String Theory on Thin Semiconductors: Holographic Realization of Fermi Points and Surfaces

TL;DR

This work bridges string theory and degenerate fermion dynamics in thin semiconductors by leveraging the AdS/CFT correspondence and tunable condensed-matter parameters. It argues that stable Fermi surfaces are classified by $K$-theory with Bott periodicity and develops two holographic realizations: a zero-dimensional Fermi point via a D3/D7 intersection and a two-dimensional Fermi surface via a charged AdS$_5$ black hole. Thermodynamics and linear response in the charged-black-hole setup reproduce features of a relativistic Fermi liquid at finite density, with a universal $\eta/s = 1/(4\pi)$ but notable deviations such as diffusive zero-temperature behavior, suggesting either disorder effects or strong interactions beyond a free gas. The results motivate tabletop experiments with multilayer graphene–like systems to probe conformal phase transitions and holographic dynamics, while highlighting caveats that require further clarification. Overall, the paper presents a concrete, testable holographic framework for Fermi-surface physics in condensed matter, linking conformal invariance, quantum criticality, and string-theoretic constructs to experimental platforms.

Abstract

I make a novel contact between string theory and degenerate fermion dynamics in thin semiconductors. Utilizing AdS/CFT correspondence in string theory and tunability of coupling parameters in condensed matter systems, I focus on the possibilities testing string theory from tabletop experiments. I first discuss the observation that stability of Fermi surface is classifiable according to K-theory. I then elaborate two concrete realization of Fermi surfaces of zero and two dimensions. Both are realized by complex of D3-branes and D7-branes of relative codimension 6 and 4, respectively. The setup with Fermi point models gauge dynamics of multiply stacked graphenes at half-filling. I show that string theory predicts dynamical generation of mass gap and metal-insulator quantum phase transition at zero temperature. I emphasize that conformally invariant gauge theory dynamics of the setup plays a crucial role, leading to novel conformal phase transition. The setup with Fermi surface is in collaboration with Dongsu Bak and is based on charged black hole and models relativistic Fermi liquid. We find positive evidence for this identification from both equilibrium thermodynamics at or near zero temperature and out-of-equilibrium linear response and transport properties. I argue that fluctuation of black hole horizon provides holographic realization consistent with Fermi liquid for thermodynamics and interesting departures therefrom in transport properties.