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Enhanced third harmonic response of the PtTe$_2$ transition metal dichalcogenide

Leone Di Mauro Villari, Simone Grillo, Olivia Pulci, Salvatore Macis, Stefano Lupi, Andrea Marini

TL;DR

This work investigates the third-harmonic generation in PtTe$_2$, a type-II Dirac semimetal, by deriving a low-energy two-band model from DFT around the A-$\Gamma$-A node and applying a diagrammatic optical Bloch formalism. The authors show that Dirac cone tilting strongly enhances THG along the tilt direction and shifts resonance features, with enhancements up to about 8× compared to untitled (type-I) cones. They provide analytical expressions for the THG conductivity, revealing a rich resonance structure governed by chemical potential and tilt parameter, implying Pt-based TMDs as promising platforms for nonlinear nanophotonics and for spectroscopic signatures of Lifshitz transitions. The study relies on a single-particle approximation but outlines a clear path to include many-body corrections for quantitative predictions.

Abstract

We investigate the third harmonic response of platinum ditelluride (PtTe$_2$), a Dirac semimetal belonging to the transition metal dichalcogenides class. Due to its topological properties, this material has drawn a lot of attention, particularly because it hosts type-II (super-critically tilted) Dirac fermions in the $\rm A-Γ-\rm A$ high symmetry direction. Adopting a low-energy model fitted directly from density functional theory band structure simulations, we calculate analytically the nonlinear conductivity. We observe that third-order optical nonlinearities are efficiently modulated by the cones tilting, which produces a significant enhancement of the nonlinear susceptibility. Our results, besides shedding light on topological transitions of platinum ditelluride, are relevant for future nanophotonic devices exploiting the tunable nonlinear properties of type-II Dirac fermions.

Enhanced third harmonic response of the PtTe$_2$ transition metal dichalcogenide

TL;DR

This work investigates the third-harmonic generation in PtTe, a type-II Dirac semimetal, by deriving a low-energy two-band model from DFT around the A--A node and applying a diagrammatic optical Bloch formalism. The authors show that Dirac cone tilting strongly enhances THG along the tilt direction and shifts resonance features, with enhancements up to about 8× compared to untitled (type-I) cones. They provide analytical expressions for the THG conductivity, revealing a rich resonance structure governed by chemical potential and tilt parameter, implying Pt-based TMDs as promising platforms for nonlinear nanophotonics and for spectroscopic signatures of Lifshitz transitions. The study relies on a single-particle approximation but outlines a clear path to include many-body corrections for quantitative predictions.

Abstract

We investigate the third harmonic response of platinum ditelluride (PtTe), a Dirac semimetal belonging to the transition metal dichalcogenides class. Due to its topological properties, this material has drawn a lot of attention, particularly because it hosts type-II (super-critically tilted) Dirac fermions in the high symmetry direction. Adopting a low-energy model fitted directly from density functional theory band structure simulations, we calculate analytically the nonlinear conductivity. We observe that third-order optical nonlinearities are efficiently modulated by the cones tilting, which produces a significant enhancement of the nonlinear susceptibility. Our results, besides shedding light on topological transitions of platinum ditelluride, are relevant for future nanophotonic devices exploiting the tunable nonlinear properties of type-II Dirac fermions.
Paper Structure (6 sections, 22 equations, 4 figures)

This paper contains 6 sections, 22 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Low-energy model from DFT band structure
  3. Feynman diagrammatic expansion of the Bloch equations
  4. Topological third harmonic response
  5. Conclusion
  6. Explicit calculation of some diagrams

Figures (4)

  • Figure 1: (a) Bulk 1T-PtTe$_2$ electronic band structure, with SOC included, calculated with Grimme’s PBE-DFT-D2 functionals, with high-symmetry directions in the hexagonal Brillouin zone at $k_z = 0.35(4)c^*$, where $c^* = 2\pi/c$ (we use $\Gamma$ as a reference as $k_z = 0$). Energy rescaled with respect to the Fermi energy. It shows two type-I Dirac points in the $\rm K$-$\Gamma$-$\rm K$ and $\rm M$-$\Gamma$-$\rm M$ high symmetry direction, and two type-II points in the $\rm A$-$\Gamma$-$\rm A$ direction. (b) Wave-vector path in the hexagonal Brillouin zone. (c) Lowest energy bands and fit with the low momentum expansion around the type-II nodes.
  • Figure 2: First order conductivity diagrams.
  • Figure 3: Third-order conductivity diagrams.
  • Figure 4: Real part of the first order and THG nonlinear conductivity tensor at $T=0$. (a) first order response for PtTe$_2$ (type-II, $xx=yy$ and $zz$-directions) and an ideal massless type-I Dirac cone $(xx=yy=zz).$(b)$\sigma^{(3)}_{zzzz}(\omega)$ and (c)$\sigma^{(3)}_{xxzz}(\omega)$ for PtTe$_2$ (type-II) and an ideal massless type-I Dirac cone. (d) THG enhancement, defined as the ratio between the maximum conductivity of the type-II and type-I nodes, as a function of chemical potential.