Heavy fermions are fascinating materials that bridge the gap between ordinary metals and strongly correlated systems. They exhibit unique properties due to strong electron interactions, including massively enhanced effective electron masses and unusual low-temperature behaviors.
These systems provide a playground for studying complex quantum phenomena. From the to , heavy fermions offer insights into fundamental physics and potential applications in areas like thermoelectrics and quantum computing.
Characteristics of heavy fermions
Heavy fermion systems exhibit unique properties in condensed matter physics due to strong electron correlations
These materials bridge the gap between conventional metals and strongly correlated electron systems, providing insights into complex quantum phenomena
Effective mass enhancement
Electrons in heavy fermion compounds behave as if they have masses 100-1000 times greater than free electrons
Renormalization of electron mass results from strong interactions between conduction electrons and localized f-electrons
Effective mass enhancement manifests in enhanced electronic specific heat coefficient (γ) and reduced Fermi velocity
Landau Fermi liquid theory describes the quasiparticle behavior with modified parameters
Low temperature behavior
Heavy fermion systems display anomalous low-temperature properties deviating from conventional metals
Specific heat follows C = γT + βT³ with an unusually large electronic contribution (γ)
Electrical resistivity exhibits a T² dependence at low temperatures, characteristic of Fermi liquid behavior
Magnetic susceptibility shows enhanced Pauli paramagnetism with temperature-independent behavior at low T
Kondo effect in heavy fermions
Kondo effect plays a crucial role in the formation of heavy fermion states
Localized magnetic moments (from f-electrons) interact with conduction electrons, leading to moment screening
Kondo temperature (TK) marks the onset of coherent scattering and formation of the heavy fermion state
Lattice of Kondo impurities in heavy fermion compounds results in a collective Kondo effect
Competition between Kondo screening and RKKY interactions determines the ground state properties
Electronic structure
Hybridization of f-electrons
f-electrons in heavy fermion compounds hybridize with conduction electrons, forming composite quasiparticles
Hybridization strength determines the degree of f-electron localization or itinerancy
Dual nature of f-electrons (localized and itinerant) leads to complex electronic properties
Hybridization gap forms near the Fermi level, influencing low-energy excitations
Fermi surface properties
Heavy fermion compounds exhibit large Fermi surfaces, including f-electron contributions
volume obeys Luttinger's theorem, counting both conduction and f-electrons
Multiple Fermi surface sheets often observed, reflecting complex band structure
Heavy quasiparticle bands lead to reduced Fermi velocities and enhanced at EF
Band structure anomalies
Flat bands near the Fermi level result from strong electron correlations and hybridization
Renormalized band structure shows narrow f-derived bands with large effective masses
Hybridization gaps and pseudogaps appear in the electronic density of states
Spin-orbit coupling and crystal field effects further complicate the band structure
Heavy fermion materials
Cerium compounds
CeAl3 first discovered heavy fermion compound, exhibiting large specific heat coefficient
displays near quantum critical point
CeRhIn5 shows interplay between antiferromagnetism and under pressure
CeCoIn5 high-temperature heavy fermion superconductor with unconventional pairing symmetry
Uranium compounds
UPt3 exhibits multiple superconducting phases with complex order parameter symmetry
URu2Si2 displays hidden order phase transition and unconventional superconductivity
UBe13 shows coexistence of superconductivity and
U-based compounds often exhibit stronger hybridization compared to Ce-based systems
Ytterbium compounds
YbRh2Si2 widely studied for its proximity to quantum criticality and non-Fermi liquid behavior
YbAlB4 first discovered Yb-based heavy fermion superconductor
YbNi2Ge2 exhibits valence fluctuations and Kondo lattice behavior
Yb compounds often considered electron-hole analogues of Ce systems due to 4f13 configuration
Quantum critical phenomena
Non-Fermi liquid behavior
Breakdown of Fermi liquid theory near quantum critical points in heavy fermion systems
Anomalous power-law temperature dependences in thermodynamic and transport properties
Divergence of effective mass and quasiparticle scattering rate at criticality
Emergence of local quantum criticality with critical destruction of Kondo effect
Quantum phase transitions
Zero-temperature phase transitions driven by non-thermal control parameters (pressure, magnetic field, doping)
Continuous quantum phase transitions characterized by quantum fluctuations and scaling behavior
Critical slowing down of characteristic energy scales near quantum critical point
Quantum critical fan in temperature-control parameter phase diagram
Magnetic instabilities
Competition between Kondo screening and RKKY interactions leads to magnetic instabilities
Antiferromagnetic ordering often observed in heavy fermion compounds at low temperatures
Suppression of by external parameters can induce quantum critical behavior
Spin density wave instabilities and unconventional magnetic phases (multipolar order)
Experimental techniques
Specific heat measurements
Crucial for determining the electronic specific heat coefficient (γ) and effective mass enhancement
Low-temperature measurements reveal power-law behaviors near quantum critical points
Entropy analysis provides insights into the degeneracy of ground states
Specific heat jumps at phase transitions indicate changes in degrees of freedom
de Haas-van Alphen effect
Quantum oscillations in magnetization reveal Fermi surface topology and quasiparticle effective masses
Measurement of angular dependence allows mapping of three-dimensional Fermi surfaces
Determination of cyclotron effective masses provides direct evidence of mass enhancement
Observation of magnetic breakdown effects in heavy fermion compounds
Neutron scattering
Probes magnetic structure and excitations in heavy fermion materials
Inelastic reveals spin fluctuation spectra and Kondo resonance
Observation of magnetic Bragg peaks confirms long-range magnetic order
Spin resonance in superconducting state provides evidence for unconventional pairing
Theoretical models
Anderson lattice model
Describes periodic array of localized f-electron states hybridizing with conduction electrons
Includes on-site Coulomb repulsion for f-electrons, capturing strong correlation effects
Hybridization leads to formation of coherent heavy quasiparticle bands
Large-N expansion and slave boson techniques used to solve the model in different limits
Kondo lattice model
Focuses on spin degrees of freedom, treating f-electrons as localized magnetic moments
Kondo coupling between local moments and conduction electrons leads to screening
RKKY interaction between local moments mediated by conduction electrons
Doniach phase diagram describes competition between Kondo effect and magnetic ordering
Periodic Anderson model
Combines features of Anderson impurity model with lattice periodicity
Includes both charge and spin fluctuations of f-electrons
Dynamical mean-field theory (DMFT) provides a powerful tool for solving the model
Captures heavy fermion formation, Kondo insulators, and mixed valence behavior
Superconductivity in heavy fermions
Unconventional pairing mechanisms
Cooper pairing mediated by spin fluctuations instead of phonons
Non-s-wave order parameter symmetry (d-wave, p-wave) common in heavy fermion superconductors
Magnetically mediated superconductivity often observed near magnetic quantum critical points
Multi-component order parameters and time-reversal symmetry breaking states
Coexistence with magnetism
Superconductivity and magnetism often compete but can coexist in some heavy fermion compounds
Microscopic coexistence observed in UPd2Al3 and CeRhIn5 under pressure
Interplay between superconducting and magnetic order parameters leads to novel phases
Magnetic fluctuations may enhance or suppress superconductivity depending on the system
Critical temperature vs pressure
Pressure often used to tune heavy fermion systems through quantum phase transitions
Superconducting dome typically observed near the suppression of magnetic order
Non-monotonic pressure dependence of critical temperature in some compounds
Valence transitions under pressure can dramatically affect superconducting properties
Applications and future prospects
Thermoelectric materials
Heavy fermion compounds exhibit enhanced thermoelectric power due to large effective masses
Potential applications in solid-state cooling and power generation devices
YbAl3 and CePd3 show promising thermoelectric performance at low temperatures
Challenges include improving efficiency and developing materials for room temperature applications
Quantum computing potential
Topological superconductivity in heavy fermion systems may host Majorana fermions
Potential applications in topological quantum computation and error-resistant qubits
UPt3 proposed as a candidate for chiral superconductivity with non-Abelian vortex states
Challenges include realizing and manipulating topological states in real materials
Challenges in heavy fermion research
Synthesizing high-quality single crystals of new heavy fermion compounds
Developing theoretical tools to accurately describe strongly correlated electron systems
Understanding the interplay between multiple degrees of freedom (charge, spin, orbital)
Exploring novel quantum phases and non-equilibrium phenomena in heavy fermion materials
Key Terms to Review (18)
Angle-resolved photoemission spectroscopy (ARPES): Angle-resolved photoemission spectroscopy (ARPES) is a powerful experimental technique used to map the electronic structure of materials by measuring the energy and momentum of electrons ejected from a sample when illuminated by ultraviolet or X-ray light. This method provides insight into the density of states, allowing researchers to investigate surface and bulk electronic properties, especially in materials exhibiting complex behaviors like topological insulators and heavy fermions.
C. s. lue: c. s. lue, or crystal structure lattice energy, refers to the energy associated with the interactions between atoms within a crystal lattice. This term is crucial in understanding how the arrangement of heavy fermions affects their properties and behavior in condensed matter systems. The c. s. lue plays a significant role in determining electronic properties, magnetism, and thermal behavior of materials featuring heavy fermions.
Cecu6: Cecu6 refers to a specific heavy fermion compound that exhibits unique electronic properties and is of great interest in condensed matter physics. It showcases fascinating behaviors such as non-Fermi liquid characteristics and magnetic order, often arising from the interplay between localized f-electrons and conduction electrons, which can lead to exotic phenomena like quantum criticality.
Density of States: The density of states (DOS) is a crucial concept that quantifies the number of available quantum states at each energy level for particles, typically electrons, within a system. It is fundamental in understanding how particles populate energy levels and relates directly to various phenomena, including conduction properties and phase transitions in materials.
Fermi surface: The Fermi surface is the boundary in momentum space that separates occupied from unoccupied electron states at absolute zero temperature. It plays a crucial role in determining the electronic properties of materials, as it defines how electrons behave in solids and influences phenomena like electrical conductivity and heat capacity.
Heavy effective mass: Heavy effective mass refers to a phenomenon in condensed matter physics where the effective mass of charge carriers, like electrons, is significantly greater than their actual mass due to strong electron correlations and interactions with the crystal lattice. This concept is particularly significant in materials known as heavy fermion systems, where the behavior of electrons deviates from classical expectations, leading to unique electrical, magnetic, and thermal properties.
Interband coupling: Interband coupling refers to the interaction between different electronic bands in a material, which can lead to mixing of states and affect the overall electronic properties. This phenomenon is particularly significant in materials where heavy fermions are present, as it can influence behaviors like conductivity and magnetic ordering. Interband coupling plays a crucial role in understanding the complex phenomena associated with heavy fermions and their unusual characteristics.
Itinerant electron model: The itinerant electron model describes the behavior of conduction electrons in a solid, emphasizing their ability to move freely throughout the material, which is essential for understanding electrical conductivity. This model is particularly relevant in the context of heavy fermion systems, where the interactions between localized magnetic moments and itinerant electrons lead to unique physical properties, such as enhanced effective mass and unusual temperature-dependent behaviors.
Kondo effect: The Kondo effect is a phenomenon observed in condensed matter physics where the electrical resistance of a metal containing magnetic impurities decreases as the temperature is lowered, resulting in an increase in the material's conductivity. This effect is tied to the interactions between conduction electrons and localized magnetic moments, leading to a unique behavior that enhances the low-temperature properties of heavy fermion systems.
Kondo lattice model: The Kondo lattice model is a theoretical framework that describes the behavior of strongly correlated electron systems, particularly in the context of heavy fermions and magnetic impurities in metals. It captures the interplay between localized magnetic moments (often from f-electrons) and the conduction electrons, leading to phenomena such as heavy fermion behavior and non-Fermi liquid properties.
Magnetic order: Magnetic order refers to the arrangement of magnetic moments in a material, leading to the emergence of a net magnetization within the material. This phenomenon can occur in various forms, such as ferromagnetism, antiferromagnetism, and ferrimagnetism, each representing different ways magnetic moments align relative to one another. Understanding magnetic order is crucial when studying materials with strong electron correlations, such as heavy fermions, as it can significantly influence their electronic properties and phase transitions.
Neutron scattering: Neutron scattering is a powerful experimental technique used to probe the structure and dynamics of materials at the atomic scale by analyzing the scattering of neutrons off atomic nuclei. This method provides valuable insights into various physical properties, such as lattice vibrations, magnetic ordering, and phase transitions, making it an essential tool for understanding complex phenomena in condensed matter physics.
Non-fermi liquid behavior: Non-fermi liquid behavior refers to the anomalous properties of certain materials that deviate from the conventional fermi liquid theory, characterized by a lack of well-defined quasiparticles and linear temperature dependence of resistivity. This behavior often arises in systems with strong correlations between electrons, where interactions lead to unconventional metallic states, which are particularly evident in heavy fermion compounds and Kondo systems.
P. W. Anderson: P. W. Anderson was a renowned physicist known for his significant contributions to condensed matter physics, particularly in the study of heavy fermions and the theory of localization. His work laid the foundation for understanding the unusual electronic properties of materials with strongly correlated electrons, which are crucial in heavy fermion systems that exhibit extraordinary behaviors like non-Fermi liquid behavior and superconductivity.
Quantum criticality: Quantum criticality refers to the behavior of a system at a continuous phase transition that occurs at absolute zero temperature, where quantum fluctuations dominate the physics. It is characterized by a critical point where the properties of the system change dramatically, influencing the system's excitations and leading to a range of phenomena such as unconventional superconductivity and magnetism. Understanding quantum criticality is crucial for exploring various complex materials and phenomena, particularly in the context of heavy fermions and the Kondo effect.
Spin fluctuations: Spin fluctuations refer to the temporary changes in the orientation of the spin of electrons or magnetic moments in a material, which can occur due to thermal energy or interactions between particles. These fluctuations play a crucial role in various physical phenomena, including magnetism and electrical conductivity, and are particularly significant in the context of strongly correlated electron systems, where they influence the behavior of Mott insulators and heavy fermion materials.
Superconductivity: Superconductivity is a phenomenon where a material can conduct electricity without any resistance when cooled below a certain critical temperature. This unique property allows superconductors to carry electric current with zero energy loss, which has implications for various advanced technologies and is deeply connected to the behavior of electrons in materials, crystal structures, and quantum mechanics.
YBrH$_2$Si$_2$: yBrH$_2$Si$_2$ is a chemical compound that is part of a family of heavy fermion materials known for exhibiting unusual electronic properties and strong correlations between electrons. This compound has garnered attention due to its potential role in understanding the behavior of electrons in low-dimensional systems and its implications in the study of quantum phase transitions and superconductivity.