Related Experiment Video
Updated: Jun 25, 2026
08:02
Rendering SiO2/Si Surfaces Omniphobic by Carving Gas-Entrapping Microtextures Comprising Reentrant and Doubly Reentrant Cavities or Pillars
Published on: February 11, 2020
Fermi surfaces in general codimension and a new controlled nontrivial fixed point
1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Physical Review Letters
|March 5, 2009
Summary
Researchers explored superconductivity transitions in Fermi systems using an epsilon expansion. They found results align with the Hertz-Millis action in higher effective dimensions, suggesting new theoretical frameworks.
Area of Science:
- Condensed Matter Physics
- Quantum Field Theory
- Many-Body Physics
Background:
- Fermi systems typically exhibit energy variations along one radial dimension.
- Understanding transitions to superconductivity is crucial in condensed matter physics.
Purpose of the Study:
- To investigate the transition to superconductivity in d-dimensional Fermi systems with d(c)=1+epsilon.
- To analyze the behavior using an epsilon expansion and identify relevant theoretical frameworks.
Main Methods:
- Employing an epsilon expansion to study the superconducting transition.
- Analyzing the system's behavior around a nontrivial fixed point.
- Comparing results with the Hertz-Millis action for superconducting order parameters.
Main Results:
- A scale-invariant theory with an effective spacetime dimension D=d(c)+1 emerges at the nontrivial fixed point.
- The study's findings are consistent with predictions from the Hertz-Millis action in higher effective dimensions.
- The transition at epsilon=1, corresponding to a linear Fermi surface in d=3, is considered for realization.
Conclusions:
- The epsilon expansion provides a valuable tool for understanding superconductivity transitions in generalized Fermi systems.
- The Hertz-Millis action effectively describes the superconducting order parameter in these higher effective dimensions.
- This work opens avenues for exploring novel superconducting phenomena in systems with linear Fermi surfaces.
More Related Videos
Related Concept Videos
01:30Oriented Surfaces
A surface is called orientable if a consistent choice of unit normal vector can be made at every point on the surface. A thin soap film stretched across a wire loop provides a familiar example. The film separates the air on one side from the air on the other, so one side can be selected as positive and the opposite side as negative. Once this choice is made, a unit normal vector can be assigned smoothly across the entire surface.At each point on the soap film, a unit normal vector points...
01:28Quadric Surfaces
Quadric surfaces are three-dimensional surfaces characterized by second-degree equations in the variables x, y, and z. These surfaces are smooth and continuous, and specific combinations of squared and linear terms define their shapes. The main types of quadric surfaces include ellipsoids, cones, paraboloids, and hyperboloids. Each type exhibits distinct geometric features depending on how the variables are arranged and related within the equation.Ellipsoids are closed surfaces formed when all...
01:22Tangent Planes to a Parametric Surface
A tangent plane provides a linear approximation to a curved surface at a specific point, capturing the local behavior of the surface. It can be understood as the plane that just touches the surface at that point and is defined by the tangent directions of curves lying on the surface. These tangent directions arise naturally when the surface is described parametrically, allowing systematic construction of the plane.For a surface expressed in parametric form, the position of any point is...
01:19Tangent Planes to Surfaces
In multivariable calculus, the concept of a tangent plane plays a central role in approximating curved surfaces. When dealing with a surface defined by a function of two variables, such as z = f(x, y), the tangent plane at a given point provides the best linear approximation to the surface near that point. This local linearization allows complex, nonlinear geometries to be treated using simpler, planar models.The construction of the tangent plane involves taking vertical slices of the surface...
01:31Tangent Planes to Level Surfaces
A level surface consists of all points in space where a function of three variables takes the same fixed value. If a point lies on this surface, understanding the surface’s geometry there requires more than just knowing the point’s coordinates; it requires describing how the surface is oriented, or how it tilts, near that point.To probe this local geometry, imagine tracing a path that stays entirely on the level surface and passes through the point of interest. This path can be described as a...
01:18Castigliano's Theorem
Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.