Topological semimetals are unique quantum materials with protected energy band crossings. They bridge the gap between topological insulators and conventional metals, exhibiting exotic electronic properties that provide insights into fundamental quantum phenomena.
These materials possess nontrivial band topology, linear energy dispersion, and symmetry-protected features. They display unique and bulk-boundary correspondence, leading to fascinating transport properties and potential applications in next-generation electronics and quantum computing.
Fundamentals of topological semimetals
Topological semimetals represent a unique class of quantum materials in condensed matter physics characterized by protected crossings of energy bands
These materials bridge the gap between topological insulators and conventional metals, exhibiting exotic electronic properties
Understanding topological semimetals provides insights into fundamental quantum phenomena and potential applications in next-generation electronics
Band structure characteristics
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Possess nontrivial band topology with protected band crossings at discrete points or along lines in momentum space
Exhibit linear energy dispersion near the crossing points, resembling massless Dirac or Weyl fermions
Feature bulk band degeneracies that cannot be removed by small perturbations without breaking certain symmetries
Display unique low-energy excitations distinct from conventional metals or semiconductors
Symmetry protection mechanisms
Rely on crystalline symmetries (inversion, rotation, mirror) to protect topological features
Time-reversal symmetry plays a crucial role in certain types of topological semimetals ()
Require the presence of specific symmetries to maintain the stability of band crossings
Breaking of symmetries can lead to transitions between different topological phases or to trivial semimetals
Bulk-boundary correspondence
Establishes a fundamental relationship between bulk topological properties and surface state characteristics
Manifests as unique surface states () connecting bulk band crossing points
Guarantees the existence of topologically protected surface states immune to backscattering
Provides a powerful tool for experimental verification of topological semimetal phases
Types of topological semimetals
Topological semimetals encompass various subclasses with distinct band structures and symmetry requirements
Each type exhibits unique physical properties and potential applications in condensed matter physics
Understanding the differences between these types aids in material design and experimental investigations
Weyl semimetals
Feature isolated band crossing points called Weyl nodes acting as monopoles of Berry curvature
Require breaking of either time-reversal or inversion symmetry
Exhibit Fermi arc surface states connecting projections of bulk Weyl nodes
Display the leading to negative magnetoresistance (, )
Dirac semimetals
Possess four-fold degenerate band crossing points protected by crystalline symmetries
Maintain both time-reversal and inversion symmetry
Can be viewed as two copies of with opposite chirality
Exhibit linear energy dispersion in all three momentum directions (Cd3As2, Na3Bi)
Nodal line semimetals
Characterized by band crossings along closed loops or lines in momentum space
Protected by combinations of symmetries such as mirror reflection and time-reversal
Display drumhead surface states nested inside the projection of bulk nodal lines
Exhibit unique and optical responses (PbTaSe2, ZrSiS)
Topological invariants
serve as mathematical tools to classify and characterize topological phases in condensed matter systems
These quantities remain unchanged under continuous deformations of the system, providing robust indicators of topological properties
Understanding topological invariants aids in predicting and analyzing the behavior of topological semimetals
Berry phase and curvature
Berry phase quantifies the geometric phase acquired by a quantum state under adiabatic evolution
Berry curvature acts as an effective magnetic field in momentum space, influencing electron dynamics
Integral of Berry curvature over a closed surface yields topological invariants (Chern numbers)
Plays a crucial role in determining the transport properties of topological semimetals
Chern number
Integer-valued topological invariant characterizing the global topology of band structures
Calculated by integrating the Berry curvature over a closed two-dimensional manifold in momentum space
Determines the number and chirality of edge states in quantum Hall systems and Weyl semimetals
Non-zero Chern number indicates the presence of topologically protected surface states
Z2 invariant
Characterizes time-reversal invariant topological insulators and some classes of topological semimetals
Takes values of either 0 (trivial) or 1 (topological) for each independent momentum direction
Determined by the parity eigenvalues of occupied bands at time-reversal invariant momenta
Predicts the existence of protected surface states in topological insulators and Dirac semimetals
Fermi arcs and surface states
Fermi arcs and surface states represent unique manifestations of bulk topology in topological semimetals
These features provide experimental signatures for identifying and characterizing topological semimetal phases
Understanding the properties of surface states aids in developing novel devices exploiting topological properties
Formation of Fermi arcs
Arise as topologically protected surface states connecting projections of bulk Weyl nodes
Result from the bulk-boundary correspondence principle in topological semimetals
Form open contours in the surface Brillouin zone, unlike closed Fermi surfaces in conventional metals
Length and shape of Fermi arcs depend on the separation and position of bulk Weyl nodes
Experimental observations
Directly visualized using
Appear as distinct features in the surface electronic structure of Weyl and Dirac semimetals
Exhibit spin-momentum locking, with spin orientation determined by the chirality of bulk nodes
Observed in various materials (TaAs, Cd3As2) confirming theoretical predictions of topological semimetal phases
Surface state properties
Display robustness against non-magnetic impurities due to topological protection
Exhibit high mobility and unique transport characteristics distinct from bulk states
Contribute to novel quantum oscillations in
Offer potential applications in spintronics and low-dissipation electronic devices
Transport properties
Transport properties of topological semimetals reveal unique signatures of their nontrivial band topology
These characteristics distinguish topological semimetals from conventional metals and semiconductors
Understanding transport phenomena aids in developing novel electronic and spintronic devices
Chiral anomaly
Quantum anomaly leading to non-conservation of chiral charge in the presence of parallel electric and magnetic fields
Manifests as pumping of electrons between Weyl nodes of opposite chirality
Results in enhanced conductivity along the direction of applied magnetic field
Provides a distinctive experimental signature for identifying Weyl and Dirac semimetals
Negative magnetoresistance
Unusual decrease in electrical resistance with increasing magnetic field
Arises from the chiral anomaly in Weyl and Dirac semimetals
Exhibits a characteristic angular dependence, maximized when electric and magnetic fields are parallel
Serves as a key experimental probe for verifying the topological nature of semimetals
Quantum oscillations
Periodic oscillations in various physical properties (resistivity, magnetization) as a function of inverse magnetic field
Reveal information about the Fermi surface topology and electron dynamics
Display unique features in topological semimetals due to the presence of Weyl or Dirac points
Provide insights into the Berry phase and non-trivial band topology of the system
Experimental techniques
Experimental techniques play a crucial role in identifying and characterizing topological semimetals
These methods provide direct evidence for the unique electronic structure and transport properties of topological materials
Combining multiple experimental approaches allows for comprehensive understanding of topological semimetal physics
ARPES for band structure
Angle-resolved photoemission spectroscopy directly maps the electronic band structure of materials
Reveals linear band crossings and Fermi arc surface states in topological semimetals
Provides information on the spin texture and momentum-dependence of electronic states
Enables visualization of bulk and surface states, confirming theoretical predictions (Cd3As2, TaAs)
Magnetotransport measurements
Probe the response of electrical conductivity to applied magnetic fields
Reveal signatures of the chiral anomaly through negative magnetoresistance
Allow for the observation of quantum oscillations providing information on Fermi surface topology
Enable the study of Berry phase effects and non-trivial band topology in topological semimetals
Scanning tunneling spectroscopy
Provides local information on the electronic density of states with atomic resolution
Allows for direct visualization of surface states and their spatial distribution
Reveals signatures of bulk band topology through quasiparticle interference patterns
Enables the study of impurity effects and local electronic structure in topological semimetals
Materials and realizations
Topological semimetals can be realized in various material systems and engineered structures
Understanding different realizations aids in exploring fundamental physics and developing practical applications
Diverse material platforms offer opportunities for tuning and optimizing topological properties
Include transition metal pnictides (TaAs, NbAs) as Weyl semimetals
Feature Dirac semimetals in compounds like Cd3As2 and Na3Bi
Display nodal line semimetal behavior in materials such as PbTaSe2 and ZrSiS
Engineered heterostructures
Artificially designed layered structures to realize topological semimetal phases
Include topological insulator/normal insulator superlattices for Weyl semimetal states
Utilize strain engineering and interface effects to induce topological phase transitions
Allow for precise control and tuning of topological properties through material composition and layer thicknesses
Photonic and acoustic analogs
Artificial structures mimicking electronic band structures in electromagnetic or acoustic systems
Realize Weyl points and nodal lines in specially designed photonic crystals
Demonstrate topological surface states and bulk-boundary correspondence in acoustic metamaterials
Provide macroscopic platforms for studying topological physics and developing novel wave-guiding devices
Applications and future prospects
Topological semimetals offer exciting possibilities for next-generation technologies and fundamental research
Their unique properties enable novel applications in various fields of condensed matter physics and beyond
Ongoing research aims to harness the potential of topological semimetals for practical device applications
Spintronics and quantum computing
Exploit spin-momentum locking of surface states for efficient spin current generation
Utilize topological protection to create robust quantum bits (qubits) for quantum computation
Explore Majorana fermions in topological superconductor heterostructures for topological quantum computing
Develop novel spintronic devices with low power consumption and high efficiency
High-performance electronics
Leverage high carrier mobility and linear dispersion for ultra-fast electronic devices
Utilize chiral anomaly for novel magnetoresistive sensors and memory devices
Explore possibilities for low-dissipation electronics exploiting topological surface states
Develop terahertz detectors and emitters based on the unique optical properties of topological semimetals
Topological quantum chemistry
Apply concepts from topological semimetals to predict and design new topological materials
Develop systematic classification schemes for topological phases in real materials
Utilize symmetry indicators and band representations to automate the discovery of topological materials
Explore the interplay between topology and strong correlations in quantum materials
Key Terms to Review (18)
Alexei Kitaev: Alexei Kitaev is a prominent theoretical physicist known for his groundbreaking contributions to the fields of quantum computing and condensed matter physics. He is particularly recognized for proposing the concept of topological quantum computation, which leverages anyons and braiding statistics to achieve fault-tolerant quantum information processing, a significant advancement in understanding topological phases of matter.
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.
Band Theory: Band theory explains the electronic properties of solids, particularly how energy levels are structured in materials like metals, semiconductors, and insulators. It describes how the overlapping atomic orbitals create energy bands, with the conduction band and valence band defining the material's conductivity. Understanding this concept is crucial for grasping the behavior of various materials in different contexts, such as electrical conduction, optical properties, and magnetic behaviors.
Chiral Anomaly: Chiral anomaly refers to a phenomenon in quantum field theory where the conservation of chirality is violated due to quantum effects, specifically in the presence of gauge fields. This violation leads to important physical consequences, especially in systems with topological features, like certain semimetals, where it manifests as a non-conservation of chiral charge and can give rise to observable effects such as a chiral magnetic effect.
Dirac Semimetals: Dirac semimetals are a class of materials characterized by the presence of Dirac points in their electronic band structure, where the conduction and valence bands meet at discrete points in momentum space. These materials exhibit massless Dirac-like excitations, leading to unique electronic properties such as high mobility and unusual transport phenomena. They are considered topological semimetals due to their non-trivial topology, which is connected to the robustness of their electronic states against perturbations.
Fermi arcs: Fermi arcs are surface states that appear in certain topological semimetals, characterized by an open curve on the Fermi surface rather than the closed loops typical in conventional metals. These arcs arise due to the nontrivial topology of the electronic band structure, indicating the presence of Weyl points, which are locations in momentum space where the conduction and valence bands touch. Fermi arcs reveal important information about the nature of surface states and their relation to bulk properties, showcasing unique electronic behaviors in topological materials.
K-space topology: K-space topology refers to the mathematical framework used to describe the properties and relationships of electronic states in momentum space, or k-space. This concept is essential in understanding how the electronic band structure of materials can lead to novel physical phenomena, particularly in the context of topological semimetals, where the arrangement of electronic states and their connectivity in k-space gives rise to unique surface states and protected band crossings.
Lifshitz Transition: A Lifshitz transition is a quantum phase transition that occurs when the topology of the Fermi surface changes as a function of external parameters, such as pressure, temperature, or doping. This change can lead to significant alterations in the electronic properties of materials, connecting deeply with the concept of Fermi surfaces and providing insights into the behavior of topological semimetals.
Magnetotransport measurements: Magnetotransport measurements refer to experimental techniques used to study the electrical transport properties of materials under the influence of a magnetic field. These measurements provide insights into how charge carriers move within materials and can reveal important characteristics like mobility, conductivity, and the presence of topologically protected states. They are especially crucial for understanding phenomena in advanced materials such as topological semimetals and fractional quantum Hall systems.
Nbas: Nodal line semimetals (nbas) are materials characterized by the presence of nodal lines in their band structure, where the conduction and valence bands touch along one-dimensional lines in momentum space. These nodal lines can lead to unique electronic properties, such as the emergence of topologically protected surface states and a highly sensitive response to external perturbations.
Non-trivial band structure: A non-trivial band structure refers to a type of electronic band structure that exhibits topological characteristics, which leads to unique physical properties not found in conventional materials. These structures often indicate the presence of protected surface states or edge states, which are robust against perturbations and disorder, making them essential for understanding phenomena like topological insulators and semimetals.
Quantum Oscillations: Quantum oscillations are phenomena observed in solid-state physics that arise due to the quantum mechanical behavior of electrons in a material, particularly under the influence of a magnetic field. These oscillations reflect the periodic nature of the energy levels and are directly related to the shape and characteristics of the Fermi surface, as well as revealing insights into topological features of materials.
Shou-Cheng Zhang: Shou-Cheng Zhang is a prominent physicist known for his significant contributions to condensed matter physics, particularly in the study of topological phases of matter and their implications. His research has played a crucial role in understanding topological semimetals and the Berry phase, advancing our knowledge of how these phenomena manifest in materials and their potential applications in future technologies.
Surface states: Surface states are electronic states that exist at the boundary of a material, particularly in low-dimensional systems like two-dimensional materials or topological semimetals. These states arise due to the disruption of periodic potential at the surface, leading to localized electronic states that can influence various physical properties such as conductivity and magnetism.
Taas: Taas refers to a topological feature associated with certain types of materials called topological semimetals, where the band structure exhibits non-trivial topology leading to unique electronic properties. This feature is crucial for understanding the behaviors of these materials, which may host exotic phenomena such as protected surface states and unusual responses to external fields. The study of taas is essential for exploring applications in next-generation electronics and quantum computing.
Topological invariants: Topological invariants are properties of a system that remain unchanged under continuous deformations, such as stretching or bending, without tearing or gluing. These invariants play a crucial role in classifying phases of matter, especially in systems exhibiting phenomena like the Quantum Hall effect, topological insulators, and topological semimetals. They help us understand how certain physical characteristics, like edge states or surface states, can arise from the underlying topology of a material's electronic structure.
Topological phase transition: A topological phase transition is a transformation between different phases of matter that is characterized by changes in the global properties of a system, rather than local order parameters. These transitions often involve changes in the topological invariants of the system, which can lead to significant changes in electronic and physical properties, particularly in materials like semimetals and insulators. Such transitions can give rise to interesting phenomena like edge states and exotic surface states that have implications for quantum computing and material science.
Weyl semimetals: Weyl semimetals are a class of materials that host Weyl fermions as low-energy excitations, characterized by the presence of Weyl points in their band structure. These points are created when conduction and valence bands touch, leading to a nontrivial topological phase. Weyl semimetals exhibit unique electronic properties, such as high mobility and chiral anomaly, making them an exciting area of study in condensed matter physics.