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The quantum geometric origin of capacitance in insulators.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Materials Science

Background:

  • Adiabatic transport in band insulators is traditionally linked to the geometry of the ground state wavefunction.
  • Understanding transport phenomena in driven systems requires considering quantum geometric effects.

Purpose of the Study:

  • To investigate the role of quantum geometry in the AC transport properties of band insulators at finite frequencies.
  • To establish a connection between dielectric response, quantum metric, and conductivity in gapped materials.

Main Methods:

  • Expressing the Kubo formula for conductivity as the variation of time-dependent polarization with respect to the applied field.
  • Analyzing systems driven at small, finite frequencies (ω).
  • Investigating various insulating systems including free electron gas in magnetic fields, twisted bilayer graphene, and diamond.

Main Results:

  • Longitudinal conductivity at linear order in frequency is determined by an intrinsic capacitance, proportional to the quantum metric and inversely proportional to the spectral gap.
  • Quantum geometry is identified as the source of the electronic contribution to the dielectric constant across diverse insulators.
  • Quantized capacitance is demonstrated in a free electron gas under a quantizing magnetic field, and a topological origin for diamond's large refractive index is found.

Conclusions:

  • A fundamental link exists between the dielectric response and the quantum metric of insulators, governing AC transport.
  • Quantum geometric effects are crucial for understanding the electronic properties and optical responses of a wide range of insulating materials.
  • Topological properties derived from quantum geometry can explain unusual material characteristics, such as the high refractive index of diamond.