontrivial Chern numbers that prevent the observation of a static magnetoelectric response. We discuss the experimental implications of our findings and provide models and analysis generalizing our results to nonmagnetic Weyl- and Dirac-CDWs.

Large, nonsaturating thermopower in a quantizing magnetic field

Abstract: The thermoelectric effect is the generation of an electrical voltage from a temperature gradient in a solid material due to the diffusion of free charge carriers from hot to cold. Identifying materials with large thermoelectric response is crucial for the development of novel electric generators and coolers. In this paper we consider theoretically the thermopower of Dirac/Weyl semimetals subjected to a quantizing magnetic field. We contrast their thermoelectric properties with those of traditional heavily-doped semiconductors and we show that, under a sufficiently large magnetic field, the thermopower of Dirac/Weyl semimetals grows linearly with the field without saturation and can reach extremely high values. Our results suggest an immediate pathway for achieving record-high thermopower and thermoelectric figure of merit, and they compare well with a recent experiment on Pb$_{1-x}$Sn$_x$Se.

L-2 localization landscape for highly excited states

Abstract: The localization landscape [M. Filoche and S. Mayboroda, Proc. Natl. Acad. Sci. USA 109, 14761 (2012)] gives direct access to the localization of bottom-of-band eigenstates in noninteracting disord ...