Fermi surfaces in general co-dimension and a new controlled non-trivial fixed point

Abstract

Traditionally Fermi surfaces for problems in $d$ spatial dimensions have dimensionality $d-1$, i.e., codimension $d_c=1$ along which energy varies. Situations with $d_c>1$ arise when the gapless fermionic excitations live at isolated nodal points or lines. For $d_c>1$ weak short range interactions are irrelevant at the non-interacting fixed point. Increasing interaction strength can lead to phase transitions out of this Fermi liquid. We illustrate this by studying the transition to superconductivity in a controlled $\epsilon$ expansion near $d_c=1$. The resulting non-trivial fixed point is shown to describe a scale invariant theory that lives in effective space-time dimension $D=d_c+1$. Remarkably, the results can be reproduced by the more familiar Hertz-Millis action for the bosonic superconducting order parameter even though it lives in different space-time dimensions.

4 pages

References in corpus (4)

• Topological Insulators in Three Dimensions
• Renormalization Group Approach to Interacting Fermions
• Influence of Generic Scale Invariance on Classical and Quantum Phase Transitions
• Critical fermi surfaces and non-fermi liquid metals

Cited by in corpus (29)

• Recent Developments in Non-Fermi Liquid Theory
• Long-range Coulomb interaction in nodal-ring semimetals
• Perturbative non-Fermi liquids from dimensional regularization
• Ising nematic quantum critical point in a metal: a Monte Carlo study
• Non-Fermi liquid fixed point in a Wilsonian theory of quantum critical metals
• Heisenberg-Kitaev model on hyperhoneycomb lattice
• Non-Fermi liquid behavior of large N_B quantum critical metals
• Renormalization group method based on the ionization energy theory
• Universal crossovers between entanglement entropy and thermal entropy
• Interacting line-node semimetal: Proximity effect and spontaneous symmetry breaking
• Ultraviolet/infrared mixing in non-Fermi liquids
• Quasi-Local Strange Metal
• Two dimensional non-Fermi liquid metals: a solvable large N limit
• Weyl and Dirac Loop Superconductors
• Superconducting instability in non-Fermi liquids
• Quantum critical metals in $4-\epsilon$ dimensions
• Instabilities of Weyl-loop semi-metals
• Non-Fermi liquid Superconductivity: Eliashberg versus the Renormalization Group
• Anisotropic Non-Fermi Liquids
• Aspects of Renormalization in Finite Density Field Theory
• Emergence of a control parameter for the antiferromagnetic quantum critical metal
• Non-Fermi liquid at the FFLO quantum critical point
• Critical Fermi surfaces in generic dimensions arising from transverse gauge field interactions
• Operator mixing in $\mathbf{\epsilon }$-expansion: scheme and evanescent (in)dependence
• Noncommutativity between the low-energy limit and integer dimension limits in the $\mathbf{\epsilon }$-expansion: a case study of the antiferromagnetic quantum critical metal
• Infinite critical boson non-Fermi liquid
• Incommensurate $2k_F$ density wave quantum criticality in two dimensional metals
• Stable non-Fermi liquid fixed point at the onset of incommensurate $2k_F$ charge density wave order
• Infinite critical boson induced non-Fermi liquid in $d=3-\epsilon$ dimensions