Inho Choi

This review is written by non-expert and used for personal study only.

Disorder-assisted assembly of strongly correlated fluids of light

  • Qubits

Synthetic materials, made up of interacting ions, atoms, or photons, provide a unique way to study the behavior of quantum systems consisting of many particles. Scientists have recently focused on understanding how these systems behave when they are out of equilibrium, which has important implications for the development of new computational tools.

Creating a balance in synthetic materials involves a process that is, by nature, not balanced. This requires special techniques to prepare the system in a way that follows the fundamental rules of quantum mechanics. To efficiently prepare these systems, scientists use methods like laser cooling, evaporative cooling, and a gradual change in the energy landscape (called adiabatic variation).

Microwave photon-containing materials can efficiently reach a balanced state by interacting with specially designed low-entropy environments. This technique has been successful in stabilizing certain types of matter, but new approaches are needed for other types, like compressible phases. Researchers have made progress in this area by taking advantage of the unique properties of photonic materials, which allow precise control over individual particles. They were able to localize all the energy states, inject particles into specific positions, and gradually remove disorder to create a strongly correlated fluid, which is a unique state where particles are closely connected to one another through quantum mechanics.

Scientists then characterized this fluid using measurements that reveal how particles are correlated and entangled with each other. These measurements showed that photons in the fluid avoid each other and exhibit a behavior characteristic of a special type of gas called a Tonks gas. They also found that photons become more spread out during the process and then localize again when the disorder is gradually reintroduced.

Researchers also introduced a technique for arranging individual particles in a special circuit called a Bose-Hubbard circuit. This technique allowed them to create unique states of light with interesting properties, like delocalization and anti-bunching. They conducted experiments using a one-dimensional (1D) version of this circuit, which relies on a special type of quantum bit called a transmon qubit. This circuit design allows particles to tunnel between neighboring sites and interact with each other in a controlled manner.

To prepare the system in a specific state, researchers developed a protocol that involves introducing strong disorder and then slowly reducing it while maintaining a key quantum mechanical property called adiabaticity. They applied this protocol to create states where a single photon behaves like a particle trapped in a box. These states exhibited interesting patterns, like sinusoidal density profiles, which matched the expected distributions for certain types of quantum states.

The researchers also developed a way to test the adiabaticity of the process by carefully controlling the rate at which the disorder was reduced and then increased again. This allowed them to find the optimal rate that would ensure the particle returns to its initial position most of the time. This method is particularly powerful because it does not depend on the specific details of the physical system or the target state.

Researchers were able to create a unique type of fluid that is compressible and strongly interacting by using a modified version of the disorder-assisted preparation technique. They also observed how photons in the fluid delocalize and interact with each other, which was consistent with a theoretical model known as the Tonks-Girardeau model.

Scientists have shown a way to use controlled disorder to prepare unique quantum fluids of light in a 1D Bose-Hubbard circuit. This work allows for the study of many different phases of quantum matter. By combining these techniques with other advanced circuit designs, it may be possible to create and study even more exotic types of light fluids and investigate complex quantum phenomena.

Required Additional Study Materials

  • Devitt, S. J., Munro, W. J. & Nemoto, K. Quantum error correction for beginners. Rep. Prog. Phys. 76, 076001 (2013).
  • Carusotto, I. et al. Photonic materials in circuit quantum electrodynamics. Nat. Phys. 16, 268–279 (2020).
  • Pezze, L., Smerzi, A., Oberthaler, M. K., Schmied, R. & Treutlein, P. Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys. 90, 035005 (2018).
  • Albash, T. & Lidar, D. A. Adiabatic quantum computation. Rev. Mod. Phys. 90, 015002 (2018).
  • Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).
  • Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nat. Phys. 8, 277–284 (2012).
  • Bloch, I., Dalibard, J. & Nascimbene, S. Quantum simulations with ultracold quantum gases. Nat. Phys. 8, 267–276 (2012).
  • Chen, Q., Stajic, J., Tan, S. & Levin, K. BCS–BEC crossover: from high temperature superconductors to ultracold superfluids. Phys. Rep. 412, 1–88 (2005).
  • Cooper, N., Dalibard, J. & Spielman, I. Topological bands for ultracold atoms. Rev. Mod. Phys. 91, 015005 (2019).
  • Eisert, J., Friesdorf, M. & Gogolin, C. Quantum many-body systems out of equilibrium. Nat. Phys. 11, 124–130 (2015).
  • Bak, P. Commensurate phases, incommensurate phases and the devil’s staircase. Rep. Prog. Phys. 45, 587 (1982).
  • Zhou, Y., Kanoda, K. & Ng, T.-K. Quantum spin liquid states. Rev. Mod. Phys. 89, 025003 (2017).
  • Cazalilla, M. A., Citro, R., Giamarchi, T., Orignac, E. & Rigol, M. One dimensional bosons: from condensed matter systems to ultracold gases. Rev. Mod. Phys. 83, 1405–1466 (2011).
Introductory material
  • “Quantum Physics” by Leonard Schiff
  • “Modern Quantum Mechanics” by J.J. Sakurai

Reference

Saxberg, B., Vrajitoarea, A., Roberts, G. et al. Disorder-assisted assembly of strongly correlated fluids of light. Nature 612, 435–441 (2022).

Majorana-like Coulomb spectroscopy in the absence of zero-bias peaks

  • Nanowires

The experimental protocol investigates the low-energy behavior of semiconductor-superconductor nanowire islands by adjusting gate-tunable barriers. The technique involves modifying the junction barriers to allow for either tunneling spectroscopy or Coulomb spectroscopy measurements on the island, controlling the transparency of the junctions by applying voltages to corresponding gates.

The study examines the Coulomb spectroscopy of a full-shell device, focusing on how the zero-bias differential conductance changes as a function of the island gate voltage and parallel magnetic field. Magnetic field intervals where the superconducting gap is not equal to zero alternate with intervals where the gap is equal to zero. Coulomb blockade peaks in zero-bias conductance occur when different particle numbers have the same free energy, marked by gate charge values where two energy parabolas intersect.

As the magnetic field increases, the superconducting gap reopens, but single-electron periodic transport is observed instead of two-electron transport. This could result from a gapless superconducting island or a subgap energy level, such as a Majorana zero mode. However, tunneling spectroscopy measurements at both ends of the device do not confirm either scenario, as no measurable conductance or zero-bias peak is observed.

The study also investigates the effect of nanowire length on observations using a shorter device. Coulomb spectroscopy measurements were performed with tunnel barriers in the intermediate-coupling regime. Coulomb peaks exhibit an even-odd pattern, and an energy value was extracted at the center of the magnetic field interval. Tunneling spectroscopy measurements from both island sides did not reveal any zero-bias peak or other discrete subgap states.

The even-odd modulation of Coulomb peaks is influenced by the voltages applied to the junctions, regardless of island length. The sensitivity of the extracted energy with junction resistance and island length is comparable in full-shell devices.

Researchers present numerical simulations based on a microscopic nanowire model to interpret their observations. They compute the subgap spectrum of an island in a regime of high density and relatively small induced superconducting pairing on core states. As the right barrier is opened for tunneling spectroscopy, the quasicontinuum of states is deconfined into the normal reservoir, smearing out the local density of states in specific magnetic field intervals into a weak, uniform background inside the gap.

The behavior of subgap states in nanowires can be explained by different regimes of electronic density and length. The lowest subgap state fluctuates with magnetic field and barrier configuration. In a topological regime with appropriate tuning of density and spin-orbit coupling, two Majorana bound states appear with a strong zero-bias anomaly in conductance. The range of behaviors observed in simulations is consistent with the variability of the extracted energy in experiments and supports the observation that the energy value tends to decrease for longer islands.

The validity of the theoretical interpretation for small or zero energy depends on the existence of a weak subgap background in tunneling conductance that increases in specific magnetic field intervals. The increase in subgap background conductance was detected by enhancing the resolution and reducing the noise floor, confirming the consistency of the interpretation.

The study shows that single-electron Coulomb peak spacing is due to a subgap spectrum at finite magnetic fields, explaining why single-electron transport is common and robust. Junction details are crucial for understanding transport spectroscopy in the pursuit of topological Majorana zero modes, and length-dependence studies should consider junction-dependent, longitudinally confined modes as potential false positives.  

Required Additional Study Materials

  • Beenakker, C. Search for Majorana fermions in superconductors. Annu. Rev. of Condens. Matter Phys. 4, 113–136 (2013).
  • Lutchyn, R. M. et al. Majorana zero modes in superconductor–semiconductor heterostructures. Nat. Rev. Mater. 3, 52–68 (2018).
  • Prada, E. et al. From andreev to Majorana bound states in hybrid superconductor–semiconductor nanowires. Nat. Rev. Phys. 2, 575–594 (2020).
Introductory material
  • “Quantum Mechanics: Concepts and Applications” by Nouredine Zettili
  • “A Modern Approach to Quantum Mechanics” by John Townsend

Reference

Valentini, M., Borovkov, M., Prada, E. et al. Majorana-like Coulomb spectroscopy in the absence of zero-bias peaks. Nature 612, 442–447 (2022).

Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires

  • Quantum Dots, Nanowires

Crossed Andreev reflection (CAR) is a process used to study Cooper pair splitting, which involves separating the two electrons in a Cooper pair and measuring their spins. Quantum dots (QDs) are tiny semiconductor particles with high charging energies, and they are used to suppress regular Andreev reflection (AR) to distinguish between elastic co-tunneling (ECT) and CAR. When a magnetic field is applied, QDs can be configured to be spin-selective, allowing for the detection of CAR with equal spins when spin precessions are induced by spin-orbit coupling (SOC).

The experimental setup for charge filtering uses two QDs on either side of a proximitized $InSb$ nanowire segment. Voltages applied to gates control the electrochemical potentials in the QDs, and bias voltages define the transport window. For ECT to occur, the energy levels in the QDs must be aligned, while CAR requires anti-symmetric alignment.

Using a scanning electron microscope, researchers observed subgap currents in the main device, which were attributed to Cooper pair splitting and elastic cotunneling. Cooper pair splitting efficiencies of $91\%$ and $98\%$ were achieved for the left and right quantum dots, respectively. The high efficiency was made possible by a hard superconducting gap in the proximitized segment and multiple independently controlled gates for each QD.

Spin blockade is a phenomenon that occurs in a double quantum dot system at charge degeneracies. It is caused by the suppression of CAR due to same-spin occupation and ECT due to same-spin tunneling. Spin-orbit coupling in $InSb$ does not lift the blockade, and the residual current under these conditions is likely a result of hyperfine interaction, which involves the interaction between nuclear and electron spins.

When a magnetic field is applied, bipolar spin filters can be created in QDs. Researchers observed spin conservation, which means that the spin of particles is preserved. Spin correlation analysis revealed that the two QD spins are anti-correlated for CAR signals when the electron pair is in a singlet state. Spin precession, which is the change in the orientation of the spin, generates a non-zero probability of coupling opposite spins via ECT.

The researchers measured the dependence of CAR and ECT on the angle of the magnetic field by rotating it in the plane of the substrate. The largest unusual signals were observed when the magnetic field was perpendicular to the substrate, indicating the presence of spin-orbit interaction.

The paper’s main findings are the oscillating CAR signals for equal-spin configurations. Non-collinear magnetic fields lead to unconventional spin pairing between QDs, which can be explained by possible microscopic scenarios resulting from SOC-induced spin precession. $InSb$ nanowires have both Rashba-type and Dresselhaus-type SOC, which can cause QD eigenstates that are nominally aligned to have a small opposite-spin component. The observed oscillations suggest the presence of triplet pairing components in the hybrid section, supporting the idea of spin-triplet superconducting coupling between QDs needed for a Kitaev chain, which is a theoretical model for studying topological superconductivity.

The $Al-InSb$ hybrid segment in the devices hosts discrete Andreev bound states that have a significant impact on CAR and ECT processes. Theoretical work predicts that these states should be affected by variations in the gate voltage beneath the hybrid segment. Observations of CAR and ECT gate tunability will be presented in a future manuscript.

This study demonstrates that the combination of superconductivity and SOC can produce triplet CAR between spin-polarized QDs, paving the way for an artificial Kitaev chain. To achieve a Kitaev chain, the coupling strength between QDs must be increased to allow for the formation of a hybridized, extended state. Enhancing the coupling strength could be accomplished by modifying the QD geometry or implementing new materials with stronger SOC.

Once an artificial Kitaev chain is realized, it could serve as a platform for exploring topological superconductivity and Majorana modes, which are of great interest for quantum computing applications. The development of such a system could enable fault-tolerant quantum computing, as topological quantum states are more resilient against decoherence and environmental noise. Furthermore, the understanding and control of Kitaev chains could lead to advances in condensed matter physics and pave the way for novel quantum technologies.

The research highlights the potential for creating an artificial Kitaev chain using spin-polarized QDs in combination with superconductivity and SOC. Further studies will need to focus on optimizing the coupling strength between QDs and exploring gate tunability of CAR and ECT processes. This work lays the foundation for future advancements in topological superconductivity and the development of new quantum devices.

Required Additional Study Materials

  • Linder, J. & Robinson, J. W. A. Superconducting spintronics. Nat. Phys. 11, 307–315 (2015).
  • Hanson, R., Kouwenhoven, L. P., Petta, J. R., Tarucha, S. & Vandersypen, L. M. K. Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007).
Introductory material
  • “Statistical Mechanics of Superconductivity” by Takafumi Kita
  • “Shortcut to Superconductivity: Superconducting Electronics via COMSOL Modeling” by Armen Gulian

Reference

Wang, G., Dvir, T., Mazur, G.P. et al. Singlet and triplet Cooper pair splitting in hybrid superconducting nanowires. Nature 612, 448–453 (2022).

Spin cross-correlation experiments in an electron entangler

  • Quantum Dots

Superconductors are materials where electrons form special pairs called Cooper pairs, allowing electricity to flow without resistance. Cooper pair splitting (CPS) can occur on tiny semiconductor islands known as quantum dots, leading to highly efficient sources of spatially separated, entangled electrons with opposite spins. Although charge correlation in CPS devices has been extensively studied, detecting the corresponding spin correlations experimentally has been challenging. In this work, the authors successfully measure these spin correlations in a solid-state superconducting device containing two adjacent quantum dots.

The researchers confirmed CPS by observing a positive charge current cross-correlation between two quantum dots, indicating that two electrons from a Cooper pair were emitted simultaneously. They quantified this current by measuring the modulation amplitude, which disappeared when an external magnetic field suppressed superconductivity.

To evaluate spin correlations, they measured charge correlations for four different spin filter settings. The maximum conductance for two parallel magnetization states was significantly lower than for two antiparallel states. The modulation amplitude also decreased by about half for the parallel states compared to the antiparallel states. They performed experiments to measure the change in current in one quantum dot when the gate voltage of the other quantum dot was altered.

The researchers measured the transconductances $G_1$ and $G_2$ as functions of gate voltages $V_{g1}$ and $V_{g2}$, respectively. They observed an anticorrelation in spin, meaning the spins of the two electrons were opposite. The experiments also took into account non-ideal quantum dot polarizations. In all cases with a measurable CPS signal, the spin cross-correlation was negative, meaning the spins were opposite.

Applying a homogeneous external magnetic field can improve the average quantum dot polarization and the spin filtering effect (how well the device can separate electrons with different spins). As the magnetic field strength increased, the spin cross-correlation became more negative, indicating a stronger opposite-spin relationship between the split Cooper pair electrons. This approach can be applied to various solid-state systems to investigate fundamental phases and processes related to electron spin, making it useful for understanding the underlying physics of these systems.

Required Additional Study Materials

  • Bergeret, F. S., Volkov, A. F. & Efetov, K. B. Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures. Rev. Mod. Phys. 77, 1321–1373 (2005).
  • Beenakker, C. W. J. Random-matrix theory of quantum transport. Rev. Mod. Phys. 69, 731–808 (1997).
  • Kurebayashi, H., Garcia, J. H., Khan, S., Sinova, J. & Roche, S. Magnetism, symmetry and spin transport in van der waals layered systems. Nat. Rev. Phys. 4, 150-166 (2022).
Introductory material
  • “Quantum Mechanics: Concepts and Applications” by Nouredine Zettili
  • “A Modern Approach to Quantum Mechanics” by John Townsend

Reference

Bordoloi, A., Zannier, V., Sorba, L. et al. Spin cross-correlation experiments in an electron entangler. Nature 612, 454–458 (2022).

Anomalous thermal transport under high pressure in boron arsenide

  • Condensed-matter Physics

Understanding the properties of materials under high pressure is essential for various fields. Typically, the thermal conductivity of crystals increases with pressure due to a decrease in volume and stronger atomic bonding. However, recent experiments on cubic boron arsenide ($BAs$) have discovered unusual pressure dependence of thermal conductivity. This is caused by competing heat conduction channels, arising from a unique band structure and complex interactions between phonons, which are vibrational modes in crystals.

$BAs$ is a semiconductor with very high thermal conductivity, making it an ideal material for managing heat in electronics. Recent studies have suggested that $BAs$ might exhibit unusual thermal behavior under high pressure, which hasn’t been explored experimentally. To investigate this, researchers synthesized high-quality, single-crystal $BAs$ and conducted ultrafast pump-probe measurements under high pressure and different temperatures.

To study the behavior of phonons in $BAs$ under pressure, researchers used various techniques like Raman spectroscopy, picosecond laser ultrasonic (PLU), and Brillouin scattering measurements. These methods revealed that as pressure increased, the phonon bandgap widened, indicating a change in the vibrational properties of the material. These experimental results were consistent with theoretical predictions, demonstrating how pressure affects the phonon band structure in BAs.

Inelastic X-ray scattering was used to measure the evolution of the phonon band structure of BAs under high pressure. The results showed that the optical phonon branches moved up, resulting in an increased bandgap, while the acoustic branches experienced a hardening effect with a higher acoustic sound velocity.

The changes in the phonon band structure of $BAs$ under high pressure impact heat conduction channels, contributing to thermal conductivity. Both three-phonon and four-phonon processes can influence thermal conductivity in $BAs$, and these processes become important at room temperature. High pressure increases the likelihood of three-phonon processes while suppressing four-phonon processes, leading to competitive effects on thermal conductivity. Theoretical models can accurately predict these complex interactions and the resulting pressure dependence of thermal conductivity in $BAs$.

Researchers measured the thermal conductivity of $BAs$ crystals as a function of pressure and temperature using time-domain thermoreflectance. The results displayed a non-monotonic trend, which depended on both pressure and temperature. The competition between three-phonon and four-phonon processes was found to be the cause of the unusual pressure-dependent thermal conductivity. Experimental outcomes agreed well with theoretical predictions.

This study revealed that the general rule of increasing thermal conductivity with pressure fails when lower-order interactions no longer dominate energy transport. This finding could impact established modeling predictions for extreme conditions, such as the Earth’s interior, and enable innovative designs for pressure-adapted thermal windows or thermal switches. By combining high-pressure transport experiments with theoretical models, researchers gained a better understanding of the complex phonon physics and the competing contributions to thermal conductivity from different phonon processes.  

Required Additional Study Materials

  • Zhang, L., Wang, Y., Lv, J. & Ma, Y. Materials discovery at high pressures. Nat. Rev. Mater. 2, 17005 (2017).
  • Bridgman, P. W. The Physics of High Pressure (MacMillan, 1931).
  • Ziman, J. M. Electrons and Phonons: The Theory of Transport Phenomena in Solids (Oxford Univ. Press, 1960).
  • Slack, G. A. The thermal conductivity of nonmetallic crystals. Solid State Phys. 34, 1–71 (1979).
Introductory material
  • “A Heat Transfer Textbook” by John H. Lienhard IV and John H. Lienhard V
  • “Nano/Microscale Heat Transfer” by Zhuomin M. Zhang

Reference

Li, S., Qin, Z., Wu, H. et al. Anomalous thermal transport under high pressure in boron arsenide. Nature 612, 459–464 (2022).

Cumulative polarization in conductive interfacial ferroelectrics

  • Condensed-matter Physics

Two-dimensional materials with the ability to switch electric dipoles have the potential to greatly impact high-density memory technology. In these materials, interfacial ferroelectricity allows for conductivity within the plane and switchable polarization perpendicular to the plane. This feature makes them more resistant to depolarization fields compared to traditional thin ferroelectric films.

Scientists investigated devices made up of two or three layers of transition metal dichalcogenides (TMDs), a class of materials known for their unique properties. These layers were artificially stacked with parallel lattice orientations and encapsulated by thin flakes of hexagonal boron nitride ($h-BN$), another 2D material. When they measured the room temperature surface potential, they discovered a pattern of triangular domains with different polarization values. These domains were separated by thin walls created by a slight twist angle between the flakes. The polarization was found to occur at the interfaces between layers, suggesting weak coupling between adjacent interfaces, which resulted in a cumulative polarization effect in layered stacks. The potential drop between points far above and below the system was consistent with the measured potential drop, emphasizing the confinement of polarization at the interfaces and the weak coupling between adjacent polarized interfaces.

To demonstrate ladder ferroelectricity, a unique feature of multi-layered systems, researchers measured the potential at the surface of stacked $MoS_2$ crystals. When additional layers with aligned polarization were added, the total polarization increased linearly with the thickness of the stack. Different stacking and polarization regions were separated by local domain walls.

The polarization in $MoS_2$ and $WSe_2$ bilayers coexists with in-plane conductance through individual layers. External gate electrodes, which induce free charge carriers, affect carrier density and enable reversible polarization orientation switching. Polarization in both materials is maintained up to the highest experimentally accessible charge density, with a reduction of $25-50\%$ observed at specific charge densities. Density Functional Theory (DFT) calculations, a computational method used to study the electronic structure of materials, reveal a difference in polarization response to doping between $MoS_2$and $WSe_2$, with each material exhibiting unique trends.

The researchers found that excess electron charge density profiles for undoped $MoS_2$ and $WSe_2$ bilayers primarily accumulate within the layers at the transition metal plane. While the asymmetric contribution of $WSe_2$ to the charge distribution largely averages out, $MoS_2$’s contribution does not. The band structures of the two interfaces explain the predicted asymmetry between the polarization response to electron and hole doping.

This research demonstrates that stacked 2D layers can support robust interfacial polarization with high polarization, distinct and switchable polarization configurations, and high charge carrier densities. These findings pave the way for designing 3D multi-ferroic structures from the bottom up.  

Required Additional Study Materials

  • Lines, M. & Glass, A. Principles and Applications of Ferroelectrics and Related Materials (Oxford Univ. Press, 2001).
  • Eerenstein, W., Mathur, N. D. & Scott, J. F. Multiferroic and magnetoelectric materials. Nature 442, 759–765 (2006).
  • Zhou, W. X. & Ariando, A. Review on ferroelectric/polar metals. Jpn. J. Appl. Phys. 59, SI0802 (2020).
  • Dawber, M., Rabe, K. M. & Scott, J. F. Physics of thin-film ferroelectric oxides. Rev. Mod. Phys. 77, 1083–1130 (2005).
  • Collins, L., Kilpatrick, J. I., Kalinin, S. V. & Rodriguez, B. J. Towards nanoscale electrical measurements in liquid by advanced KPFM techniques: a review. Reports Prog. Phys. 81, 086101 (2018).
Introductory material
  • “Physics of Ferroelectrics: A Modern Perspective” edited by Karin M. Rabe, Charles H. Ahn, and Jean-Marc Triscone
  • “Principles and Applications of Ferroelectrics and Related Materials” by M. E. Lines and A. M. Glass

Reference

Deb, S., Cao, W., Raab, N. et al. Cumulative polarization in conductive interfacial ferroelectrics. Nature 612, 465–469 (2022).

Enantioselective sensing by collective circular dichroism

  • Nanophotonics and plasmonics

Two-dimensional helicoid crystals have five essential characteristics, including the excitation of both transverse electric (TE) and transverse magnetic (TM) polarized surface waves and their unique 3D chiral feature. The optically induced dipole moment of each helicoid in 2D crystals can collectively spin, providing scattered electromagnetic fields with a uniform distribution of the optical helicity density. Two enantiomers within the induced optical helicity density show different back actions on the collective resonances (CR), producing different shifts of the CR frequency. The uniformity and strength of the optical helicity density in the CR mode of 2D helicoid crystals can outperform those of other modes in 2D crystals.

The optical helicity uniformity, $\int h_{\text{sca}} (\textbf{r}) \text{dV}$, determines the enantioselectivity in 2D helicoid crystals. The chiral energy expressed by the CR frequency can shift differently for two enantiomers, resulting in energy state back actions. The direction of energy shift depends on the handedness of the chiral molecular response. The volume run over the sensing volume and the volume inside helicoids, respectively.

The strength and uniformity of $h_{\text{sca}}(\textbf{r})$ are important factors in determining the chiral energy shift in circularly polarized light (CPL) excitations. The sign of the chiral energy shift is determined by the multiplication of two pseudoscalars $\Delta \kappa$ and $\int h_{\text{sca}} (\textbf{r}) \text{dV}$, resulting in four different energy shifts in CRs. The chiral energy shift changes the transmittance spectra $T_\pm$ of two opposite CPL beams, leading to a redshift and increased intensity of $T_+$ and a blueshift and decreased intensity of $T_-$. The spectral position and intensity in $T_+$ and $T_-$ at the CR sensitively shift with changes in $\Delta \kappa$, resulting in a stark peak change in the collective CD between $\Delta \kappa < 0$ and $\Delta \kappa > 0$ at the CR.

Researchers fabricated 2D helicoid crystals with high lattice fidelity using interfacial self-assembly and mechanical rubbing. The crystals were uniformly assembled over a large area and characterized using custom-built optical rotatory dispersion spectroscopy. The size of the plasmonic unit for a fixed lattice periodicity can determine the excitation efficiency of collective circular dichroism (CD), and the 180-nm helicoid showed the maximum collective CD among the fabricated 2D helicoid crystals.

The researchers chose a specific wavevector of incident light to mix TE and TM modes at certain diffraction orders. By increasing the incidence angle, a large in-plane momentum was generated, activating collective resonances (CRs). The strongest signal was induced at an incidence angle of $(\theta, \phi) = (60^\circ, 0^\circ)$, which was used for subsequent experimental CD measurements. The researchers were able to deterministically induce collective CD from assembled 2D helicoid crystals at $(\theta, \phi) = (60^\circ, 0^\circ)$, matching specific diffraction orders.

A 2D helicoid crystal was used for enantioselective sensing. The collective CD peak and dip redshifted for higher concentrations of L-proline and D-proline, with larger changes for D-proline. The enantioselective spectral change can be used to quantify the L:D ratio in a racemic solution. Empirical relations allow for precise quantification of molecular handedness and concentration.

A colorimetric sensor was developed using polarization colorimetry to visually quantify molecular chirality based on the marked change in spectral features of the collective CD. The enantioselective optical response was distinctly visible in the polarization colorimetry result, with a higher sensitivity to D-proline than to L-proline. The analyte chamber was fabricated with PDMS and enclosed a 2D helicoid crystal within it, achieving a clearer enantioselective response of the collective CD with a detection limit for D-proline of up to $10^{-4}$ M.

The researchers demonstrated the versatility of their biomolecular sensor platform by testing it on microRNA-21 and the SNARE complex. The platform was able to detect changes in the collective circular dichroism (CD) of the biomolecules, with a limit of detection of 114 pM for miR-21. The enantioselective response of the platform was also observed in reflection mode, with higher sensitivity to D-proline than L-proline.

The collective CD of 2D helicoid crystals can advance enantioselective sensing by boosting chiral light-matter interactions and providing robustness against molecular stochasticity. With potential applications in monitoring conformational changes at the molecular resolution, this sensor platform offers promising advancements in the field of chiral sensing and molecular analysis. This technology’s ability to detect and differentiate between different chiral molecules and biomolecules, such as microRNA and protein complexes, highlights its potential for a wide range of scientific and industrial applications.

Required Additional Study Materials

  • Fasman, G. D. Circular Dichroism and the Conformational Analysis of Biomolecules (Springer, 1996).
  • Barron, L. D. Molecular Light Scattering and Optical Activity (Cambridge Univ. Press, 2004).
  • Ranjbar, B. & Gill, P. Circular dichroism techniques: biomolecular and nanostructural analyses- a review. Chem. Biol. Drug Des. 74, 101–120 (2009).
  • Hentschel, M., Schäferling, M., Duan, X., Giessen, H. & Liu, N. Chiral plasmonics. Sci. Adv. 3, e1602735 (2017).
  • Kittel, C. & McEuen, P. Introduction to Solid State Physics (Wiley, 1996).
Introductory material
  • “Circular Dichroism: Principles and Applications” edited by Nakanishi, Berova, and Woody
  • “Linear Dichroism and Circular Dichroism” by Bengt Nordén, Alison Rodger, and Timothy Dafforn

Reference

Kim, R.M., Huh, JH., Yoo, S. et al. Enantioselective sensing by collective circular dichroism. Nature 612, 470–476 (2022).

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