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Conformal QED in two-dimensional topological insulators.

Natália Menezes1, Giandomenico Palumbo1, Cristiane Morais Smith2

  • 1Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584, CC, Utrecht, The Netherlands.

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Summary
This summary is machine-generated.

Local four-fermion interactions create a helical Luttinger liquid (HLL) phase at topological insulator edges. This study derives the HLL from first principles using a gauge-theory approach, revealing its conformal quantum electrodynamics nature.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Materials Science

Background:

  • Topological insulators possess unique edge states with potential for novel electronic phases.
  • Previous work suggested four-fermion interactions on these edges lead to a non-Fermi-liquid phase.
  • The helical Luttinger liquid (HLL) phase arises from these interactions.

Purpose of the Study:

  • To provide a first-principle derivation of the helical Luttinger liquid (HLL) phase.
  • To elucidate the underlying gauge theory governing the edge states of topological insulators.
  • To establish the connection between HLL and conformal quantum electrodynamics (CQED).

Main Methods:

  • Considered massless Dirac fermions on the 1D boundary of a topological insulator.
  • Incorporated interactions with a 3D quantum dynamical electromagnetic field.
  • Employed a dimensional-reduction procedure to derive an effective 1+1D fermionic theory.
  • Analyzed the low-energy regime using a gauge-theory approach.

Main Results:

  • Derived the effective 1+1-dimensional interacting fermionic theory from first principles.
  • Revealed the underlying gauge theory governing the edge states.
  • Identified the low-energy effective theory as conformal quantum electrodynamics (CQED).
  • Established an exact mapping from CQED to a helical Luttinger liquid (HLL).

Conclusions:

  • The helical Luttinger liquid (HLL) phase is rigorously derived from fundamental principles.
  • The edge states of topological insulators are described by conformal quantum electrodynamics (CQED).
  • The HLL phase exhibits renormalized Fermi velocity and Luttinger parameter dependent on the fine-structure constant.