Landau theory of helical Fermi liquids

Abstract

Landau's phenomenological theory of Fermi liquids is a fundamental paradigm in many-body physics that has been remarkably successful in explaining the properties of a wide range of interacting fermion systems, such as liquid helium-3, nuclear matter, and electrons in metals. The d-dimensional boundaries of (d+1)-dimensional topological phases of matter such as quantum Hall systems and topological insulators provide new types of many-fermion systems that are topologically distinct from conventional d-dimensional many-fermion systems. We construct a phenomenological Landau theory for the two-dimensional helical Fermi liquid found on the surface of a three-dimensional time-reversal invariant topological insulator. In the presence of rotation symmetry, interactions between quasiparticles are described by ten independent Landau parameters per angular momentum channel, by contrast with the two (symmetric and antisymmetric) Landau parameters for a conventional spin-degenerate Fermi liquid. We then project quasiparticle states onto the Fermi surface and obtain an effectively spinless, projected Landau theory with a single projected Landau parameter per angular momentum channel that captures the spin-momentum locking or nontrivial Berry phase of the Fermi surface. As a result of this nontrivial Berry phase, projection to the Fermi surface can increase or lower the angular momentum of the quasiparticle interactions. We derive equilibrium properties, criteria for Fermi surface instabilities, and collective mode dispersions in terms of the projected Landau parameters. We briefly discuss experimental means of measuring projected Landau parameters.

6 pages + 20 pages of supplementary information

References in corpus (10)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Correlation effects in two-dimensional topological insulators
• Topological Surface States and Dirac point tuning in ternary Bi2Te2Se class of topological insulators
• Parity-breaking phases of spin-orbit-coupled metals with gyrotropic, ferroelectric and multipolar orders
• Fractionalized Topological Insulators
• Singular robust room-temperature spin response from topological Dirac fermions
• Surface Majorana fermions and bulk collective modes in superfluid 3He-B
• 2D compressibility of surface states on 3D topological insulators

Cited by in corpus (9)

• Optical conductivity of topological surface states with emergent supersymmetry
• Spin susceptibility of three-dimensional Dirac semimetals
• Collective spin modes in Fermi liquids with spin-orbit coupling
• Soft Modes and Nonanalyticities in a Clean Dirac Metal
• Nematic order on the surface of a three-dimensional topological insulator
• Correlation and current anomalies in helical quantum dots
• Chiral second-sound collective mode at the edge of 2D systems with nontrivial Berry curvature
• Fermi surface instabilities of symmetry-breaking and topological types on the surface of a three-dimensional topological insulator
• Intertwined geometries in collective modes of two dimensional Dirac fermions