Pulse-duration-sensitive high harmonics and attosecond locally-chiral light from a chiral topological Weyl semimetal

This theoretical study demonstrates that pulse-duration-sensitive high harmonic generation in the chiral Weyl semimetal RhSi not only extends to higher photon energies by promoting multi-band excitations but also enables the synthesis of attosecond locally chiral light with pronounced circular dichroism, offering a pathway toward compact chiral light sources and topological electronics.

The Gist

Imagine you have a crystal, like a tiny, perfect diamond, but instead of being clear and symmetrical, it's twisted like a spiral staircase. This is a chiral Weyl semimetal (specifically a material called RhSi). Now, imagine shining a super-powerful, ultra-fast laser beam at it.

Usually, when you hit a material with light, it bounces back or glows a little. But if you hit this special crystal with the right kind of laser, it acts like a cosmic guitar string, vibrating so violently that it spits out new, incredibly high-energy flashes of light. This process is called High Harmonic Generation (HHG).

This paper is about two major discoveries regarding how we can control this "cosmic guitar" to make it play higher notes and create a very special kind of "twisting" light.

1. The "Longer Runway" Analogy (Pulse Duration)

The Problem:
Think of an electron inside the crystal as a race car. When the laser hits, it kicks the car into overdrive. To get the car to go fast enough to produce the highest-energy light (the "highest notes"), it needs to climb a very tall ladder of energy levels.

The Discovery:
The researchers found that the length of time the laser shines on the crystal matters immensely.

• Short Laser Pulse (4 cycles): Imagine the laser is a quick, sharp tap. The electron gets a little boost, climbs a few rungs of the ladder, and then the light stops. The resulting light isn't very energetic.
• Long Laser Pulse (20 cycles): Now, imagine the laser is a long, steady ramp. The electron has more time to run. It doesn't just climb the first few rungs; it keeps running up the ladder, reaching the very top floors (high-energy bands) that it couldn't reach before.

The Result:
In the twisted RhSi crystal, a longer laser pulse allows the electrons to climb much higher. This creates light with much higher energy (extreme ultraviolet and soft X-rays).

• Analogy: It's like the difference between a sprinter getting a quick push off the starting blocks versus a sprinter getting a long, accelerating runway. The longer runway lets them reach a much higher top speed.
• Why it matters: This helps scientists create compact, powerful light sources that can see things we've never seen before, like the inner workings of atoms.

2. The "Twisting Light" Analogy (Locally Chiral Light)

The Problem:
Most light we know is like a straight beam or a simple circle (like a spinning top). But nature has "handedness" (chirality), like a left hand vs. a right hand. To study molecules that are also "handed" (like the building blocks of life), we need light that is also "handed" in a very complex, 3D way. This is called locally chiral light.

The Discovery:
Because the RhSi crystal is naturally twisted (like a spiral staircase), it imprints its own twist onto the light it generates.

• The Magic: When the researchers used a circularly polarized laser (a spinning laser) on this twisted crystal, the crystal didn't just reflect the spin. It created a 3D electric field that twists and turns in a way that cannot be superimposed on its mirror image.
• The "Torsion": Think of the light's electric field not as a flat wave, but as a corkscrew or a helix that is constantly twisting and untwisting on a timescale of attoseconds (one quintillionth of a second).

The Result:
They found that by tuning the laser, they could create a "twisting" light pulse that is incredibly sensitive to the "handedness" of other materials.

• Analogy: Imagine trying to fit a left-handed glove on a right hand. It doesn't work well. Now, imagine this "twisting light" is a glove that can instantly tell if it's touching a left-handed or right-handed molecule.
• Why it matters: This could revolutionize how we detect diseases or design drugs, as many biological molecules are "handed." This light could act as an ultra-sensitive detector for these molecular shapes.

Summary: Why Should You Care?

This paper is like finding a new, super-efficient way to build a microscopic flashlight and a molecular fingerprint scanner at the same time.

1. Better Light Sources: By just making the laser pulse slightly longer, they can generate much brighter, higher-energy light without needing massive, expensive machines. This could lead to smaller, cheaper medical imaging devices.
2. New Physics: They proved that the shape of a crystal (its "twist") can be used to sculpt light into complex 3D shapes that exist for only a fraction of a second.
3. Future Tech: This opens the door to "light-wave electronics," where we control computers using light waves instead of electricity, potentially making devices thousands of times faster.

In short, the researchers took a twisted crystal, gave it a long laser "push," and turned it into a machine that spits out high-energy, twisting light pulses capable of seeing the invisible world of atoms and molecules.

Technical Summary

Here is a detailed technical summary of the paper "Pulse-duration-sensitive high harmonics and attosecond locally-chiral light from a chiral topological Weyl semimetal."

1. Problem Statement

High Harmonic Generation (HHG) in solids is a complex process driven by the interplay of intraband acceleration and interband electron-hole recombination. While HHG in gases is well-understood via the three-step model, solid-state HHG involves intricate band structures and symmetries. Two specific gaps in current knowledge were addressed:

1. Pulse Duration Dependence: The role of the driving laser pulse duration in extending the HHG cutoff energy in solids has been predicted in 1D models but lacks experimental or comprehensive 3D simulation evidence. It is unclear how pulse duration affects electron excitation to higher conduction bands across different material classes (semiconductors, insulators, and topological semimetals).
2. Locally Chiral Light Synthesis: Generating "locally chiral light" (electric fields with non-superimposable mirror images on attosecond timescales) is experimentally challenging. While chiral crystals possess structural handedness, their potential to imprint this chirality directly onto the emitted HHG field to create 3D locally chiral light has not been fully explored.

2. Methodology

The authors employed Time-Dependent Density-Functional Theory (TDDFT) using the open-source Octopus code to simulate the ultrafast electron dynamics in three distinct materials:

• RhSi: A prototypical chiral Weyl semimetal with a B20 cubic structure (space group 198), featuring numerous band crossings and multifold fermions.
• Si: A conventional semiconductor.
• MgO: A large-gap insulator.

Simulation Parameters:

• Laser Pulse: Linearly polarized along the [111] direction for cutoff studies; Circularly polarized (RCP/LCP) for chirality studies.
• Pulse Durations: Varied systematically (4, 12, and 20 optical cycles) to isolate duration effects.
• Intensities: 1 TW/cm² for RhSi and Si; 3 TW/cm² for MgO (due to its larger band gap).
• Analysis Tools:
  • Calculation of the change in density of occupied states ($|\Delta DOOS|$) to track electron population in higher bands.
  • Time-resolved Gabor spectrograms to analyze emission timing.
  • Synthesis of electric fields by filtering specific harmonic orders.
  • Quantification of local chirality via instantaneous torsion ($\chi(t)$) and net torsion ($\zeta$).

3. Key Contributions

1. Discovery of Pulse-Duration Sensitivity: The study establishes that driving pulse duration is a critical control parameter for extending the HHG cutoff in solids, specifically by promoting the population of higher conduction bands ("excited ladder electrons").
2. Material-Specific Mechanisms: The authors demonstrate that this effect is most prominent in chiral Weyl semimetals (RhSi) due to their dense network of band crossings and strong multiband coupling, moderate in Si, and suppressed in wide-gap insulators like MgO.
3. Selection Rules for Locally Chiral Light: The paper identifies specific dynamical symmetry selection rules ($C_3^{(\pm)}$ and $C_2^{(\pm)}$) in RhSi that allow the synthesis of 3D locally chiral light.
4. Attosecond Torsion: The work demonstrates the generation of electric fields with asymmetric instantaneous torsion on attosecond timescales, driven by the interplay of longitudinal and transverse harmonic components.

4. Key Results

A. Pulse Duration and Cutoff Extension

• RhSi and Si: Increasing the pulse duration from 4 to 20 cycles significantly extended the HHG cutoff energy.
  • Si: Cutoff extended from ~25 eV to ~60 eV. The spectrum showed multiplateau behavior with abrupt yield drops.
  • RhSi: Cutoff extended from ~7 eV to ~35 eV with a smoother decay and higher yield in the high-energy region compared to Si.
• Mechanism: Longer pulses allow electrons to undergo multiple interaction cycles, climbing the "excited ladder" through band crossings to populate high-energy conduction bands. This increases the maximum electron-hole recombination energy.
• MgO: Showed negligible cutoff extension with pulse duration. The large band gap prevents strong coupling to higher bands; electrons remain confined to the first conduction band, limiting the cutoff regardless of pulse length.

B. Locally Chiral Light and Symmetry Selection Rules

Using circularly polarized drivers on RhSi, the authors synthesized 3D electric fields exhibiting local chirality:

• $C_3^{(\pm)}$ Symmetry (Propagation along [111]):
  • The spectrum consists of triplets: Right Circular Polarization (RCP), Left Circular Polarization (LCP), and Longitudinal components.
  • The longitudinal component (evanescent field) is crucial. When coherently superposed with RCP and LCP harmonics (e.g., orders 3, 4, and 9), it creates a non-vanishing net torsion ($\zeta = 0.3679$ n.u.).
  • The resulting field exhibits asymmetric instantaneous torsion varying on attosecond scales (periods of ~296 as).
• $C_2^{(\pm)}$ Symmetry (Propagation along [001]):
  • The spectrum is governed by two-fold symmetry, mixing counter-rotating polarizations in even harmonics.
  • While locally chiral light is still generated, the net torsion is lower ($\zeta = -0.1402$ n.u.) and the torsion envelope is more symmetric compared to the $C_3$ case.
• Circular Dichroism: A strong circular dichroism was observed when the driving helicity was aligned or anti-aligned with the crystal's handedness, particularly along the [111] axis.

5. Significance and Impact

• Compact EUV Sources: RhSi and similar chiral Weyl semimetals are identified as superior candidates for generating high-energy, coherent extreme-ultraviolet (EUV) light via HHG, surpassing the 50 eV limit previously observed in MgO.
• New Chiral Probes: The ability to generate attosecond locally chiral light directly from a solid-state source offers a new tool for probing chiral dynamics in matter with unprecedented temporal resolution. This is vital for enantiomer-sensitive detection and studying chiral catalysis.
• Topological Electronics: The findings pave the way for light-wave-driven topological electronics, where the structural chirality of the material is directly mapped to the control of electron dynamics and emitted radiation.
• Theoretical Validation: The results challenge few-band theoretical models, proving that accurate simulation of solid-state HHG requires accounting for complex multiband couplings and "excited ladder" electron pathways.

In summary, this work bridges the gap between topological material science and attosecond optics, demonstrating that the structural chirality of Weyl semimetals can be harnessed to generate tunable, high-energy, and locally chiral light pulses.