Temperature Dependence of the Response Functions of Graphene: Impact on Casimir and Casimi-Polder Forces in and out of Thermal Equilibrium

Abstract

We review and obtain some new results on the temperature dependence of spatially nonlocal response functions of graphene and their applications to calculation of both the equilibrium and nonequilibrium Casimir and Casimir-Polder forces. After a brief summary of the properties of the polarization tensor of graphene obtained within Dirac model in the framework of quantum field theory, we derive the expressions for the longitudinal and transverse dielectric functions. The behavior of these functions at different temperatures is investigated in the regions below and above the threshold. Special attention is paid to the double pole at zero frequency which is present in the transverse response function of graphene. An application of the response functions of graphene to calculation of the equilibrium Casimir force between two graphene sheets and Casimir-Polder forces between an atom (nanoparticle) and a graphene sheet is considered with due attention to the role of a nonzero energy gap, chemical potential and a material substrate underlying the graphene sheet. The same subject is discussed for out-of-thermal-equilibrium Casimir and Casimir-Polder forces. The role of the obtained and presented results for fundamental science and nanotechnology is outlined.

21 pages, 7 figures

References in corpus (61)

• The electronic properties of graphene
• A tight-binding approach to uniaxial strain in graphene
• Optical properties of graphene
• Colloquium: The transport properties of graphene: An introduction
• Optical far-infrared properties of graphene monolayer and multilayers
• The optical conductivity of graphene in the visible region of the spectrum
• Magneto-optical conductivity in Graphene
• Space-time dispersion of graphene conductivity
• Electronic transport in graphene: A semi-classical approach including midgap states
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• On the minimal conductivity of graphene
• Dynamical polarization, screening, and plasmons in gapped graphene
• Robust Transport Properties in Graphene
• New asymptotic behaviour of the surface-atom force out of thermal equilibrium
• Anomalous Absorption Line in the Magneto-Optical Response of Graphene
• Germanene termination of Ge${}_2$Pt crystals on Ge(110)
• Casimir-Lifshitz force out of thermal equilibrium
• Phenomenological study of the electronic transport coefficients of graphene
• Ultrafast Radiative Heat Transfer
• Retarded interactions in Graphene systems
• Casimir-Lifshitz force out of thermal equilibrium and asymptotic non-additivity
• Van der Waals and Casimir interactions between two graphene sheets
• Theory of the Casimir interaction for graphene-coated substrates using the polarization tensor and comparison with experiment
• Dynamics of the particle - hole pair creation in graphene
• Low frequency optical conductivity in graphene and in other scale-invariant two-band systems
• Measurement of the Casimir Force between 0.2 and 8 mum: Experimental Procedures and Comparison with Theory
• Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation
• Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution
• Observability of thermal effects in the Casimir interaction from graphene-coated substrates
• Ground-state properties of gapped graphene using the random phase approximation
• Origin of large thermal effect in the Casimir interaction between two graphene sheets
• Demonstration of an Unusual Thermal Effect in the Casimir Force from Graphene
• Tuning quantum fluctuations with an external magnetic field: Casimir-Polder interaction between an atom and a graphene sheet
• Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene
• Dynamical Polarizability of Graphene with Spatial Dispersion
• Transport in a Clean Graphene Sheet at Finite Temperature and Frequency
• Emending thermal dispersion interactions of Li, Na, K and Rb alkali metal-atoms with graphene in the Dirac model
• Numerical study of the conductivity of graphene monolayer within the effective field theory approach
• Experimental and theoretical investigation of the thermal effect in the Casimir interaction from graphene
• Dynamical current-current susceptibility of gapped graphene
• Conductivity of graphene in the framework of Dirac model: Interplay between nonzero mass gap and chemical potential
• Thermal effect in the Casimir force for graphene and graphene-coated substrates: Impact of nonzero mass gap and chemical potential
• Numerical calculation of the Casimir-Polder interaction between a graphene sheet with vacancies and an atom
• Quantum electrodynamic approach to the conductivity of gapped graphene
• Temperature dependent screened electronic transport in gapped graphene
• Surface plasmons for doped graphene
• Electric conductivity in graphene: Kubo model versus a nonlocal quantum field theory model
• Graphene through the looking glass of QFT
• Current status of the problem of thermal Casimir force
• Casimir interactions in strained graphene systems
• Nonequilibrium effects in the Casimir force between two similar metallic plates kept at different temperatures
• Casimir-Polder attraction and repulsion between nanoparticles and graphene in out-of-thermal-equilibrium conditions
• Quantum field theoretical framework for the electromagnetic response of graphene and dispersion relations with implications to the Casimir effect
• The low-temperature expansion of the Casimir-Polder free energy of an atom with graphene
• On the convergence of the polarization tensor in space-time of three dimensions
• Impact of Mass-Gap on the Dispersion Interaction of Nanoparticles with Graphene out of Thermal Equilibrium
• The Casimir Force between Two Graphene Sheets: 2D Fresnel Reflection Coefficients, Contributions of Different Polarizations, and the Role of Evanescent Waves
• Nonequilibrium Casimir-Polder Force between Nanoparticles and Graphene-Coated Silica Plate: Combined Effect of the Chemical Potential and Mass Gap
• Casimir-Polder Force on Atoms or Nanoparticles from the Gapped and Doped Graphene: Asymptotic Behavior at Large Separations
• Nonequilibrium Casimir pressure for two graphene-coated plates: Quantum field theoretical approach
• Large-Separation Behavior of the Casimir-Polder Force from Real Graphene Sheet Deposited on a Dielectric Substrate