M. J. Pacholski

Bio: M. J. Pacholski is an academic researcher from Leiden University. The author has contributed to research in topics: Fermion & Landau quantization. The author has an hindex of 6, co-authored 19 publications receiving 67 citations. Previous affiliations of M. J. Pacholski include University of Warsaw & Lorentz Institute.

Topologically Protected Landau Level in the Vortex Lattice of a Weyl Superconductor

Abstract: The question whether the mixed phase of a gapless superconductor can support a Landau level is a celebrated problem in the context of d-wave superconductivity, with a negative answer: the scattering of the subgap excitations (massless Dirac fermions) by the vortex lattice obscures the Landau level quantization. Here we show that the same question has a positive answer for a Weyl superconductor: the chirality of the Weyl fermions protects the zeroth Landau level by means of a topological index theorem. As a result, the heat conductance parallel to the magnetic field has the universal value G=1/2g_{0}Φ/Φ_{0}, with Φ as the magnetic flux through the system, Φ_{0} as the superconducting flux quantum, and g_{0} as the thermal conductance quantum.

Time-resolved electrical detection of chiral edge vortex braiding

Abstract: A 2 pi phase shift across a Josephson junction in a topological superconductor injects vortices into the chiral edge modes at opposite ends of the junction. When two vortices are fused they transfer charge into a metal contact. We calculate the time dependent current profile for the fusion process, which consists of +/- e/2 charge pulses that flip sign if the world lines of the vortices are braided prior to the fusion. This is an electrical signature of the non-Abelian exchange of Majorana zero-modes.

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.

Half-integer charge injection by a Josephson junction without excess noise

Abstract: A Josephson junction in a topological superconductor can inject a charge e/2 into a normal-metal contact, carried by chiral Majorana edge modes. Here, we address the question whether this half-integer charge is a sharp observable, without quantum fluctuations. Because the Majorana modes are gapless, they support charge fluctuations in equilibrium at zero temperature. But we find that the excess noise introduced out of equilibrium by the e/2 charge transfer vanishes. We discuss a strategy to reduce the equilibrium fluctuations, by means of a heavy-tailed time-dependent detection efficiency, to achieve a nearly noiseless half-integer charge transfer.

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.

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.

Search for non-Abelian Majorana braiding statistics in superconductors

Abstract: This is a tutorial review of methods to braid the world lines of non-Abelian anyons (Majorana zero-modes) in topological superconductors. That "Holy Grail" of topological quantum information processing has not yet been reached in the laboratory, but there now exists a variety of platforms in which one can search for the Majorana braiding statistics. After an introduction to the basic concepts of braiding we discuss how one might be able to braid immobile Majorana zero-modes, bound to the end points of a nanowire, by performing the exchange in parameter space, rather than in real space. We explain how Coulomb interaction can be used to both control and read out the braiding operation, even though Majorana zero-modes are charge neutral. We ask whether the fusion rule might provide for an easier pathway towards the demonstration of non-Abelian statistics. In the final part we discuss an approach to braiding in real space, rather than parameter space, using vortices injected into a chiral Majorana edge mode as "flying qubits". Contents: I. Introduction II. Basic Concepts (The magic of braiding; Non-Abelian statistics; Fusion rules; Clifford gates; Topological protection) III. Braiding of Majorana zero-modes in nanowires (The three-point turn; Non-Abelian Berry phase; Coulomb-assisted braiding; Anyon teleportation) IV. Read-out of Majorana qubits (Majorana interferometry; Inductive coupling to a flux qubit; Microwave coupling to a transmon qubit; Capacitive coupling to a quantum dot; Random Access Majorana Memory) V. Fusion of Majorana zero-modes in nanowires (Linear junction or tri-junction; If we can fuse, do we need to braid?) VI. How to braid Majorana edge modes (Chiral edge modes in a superconductor; Edge vortex injection; Construction of the vortex operator; Edge vortex braiding)

Type-II Weyl semimetals

Abstract: Fermions--elementary particles such as electrons--are classified as Dirac, Majorana or Weyl. Majorana and Weyl fermions had not been observed experimentally until the recent discovery of condensed matter systems such as topological superconductors and semimetals, in which they arise as low-energy excitations. Here we propose the existence of a previously overlooked type of Weyl fermion that emerges at the boundary between electron and hole pockets in a new phase of matter. This particle was missed by Weyl because it breaks the stringent Lorentz symmetry in high-energy physics. Lorentz invariance, however, is not present in condensed matter physics, and by generalizing the Dirac equation, we find the new type of Weyl fermion. In particular, whereas Weyl semimetals--materials hosting Weyl fermions--were previously thought to have standard Weyl points with a point-like Fermi surface (which we refer to as type-I), we discover a type-II Weyl point, which is still a protected crossing, but appears at the contact of electron and hole pockets in type-II Weyl semimetals. We predict that WTe2 is an example of a topological semimetal hosting the new particle as a low-energy excitation around such a type-II Weyl point. The existence of type-II Weyl points in WTe2 means that many of its physical properties are very different to those of standard Weyl semimetals with point-like Fermi surfaces.

Crystalline symmetry protected helical Majorana modes in the iron pnictides

Abstract: We propose that propagating one-dimensional Majorana fermions will develop in the vortex cores of certain iron-based superconductors, most notably $\mathrm{Li}({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})\mathrm{As}$. A key ingredient of this proposal is the 3D Dirac cones recently observed in photoemission experiments [P. Zhang et al., Nat. Phys. 15, 41 (2019)]. Using an effective Hamiltonian around the $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}Z$ line we demonstrate the development of gapless one-dimensional helical Majorana modes, protected by ${C}_{4}$ symmetry. A topological index is derived which links the helical Majorana modes to the presence of monopoles in the Berry curvature of the normal state. We present various experimental consequences of this theory and discuss its possible connections with cosmic strings.

Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles

Abstract: This paper presents a mathematical and numerical analysis of the flatband wavefunctions occurring in the chiral model of twisted bilayer graphene at the "magic" twist angles. We show that the chiral model possesses an exact intra-valley inversion symmetry. Writing the flatband wavefunction as a product of a lowest Landau level quantum Hall state and a spinor, we show that the components of the spinor are anti-quantum Hall wavefunctions related by the inversion symmetry operation introduced here. We then show numerically that as one moves from the lowest to higher magic angles, the spinor components of the wavefunction exhibit an increasing number of zeros, resembling the changes in the quantum Hall wavefunction as the Landau level index is increased. The wavefunction zeros are characterized by a chirality, with zeros of the same chirality clustering near the center of the moire unit cell, while opposite chirality zeros are pushed to the boundaries of the unit cell. The enhanced phase winding at higher magic angles suggests an increased circulating current. Physical implications for scanning tunneling spectroscopy, orbital magnetization and interaction effects are discussed.