[Paper Review] Flat band in topological matter: possible route to room-temperature superconductivity

G. E. Volovik|arXiv (Cornell University)|Oct 20, 2011

Topological Materials and PhenomenaPhysics and Astronomy25 references17 citations

TL;DR

This paper proposes that topologically protected flat bands—exhibited on the surfaces of 3D topological semimetals with nodal lines or in vortex cores of topological superconductors—can enable surface superconductivity with a critical temperature linearly dependent on electron coupling. This linear dependence, due to the flat band's singular density of states, offers a viable route to room-temperature superconductivity, contrasting sharply with the exponentially suppressed transition temperatures in conventional bulk superconductors.

ABSTRACT

Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the gapless Weyl, Dirac or Majorana fermions on the surface of the system and inside vortex cores. In gapless topological media, the bulk-surface and bulk-vortex correspondence produce topologically protected gapless fermions without dispersion - the flat band. Fermion zero modes forming the flat band are localized on the surface of topological media with protected nodal lines and in the vortex core in systems with topologically protected Fermi points (Weyl points). Flat band has an extremely singular density of states, and this property may give rise in particular to surface superconductivity which in principle could exist even at room temperature.

Motivation & Objective

• To explore the role of topological flat bands in enabling high-temperature surface superconductivity.
• To establish the connection between momentum-space topology and the emergence of dispersionless fermionic modes.
• To demonstrate that the singular density of states in flat bands leads to a linear dependence of superconducting critical temperature on coupling strength.
• To identify materials or engineered systems where topologically protected flat bands can be realized for potential room-temperature superconducting applications.
• To extend the bulk-surface and bulk-vortex correspondence to include flat bands in nodal-line and Weyl-point systems.

Proposed method

• Analyzing the momentum-space topology of fermionic systems using topological invariants such as winding numbers and Chern numbers.
• Applying the bulk-surface and bulk-vortex correspondence to show that nodal lines and Weyl points in momentum space lead to flat bands on surfaces and in vortex cores.
• Using the Green’s function formalism to describe the phase winding around topological defects, linking them to fermion zero modes.
• Deriving the density of states (DoS) for flat bands, showing ν(ε) ∼ ε⁻¹ for surface flat bands in 3D nodal-line systems.
• Modeling the superconducting transition temperature Tc as linear in the coupling strength g and the area S_FB of the flat band in momentum space: Tc ∼ gS_FB.
• Drawing analogies between topological flat bands and solitons, half-quantum vortices, and Dirac strings to explain their stability and localization.

Experimental results

Research questions

• RQ1 Can topologically protected flat bands in topological semimetals or superconductors support surface superconductivity with enhanced critical temperatures?
• RQ2 How does the singular density of states ν(ε) ∼ ε⁻¹ in flat bands influence the superconducting transition temperature compared to conventional systems?
• RQ3 What is the role of momentum-space topology—such as nodal lines or Weyl points—in stabilizing dispersionless fermion modes?
• RQ4 How does the bulk-surface correspondence in topological matter lead to the formation of flat bands on surfaces and in vortex cores?
• RQ5 Can engineered systems with multiple twin boundaries or grain interfaces realize bulk superconductivity with high Tc via localized flat-band domains?

Key findings

• Topologically protected flat bands emerge on the surface of 3D topological semimetals with nodal lines, where all states in the band have zero energy and terminate at the projected nodal line.
• The density of states for such flat bands exhibits a singular behavior ν(ε) ∼ ε⁻¹, which is a direct consequence of the topological protection and momentum-space structure.
• The critical temperature for surface superconductivity is linearly proportional to the coupling strength and the area of the flat band in momentum space: Tc ∼ gS_FB, in contrast to the exponential suppression in conventional superconductors.
• In vortex cores of topological superfluids like 3He-A, a one-dimensional flat band of zero-energy bound states forms, with endpoints determined by the projection of Weyl points.
• The Fermi arc on the surface of Weyl semimetals is topologically analogous to a Dirac string terminating on magnetic monopoles, and it is linked to the bulk-vortex correspondence.
• The flat band's singular DoS enables superconductivity to emerge earlier on the surface than in the bulk, suggesting a mechanism for high-temperature surface superconductivity.