Field theoretic study of electron-electron interaction effects in Dirac liquids

Abstract

The aim of this habilitation thesis is to present recent results, obtained during the period 2012-2017, related to interaction effects in condensed matter physics systems such as planar Dirac liquids, e.g., graphene and graphene-like systems, the surface states of some topological insulators and possibly half-filled fractional quantum Hall systems (for their Dirac composite fermions). These liquids are characterized by gapless bands, strong electron-electron interactions and emergent Lorentz invariance deep in the infra-red. We address a number of important issues raised by experiments on these systems covering subjects of wide current interest in low-energy (condensed matter) as well as high-energy (particle) physics. We shall consider in particular the subtle influence of interactions on transport properties and their supposedly crucial influence on a potential dynamical mass generation. The resolution of these problems will guide us from the thorough examination of the perturbative structure of gauge field theories to the development and application of non-perturbative approaches known from quantum electro/chromo-dynamics to address strong coupling issues.

Habilitation thesis, 188 pages, LaTeX file with feynMF package

References in corpus (56)

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• The electronic properties of graphene
• Two Dimensional Atomic Crystals
• Universal Dynamic Conductivity and Quantized Visible Opacity of Suspended Graphene
• The structure of suspended graphene sheets
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
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• Measurement of the Optical Conductivity of Graphene
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• Colloquium: The transport properties of graphene: An introduction
• Dirac materials
• Unusual Microwave Response of Dirac Quasiparticles in Graphene
• Scanning Tunneling Spectroscopy of Graphene on Graphite
• Interactions and phase transitions on graphene's honeycomb lattice
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• On the stability of U(1) spin liquids in two dimensions
• Is graphene in vacuum an insulator?
• On the universal AC optical background in graphene
• Probing spin-charge separation in a Tomonaga-Luttinger liquid
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Coulomb interaction, ripples, and the minimal conductivity of graphene
• Many-body interactions in quasi-freestanding graphene
• Lattice field theory simulations of graphene
• Resolution of singularities for multi-loop integrals
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Drude weight, plasmon dispersion, and a.c. conductivity in doped graphene sheets
• Boundary Conformal Field Theory and a Boundary Central Charge
• Five-loop quark mass and field anomalous dimensions for a general gauge group
• Interaction corrections to the polarization function of graphene
• On the Phase Structure of Many-Flavor QED${}_3$
• Monte-Carlo study of the electron transport properties of monolayer graphene within the tight-binding model
• Electromagnetic current correlations in reduced quantum electrodynamics
• Why does graphene behave as a weakly interacting system?
• Renormalization group approach to 2D Coulomb interacting Dirac fermions with random gauge potential
• Conductivity of interacting massless Dirac particles in graphene: Collisionless regime
• Four loop renormalization of the Gross-Neveu model
• Interaction corrections to the minimal conductivity of graphene via dimensional regularization
• Landau level spectroscopy of electron-electron interactions in graphene
• Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
• Unitarity of theories containing fractional powers of the d'Alembertian operator
• Two-loop five-point massless QCD amplitudes within the IBP approach
• Critical behaviour of reduced QED${}_{4,3}$ and dynamical fermion gap generation in graphene
• Note on an application of the method of uniqueness to reduced quantum electrodynamics
• On the exact quantum scale invariance of three-dimensional reduced QED theories
• Critical behaviour of ($2+1$)-dimensional QED: $1/N_f$-corrections in an arbitrary non-local gauge
• Two-loop fermion self-energy and propagator in reduced QED${}_{3,2}$
• Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultra-relativistic limit of Dirac liquids
• A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories
• Fermion bilinear operator critical exponents at $O(1/N^2)$ in the QED-Gross-Neveu universality class
• Magnetic Catalysis in Graphene Effective Field Theory
• GraphState - a tool for graph identification and labelling
• The role of frequency dependence in dynamical gap generation in graphene
• Quantum Valley Hall Effect in Massive Dirac Systems Coupled to a Scalar Field
• Critical number of fermions in three-dimensional QED

Cited by in corpus (5)

• Multi-loop techniques for massless Feynman diagram calculations
• On Marginal Operators in Boundary Conformal Field Theory
• The Casimir energy in terms of boundary quantum field theory: the QED case
• Critical properties of three-dimensional many-flavour QEDs
• $\mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene