Physics and Astronomy

Permanent URI for this collectionhttps://uwspace.uwaterloo.ca/handle/10012/9949

This is the collection for the University of Waterloo's Department of Physics and Astronomy.

Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).

Waterloo faculty, students, and staff can contact us or visit the UWSpace guide to learn more about depositing their research.

Browse

Now showing 1 - 5 of 5

Interactions, Entanglement, and Anomalies in Topological Semimetals
(University of Waterloo, 2023-08-04) Yang, Lei; Burkov, Anton; Wang, Chong
Topology and symmetry have become one of the backbones of modern condensed matter physics. These concepts play a large role in determining the possible effects of interactions and entanglement in both gapped and gapless systems. Gapped systems possess a well-developed description via topological quantum field theory (TQFT) that has given rise to many exciting concepts such as topological orders. However gapless systems are far less well-understood in the context of topology as they cannot be described by a simple TQFT due to the presence of local degrees of freedom at low energy. In this thesis I will explore these concepts in the framework of topological response in gapless systems with a focus on 3+1d Weyl and Dirac semimetallic systems. I develop a theory of unquantized topological response, as opposed to the usual quantized response of gapped systems, and explore the effects of strong interaction in the presence of these terms. I show that the associated unquantized topological quantities arise from crystalline symmetries such as discrete translations and rotations. Inspired by the topological crystalline quantity of momentum, I also develop a general theorem involving just discrete translation symmetry that can distinguish long-range entangled states from short-range entangled states. Such a statement can be seen as a generalisation of the well-known Lieb-Schultz-Mattis theorems and many are shown to be consequences from the pure translation theorem that I develop here.
Topological and superconducting properties of Weyl and Dirac metals
(University of Waterloo, 2018-08-30) Bednik, Grigory; Burkov, Anton
In this work we explore superconductivity and surface states in topological semimetals. We start from general overview of basic properties of topological semimetals. We review general concepts of Chern insulators, their surface states, and use it as a building block for construction of Weyl metals. We also construct double Weyl metals, which are protected both by topology and discrete rotational symmetry. In addition, we study Luttinger model of semimetals - it the simplest case, it is non-topological, but it can acquire topological Weyl points in the presence of non-zero Zeeman field. We present study of its surface states, and also consider its possible critical points. Next, we turn to the problem of superconductivity in Weyl metals. We demonstrate that Weyl metals are natural candidates for hosting unconventional superconductivity. Specifically, we consider two possible superconducting instabilities: unconventional finite momentum FFLO pairing, and zero momentum BCS pairing, which is also unconventional due to spin-momentum locking in Weyl metals. We demonstrate that its BCS phase is more favorable. In addition, we compute its anomalous Hall conductivity, and demonstrate that it is universal, i.e. not affected by the presence of superconductivity. Finally, we consider Dirac metals, which are protected solely by rotational symmetry. We point out, that mirror symmetry along its Dirac points plays special role. We demonstrate, that by breaking the rotational symmetry, it is possible to convert Dirac metal into a topological crystalline insulator, and Dirac metal itself can be viewed as a critical point between its different topological phases. We explore surface states spectrum in the resulting picture, and demonstrate, that this mechanism can be used to show that surface states in Dirac metal always terminate at Dirac points despite being not topologically protected.
Topological aspects of nodal-loop semimetals and the nature of spin-orbit coupling in Lu₂V₂O₇
(University of Waterloo, 2021-09-27) Hickey, Alexander; Gingras, Michel; Burkov, Anton
This thesis is presented in two parts: (I) understanding the topological aspects of nodal-loop semimetals in the presence of interactions and (II) exploring the nature of spin-orbit coupling in the pyrochlore oxide Lu₂V₂O₇. Each of these parts correspond to distinct research projects, sharing an underlying theme of topology and spin-orbit coupling. (I) Topological nodal-loop semimetals are characterized by a symmetry protected 1D line of band touching points, dispersionless surface states, and an electromagnetic response in the form of an induced magnetization and polarization. While this characterization holds true for free fermions, there has recently been increased interest in how topological order manifests in the presence of interactions, particularly in the gapless topological semimetals. This thesis explores the effect of interactions in nodal-loop semimetals, in the framework of a mean-field BCS theory. It is found that the surface states are preserved for p-wave pairing when the gap function preserves the symmetries that protect the nodal-loop. Furthermore, it is shown that this state hosts a single Dirac mode in the core of any vortex line of odd vorticity. This result highlights that the topological order of a nodal-loop can remain stable in the presence of interactions. (II) Pyrochlore oxides geometrically support a magnetic interaction of spin-orbit origin known as the Dzyaloshinskii-Moriya interaction, due to the lack of inversion symmetry between neighbouring magnetic ions. In magnetically ordered quantum systems, such an interaction has been shown to give rise to a thermal Hall effect of magnons, the quasiparticles arising from spin fluctuations. Such an effect was subsequently observed in thermal transport measurements of the pyrochlore oxide Lu₂V₂O₇, however, these measurements seem to overestimate the magnitude of the DM interaction. This draws into question the nature of spin-orbit coupling in this material. An overview of the low-energy properties of Lu₂V₂O₇ is presented, along with a re-investigation of the thermal transport data. This leads to an apparent discrepancy in the value of the DM interaction, motivating future investigations of this material.
Topological Order in String Liquids and Weyl Semimetals
(University of Waterloo, 2022-08-22) Sehayek, Dan; Melko, Roger; Burkov, Anton
Outside Landau's paradigm of symmetry-breaking orders is the class of topological orders, which cannot be described by a local order parameters. Such orders are generally defined by the presence of a gauge symmetry and possess many interesting features, including fractionalized excitations and topological degeneracy on closed manifolds. The first half of thesis will be dedicated to exploring various techniques for detecting topological order in string liquids, which are spin-1/2 systems with a local $\mathbb{Z}_2$ symmetry. Such a local symmetry gives rise to a loop condensate in the low temperature regime, which allows for emergent fractionalized excitations and topological degeneracy defined by the presence of non-contractible loops. Generally, such phases can be described by the Wegner-Wilson and 't Hooft loop observables, which are non-local string order parameters, and possess a phase transition between perimeter and area laws in spatial dimensions $D\geq{3}$. We will demonstrate the ability of various numerical techniques to detect this $\mathbb{Z}_2$ topological order based on $\sigma^z$ measurements sampled using a Monte Carlo algorithm for the classical $\mathbb{Z}_2$ gauge theory. First, we will show that the diffusion map algorithm can be used to cluster spin configurations according to their topological sector and hence identify the topological degeneracy for the 3-dimensional case. Next, we will show that the first Betti number of geometric complex constructions of spin configurations can be used to measure the prominence of closed loops defined by the local $\mathbb{Z}_2$ symmetry, and that a persistent homology analysis can be used to distinguish loop structures according to their geometry. We will additionally show that both the diffusion map algorithm and the first Betti number of geometric complex constructions can be used to detect the topological phase transition in the Wegner-Wilson loop between perimeter and area laws. The second half of thesis will be dedicated to exploring a construction of $\mathbb{Z}_4$ topological order in Weyl semimetals, which possess topologically protected gapless nodes hosting Weyl fermions and a chiral anomaly response. Such a construction was first proposed by C. Wang, L. Gioia and A. Burkov, and involves superconducting pairing and vortex condensation. We will show that the same $\mathbb{Z}_4$ topological can be obtained from charge density wave (CDW) interactions, which involves applying a similar vortex condensation procedure to 2D Dirac fermions at the interface between the two degenerate CDW ground states at a Weyl node separation of $2Q=\pi$. As in the original construction, fractionalized statistics will emerge in the uncondensed vortices, with odd flux vortices possessing Majorana zero modes and flux $2\pi$ vortices possessing semions. Finally, we will derive the theory of the surface states based on the hydrodynamic BF theory for this $\mathbb{Z}_4$ topological order.
Topology and interactions in Weyl metals and quantum Hall systems
(University of Waterloo, 2017-05-10) Panfilov, Ivan; Burkov, Anton
In recent years it became clear that in the Condensed Matter physics, the study of the interactions and the topology allows one to find and to describe many new phases of matter. Even more interest was drawn by the systems, where the topology is nontrivial and the interactions are not negligible, such as fractional quantum Hall effect. Therefore, in this thesis we study two examples of the interacting systems that have non-trivial topological properties. First, we consider the Weyl metals - a class of material that were suggested theoretically few years ago and observed on experiments first time in 2015. We study the behavior of the theoretical model of Weyl metal in the presence of an external magnetic field. Using the random field approximation, we show that the applied field gives the correction to the density response, that is topological in nature and is closely related to the phenomenon of chiral anomaly. This contribution manifests in a nonanalytic nonclassical corrections to the electronic compressibility and the plasmon frequency, proportional to the magnitude of the magnetic field. Such a nonanalytic correction to the electronic compressibility clearly distinguishes Weyl metals from ordinary ferromagnetic metals and hence can be used to identify the Weyl metals. Next, we study the connection between the bosonic quantum Hall systems and the lattice models. We present a mapping of a two-dimensional system of interacting bosons in a strong perpendicular magnetic field to an equivalent system of interacting bosons on the square lattice in the absence of the field. This mapping utilizes a magnetic Bloch and the corresponding magnetic Wannier single particle bases in the lowest Landau level. We demonstrate that, by construction, the ground states of the resulting model of interacting bosons on the square lattice are gapped fractionalized liquids or gapless Bose metal states with broken time reversal symmetry at speci c rational filling fractions.

Browse

Browsing Physics and Astronomy by Author "Burkov, Anton"