Dominik Gresch

Selected Publications

1. Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials

   Gresch, Dominik, Autès, Gabriel, Yazyev, Oleg V., Troyer, Matthias, Vanderbilt, David, Bernevig, B. Andrei, and Soluyanov, Alexey A.

   Physical Review B 2017

   Abstract PDF

   The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but often challenging, problem, with no exhaustive solution at the present time. In this work we compile a series of techniques, some previously known, that allow for a solution to this problem for a large set of the possible band topologies. The method is based on tracking hybrid Wannier charge centers computed for relevant Bloch states, and it works at all levels of materials modeling: continuous k⋅p models, tight-binding models, and ab initio calculations. We apply the method to compute and identify Chern, Z2, and crystalline topological insulators, as well as topological semimetal phases, using real material examples. Moreover, we provide a numerical implementation of this technique (the Z2Pack software package) that is ideally suited for high-throughput screening of materials databases for compounds with nontrivial topologies. We expect that our work will allow researchers to (a) identify topological materials optimal for experimental probes, (b) classify existing compounds, and (c) reveal materials that host novel, not yet described, topological states.

2. Type-II Weyl semimetals

   Soluyanov, Alexey A., Gresch, Dominik, Wang, Zhijun, Wu, QuanSheng, Troyer, Matthias, Dai, Xi, and Bernevig, B. Andrei

   Nature 2015

   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.

3. Identifying Topological Semimetals

   Gresch, Dominik

   2018

   Abstract PDF

   Geometric properties of electron states in crystalline solids lead to a topological classification of materials. A remarkable consequence of this topological viewpoint is that it reveals a deep link between the bulk properties of a material and electronic states which form on its surface. This leads to unique transport properties, the most well-known example being the integer quantum Hall effect. In topological semimetals, the bulk features of interest are nodes in the band structure, where occupied and unoccupied states are not separated by an energy gap. This leads to interesting low-energy excitations, some of which are the condensed matter equivalent of fundamental particles. The Weyl Fermion for example is realized in topological semimetals, which is theoretically postulated but eludes experimental verification in high-energy physics. Crystals however do not have a continuous translational symmetry, and thus do not need to fulfill the so-called Lorentz invariance present in high-energy physics. This allows for Fermions to exist in materials which do not have a fundamental counterpart. The main topic of this thesis is the study and identification of topological semimetals. We propose a mechanism for Weyl Fermions to form under the influence of an external magnetic field. This effect could help explain the anisotropic negative magnetoresistance in transition metal dipnictides. We also study several novel topological material candidates, hosting a plethora of Weyl Fermions and topological nodal lines. In addition to studying specific material examples, we also present several tools and algorithms which enhance the process of identifying topological materials. First, we present an algorithm for evaluating the phase diagram of a system with discrete phases. This is useful in identifying topological phases, but also applicable to other fields of computational physics. Furthermore, we develop tools that simplify the creation of k·p and tight-binding models to study crystalline systems. A particular focus lies on the construction of models which preserve the crystal symmetries, since these play a crucial role in determining the topology of a material. And finally, we develop an algorithm that reliably finds and classifies topological nodal features.