Optical conductivity of topological surface states with emergent supersymmetry

Abstract

Topological states of electrons present new avenues to explore the rich phenomenology of correlated quantum matter. Topological insulators (TIs) in particular offer an experimental setting to study novel quantum critical points (QCPs) of massless Dirac fermions, which exist on the sample's surface. Here, we obtain exact results for the zero- and finite-temperature optical conductivity at the semimetal-superconductor QCP for these topological surface states. This strongly interacting QCP is described by a scale invariant theory with emergent supersymmetry, which is a unique symmetry mixing bosons and fermions. We show that supersymmetry implies exact relations between the optical conductivity and two otherwise unrelated properties: the shear viscosity and the entanglement entropy. We discuss experimental considerations for the observation of these signatures in TIs.

5 pages, 1 figure; 12 pages of supplemental material. v2: presentation substantially simplified; published version. v3: included missing supplemental material

References in corpus (12)

• Conformal collider physics: Energy and charge correlations
• Universality of corner entanglement in conformal field theories
• Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
• Emergence of supersymmetry at a critical point of a lattice model
• Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
• Simulating Wess-Zumino Supersymmetry Model in Optical Lattices
• The quasi-normal modes of quantum criticality
• Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions
• Bounds on corner entanglement in quantum critical states
• Sum Rules from an Extra Dimension
• Critical capacitance and charge-vortex duality near the superfluid to insulator transition
• Constraining quantum critical dynamics: 2+1D Ising model and beyond

Cited by in corpus (41)

• Emergence of supersymmetric quantum electrodynamics
• Superconducting quantum criticality of topological surface states at three loops
• High-harmonic generation approaching the quantum critical point of strongly correlated systems
• Decoding a Three-Dimensional Conformal Manifold
• Observation of Emergent Spacetime Supersymmetry at Superconducting Quantum Criticality
• Majorana-Hubbard model on the square lattice
• Quantum phase transitions in Dirac fermion systems
• Comments on Squashed-sphere Partition Functions
• Dynamical response near quantum critical points
• Partition functions on slightly squashed spheres and flux parameters
• Yukawa CFTs and Emergent Supersymmetry
• Quantum critical response: from conformal perturbation theory to holography
• Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere
• Finite-Scale Emergence of 2+1D Supersymmetry at First-Order Quantum Phase Transition
• Phase diagrams of Majorana-Hubbard ladders
• Superconductivity in two-dimensional disordered Dirac semimetals
• 3d $\mathcal{N}=2$ minimal SCFTs from Wrapped M5-branes
• Holographic response from higher derivatives with homogeneous disorder
• Long-range Coulomb Interaction effects on Topological Phase Transitions between Semi-metals and Insulators
• Supersymmetry in Closed Chains of Coupled Majorana Modes
• Shear viscosity as a probe of nodal topology
• Conformal bounds in three dimensions from entanglement entropy
• Random-mass disorder in the critical Gross-Neveu-Yukawa models
• Gapless helical superconductivity on the surface of a three-dimensional topological insulator
• Phase transition with trivial quantum criticality in anisotropic Weyl semimetal
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals
• Supersymmetry in an interacting Majorana model on the kagome lattice
• Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials
• Fermion-induced quantum critical point in the Landau-Devonshire model
• Dual dynamic scaling in deconfined quantum criticality
• Lattice vibration as a knob for novel quantum criticality: Emergence of supersymmetry from spin-lattice coupling
• Absence of emergent supersymmetry at superconducting quantum critical points in Dirac and Weyl semimetals
• Nematic order on the surface of a three-dimensional topological insulator
• Momentum dissipation and holographic transport without self-duality
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
• Critical structure and emergent symmetry of Dirac fermion systems
• Critical properties of three-dimensional many-flavour QEDs
• $\mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene
• Fermi surface instabilities of symmetry-breaking and topological types on the surface of a three-dimensional topological insulator
• Emergent spacetime supersymmetry at 2D fractionalized quantum criticality