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Interacting Dirac Matter
KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory. (Condensed Matter, Statistical and Biological Physics Nordita)
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The discovery of graphene in 2004 has led to a surge of activities focused on the theoretical and experimental studies of materials hosting linearly dispersive quasiparticles during the last decade. Rapid expansion in the list of materials having similar properties to graphene has led to the emergence of a new class of materials known as the Dirac materials. The low energy quasiparticles in this class of materials are described by a Dirac-like equation in contrast to the Schrödinger equation which governs the low energy dynamics in any conventional materials such as metals. The Dirac fermions, as we call these low-energy quasiparticles, in a wide range of materials ranging from the d-wave superconductors, graphene to the surface states of topological insulators share the common property. The particles move around as if they have lost their mass. This feature results in a completely new set of physical effects consisting of various transport and thermodynamic quantities, that are absent in conventional metals.

This thesis is devoted to studying the properties of bosonic analogs of the commonly known Dirac materials where the quasiparticle are fermionic. In chapter one, we discuss the microscopic origin of the Dirac equation in several fermionic and bosonic systems. We observe identical features of the Dirac materials with quasiparticles of either statistics when the interparticle interaction is absent. Dirac materials with both types of quasiparticles possess the nodal excitations that are described by an effective Dirac-like equation. The possible physical effects due to the linear dispersions in fermionic and bosonic Dirac materials are also outlined.

In chapter two, we propose a system of superconducting grains arranged in honeycomb lattice as a realization for Bosonic Dirac Materials (BDM). The underlying microscopic dynamics, which give rise to the emergence of Dirac structure in the spectrum of the collective phase oscillations, is discussed in detail. Similarities and differences of BDM systems to the conventional Dirac materials with fermionic quasiparticles are also mentioned. Chapter three is dedicated to the detailed analysis of the interaction effects on the stability and renormalization of the conical Dirac band structure. We find that the type of interaction dictates the possible fate of renormalized Dirac cone in both fermionic and bosonic Dirac materials. We study interaction effects in four different individual systems : (a) Dirac fermions in graphene interacting via Coulomb interactions, (b) Dirac fermions subjected to an onsite Hubbard repulsion, (c) Coulomb repulsion in charged Cooper pairs in honeycomb lattice and (d) Dirac magnons interacting via Heisenberg exchange interaction. The possibility of interaction induced gap opening at the Dirac nodal point described is also discussed in these cases.

Chapter four mainly concerns the study of a related topic of the synthetic gauge fields. We discuss the possibility of Landau quantization in neutral particles. Possible experimental evidence in toroidal cold atomic traps is also mentioned. A connection to Landau levels in case of magnons is also described. We finally conclude our thesis in chapter five and discuss the possible future directions that can be taken as an extension for our works in interacting Dirac materials.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2018. , p. 102
Series
TRITA-SCI-FOU ; 2018:22
Keywords [en]
Dirac, superconductor, magnon, interaction, Fermi liquid theory, renormalization
National Category
Condensed Matter Physics
Research subject
Physics
Identifiers
URN: urn:nbn:se:kth:diva-227997ISBN: 978-91-7729-821-2 (print)OAI: oai:DiVA.org:kth-227997DiVA, id: diva2:1206202
Public defence
2018-06-13, A3: 1077, Roslagstullsbacken 21, Main Building, Floor 3, AlbaNova, Stockholm-106 91, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20180516

This thesis contains all the works performed during my doctoral study in physics at Nordita, Sweden.

Available from: 2018-05-16 Created: 2018-05-16 Last updated: 2018-06-19Bibliographically approved
List of papers
1. Granular superconductor in a honeycomb lattice as a realization of bosonic Dirac material
Open this publication in new window or tab >>Granular superconductor in a honeycomb lattice as a realization of bosonic Dirac material
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2016 (English)In: PHYSICAL REVIEW B, ISSN 2469-9950, Vol. 93, no 13, article id 134502Article in journal (Refereed) Published
Abstract [en]

We examine the low-energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in a honeycomb lattice structure. Using the example of graphene, we present evidence for the engineered Dirac nodes in the bosonic excitations: the spectra of the collective bosonic modes cross at the K and K' points in the Brillouin zone and form Dirac nodes. We show how two different types of collective phase oscillations are obtained and that they are analogous to the Leggett and the Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. We show that the Dirac node is preserved in the presence of an intergrain interaction, despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sublattice symmetry by choosing different on-site potentials for the two sublattices leads to a gap opening near the Dirac node, in analogy with fermionic Dirac materials. The Dirac node dispersion of bosonic excitations is thus expanding the discussion of the conventional Dirac cone excitations to the case of bosons. We call this case as a representative of bosonic Dirac materials (BDM), similar to the case of Fermionic Dirac materials extensively discussed in the literature.

Place, publisher, year, edition, pages
American Physical Society, 2016
National Category
Theoretical Chemistry Physical Sciences
Identifiers
urn:nbn:se:kth:diva-185977 (URN)10.1103/PhysRevB.93.134502 (DOI)000373566000006 ()2-s2.0-84963616046 (Scopus ID)
Note

QC 20160504

Available from: 2016-05-04 Created: 2016-04-29 Last updated: 2018-05-16Bibliographically approved
2. Dirac Magnons in Honeycomb Ferromagnets
Open this publication in new window or tab >>Dirac Magnons in Honeycomb Ferromagnets
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2018 (English)In: Physical Review X, ISSN 2160-3308, E-ISSN 2160-3308, Vol. 8, no 1, article id 011010Article in journal (Refereed) Published
Abstract [en]

The discovery of the Dirac electron dispersion in graphene [A. H. Castro Neto, The Electronic Properties of Graphene, Rev. Mod. Phys. 81, 109 (2009)RMPHAT0034-686110.1103/RevModPhys.81.109] led to the question of the Dirac cone stability with respect to interactions. Coulomb interactions between electrons were shown to induce a logarithmic renormalization of the Dirac dispersion. With a rapid expansion of the list of compounds and quasiparticle bands with linear band touching [T. O. Wehling, Dirac Materials, Adv. Phys. 63, 1 (2014)ADPHAH0001-873210.1080/00018732.2014.927109], the concept of bosonic Dirac materials has emerged. We consider a specific case of ferromagnets consisting of van der Waals-bonded stacks of honeycomb layers, e.g., chromium trihalides CrX3 (X=F, Cl, Br and I), that display two spin wave modes with energy dispersion similar to that for the electrons in graphene. At the single-particle level, these materials resemble their fermionic counterparts. However, how different particle statistics and interactions affect the stability of Dirac cones has yet to be determined. To address the role of interacting Dirac magnons, we expand the theory of ferromagnets beyond the standard Dyson theory [F. J. Dyson, General Theory of Spin-Wave Interactions, Phys. Rev. 102, 1217 (1956)PHRVAO0031-899X10.1103/PhysRev.102.1217, F. J. Dyson, Thermodynamic Behavior of an Ideal Ferromagnet, Phys. Rev. 102, 1230 (1956)PHRVAO0031-899X10.1103/PhysRev.102.1230] to the case of non-Bravais honeycomb layers. We demonstrate that magnon-magnon interactions lead to a significant momentum-dependent renormalization of the bare band structure in addition to strongly momentum-dependent magnon lifetimes. We show that our theory qualitatively accounts for hitherto unexplained anomalies in nearly half-century-old magnetic neutron-scattering data for CrBr3 [W. B. Yelon and R. Silberglitt, Renormalization of Large-Wave-Vector Magnons in Ferromagnetic CrBr3 Studied by Inelastic Neutron Scattering: Spin-Wave Correlation Effects, Phys. Rev. B 4, 2280 (1971)PLRBAQ0556-280510.1103/PhysRevB.4.2280, E. J. Samuelsen, Spin Waves in Ferromagnetic CrBr3 Studied by Inelastic Neutron Scattering, Phys. Rev. B 3, 157 (1971)PLRBAQ0556-280510.1103/PhysRevB.3.157]. We also show that honeycomb ferromagnets display dispersive surface and edge states, unlike their electronic analogs.

Place, publisher, year, edition, pages
American Physical Society, 2018
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-222251 (URN)10.1103/PhysRevX.8.011010 (DOI)2-s2.0-85041071242 (Scopus ID)
Note

QC 20180205

Available from: 2018-02-05 Created: 2018-02-05 Last updated: 2018-05-16Bibliographically approved
3. Universal trends in interacting two-dimensional Dirac materials
Open this publication in new window or tab >>Universal trends in interacting two-dimensional Dirac materials
(English)Manuscript (preprint) (Other academic)
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-228000 (URN)
Note

QC 20180516

Available from: 2018-05-16 Created: 2018-05-16 Last updated: 2018-05-16Bibliographically approved
4. Landau-like states in neutral particles
Open this publication in new window or tab >>Landau-like states in neutral particles
2016 (English)In: PHYSICAL REVIEW B, ISSN 2469-9950, Vol. 93, no 23, article id 235134Article in journal (Refereed) Published
Abstract [en]

We show the emergence of a new type of dispersion relation for neutral atoms with an interesting similarity to the spectrum of two-dimensional electrons in an applied perpendicular constant magnetic field. These neutral atoms can be confined in toroidal optical traps and give quasi-Landau spectra. In strong contrast to the equidistant infinitely degenerate Landau levels for charged particles, the spectral gap for such two-dimensional neutral particles increases in particular electric-field configurations. The idea in the paper is motivated by the development in cold atom experiments and builds on the seminal paper of Aharonov and Casher.

National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-189803 (URN)10.1103/PhysRevB.93.235134 (DOI)000378105400001 ()2-s2.0-84976587185 (Scopus ID)
Funder
EU, European Research Council, DM 321031Swedish Research Council, 2012-3447Knut and Alice Wallenberg Foundation, KAW-2013.0020
Note

QC 20160720

Available from: 2016-07-20 Created: 2016-07-15 Last updated: 2018-05-16Bibliographically approved

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