- Open Access
Crystallization of chiral active Brownian particles at low densities
Phys. Rev. Research 7, 043212 – Published 24 November, 2025
DOI: https://doi.org/10.1103/yntx-ss9r
Abstract
Chiral active matter is a variant of active matter systems in which the motion of the constituent particles violates mirror symmetry. In this article, we simulate two-dimensional chiral Active Brownian Particles, the simplest chiral model in which each particle undergoes circular motion, and show that the system crystallizes at low densities well below the melting point of the equilibrium counterpart. Crystallization is only possible if the orbital radius is long enough to align the circulating particles, but short enough for neighboring particles to avoid collisions. Of course, the system must be driven sufficiently far from equilibrium, since chirality cannot affect thermodynamic properties in classical equilibrium systems. The fluid-crystal phase diagram shows a re-entrant melting transition as a function of the radius of the circles. We show that at least one of the two transitions follows the same two-step melting scenario as in equilibrium systems.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (48)
- L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon, New York, 1968).
- R. Kubo, Statistical Physics (North Holland, Amsterdam, 1990).
- N. Bohr, Studier Over Metallernes Elektrontheori (University of Copenhagen, Copenhagen, 1911).
- H. J. van Leeuwen, Problèmes de la théorie électronique du magnétisme, J. Phys. Radium 2, 361 (1921).
- B. Liebchen and D. Levis, Chiral active matter, Europhys. Lett. 139, 67001 (2022).
- E. Lauga, W. R. DiLuzio, G. M. Whitesides, and H. A. Stone, Swimming in circles: Motion of bacteria near solid boundaries, Biophys. J. 90, 400 (2006).
- I. H. Riedel, K. Kruse, and J. Howard, A self-organized vortex array of hydrodynamically entrained sperm cells, Science 309, 300 (2005).
- M. Huang, W. Hu, S. Yang, Q.-X. Liu, and H. P. Zhang, Circular swimming motility and disordered hyperuniform state in an algae system, Proc. Natl. Acad. Sci. USA 118, e2100493118 (2021).
- F. Kümmel, B. ten Hagen, R. Wittkowski, I. Buttinoni, R. Eichhorn, G. Volpe, H. Löwen, and C. Bechinger, Circular motion of asymmetric self-propelling particles, Phys. Rev. Lett. 110, 198302 (2013).
- H. Zhang, K. Qiao, and Y. Han, Power laws in pressure-induced structural change of glasses, Nat. Commun. 11, 2005 (2020).
- D. Banerjee, A. Souslov, A. G. Abanov, and V. Vitelli, Odd viscosity in chiral active fluids, Nat. Commun. 8, 1573 (2017).
- A. P. Petroff, X.-L. Wu, and A. Libchaber, Fast-moving bacteria self-organize into active two-dimensional crystals of rotating cells, Phys. Rev. Lett. 114, 158102 (2015).
- T. H. Tan, A. Mietke, J. Li, Y. Chen, H. Higinbotham, P. J. Foster, S. Gokhale, J. Dunkel, and N. Fakhri, Odd dynamics of living chiral crystals, Nature (London) 607, 287 (2022).
- E. S. Bililign, F. Balboa Usabiaga, Y. A. Ganan, A. Poncet, V. Soni, S. Magkiriadou, M. J. Shelley, D. Bartolo, and W. T. M. Irvine, Motile dislocations knead odd crystals into whorls, Nat. Phys. 18, 212 (2022).
- C. B. Caporusso, G. Gonnella, and D. Levis, Phase coexistence and edge currents in the chiral Lennard-Jones fluid, Phys. Rev. Lett. 132, 168201 (2024).
- V. E. Debets, H. Löwen, and L. M. C. Janssen, Glassy dynamics in chiral fluids, Phys. Rev. Lett. 130, 058201 (2023).
- P. Arora, S. Sadhukhan, S. K. Nandi, D. Bi, A. K. Sood, and R. Ganapathy, A shape-driven reentrant jamming transition in confluent monolayers of synthetic cell-mimics, Nat. Commun. 15, 5645 (2024).
- Z. Ma, Q.-l. Lei, and R. Ni, Driving dynamic colloidal assembly using eccentric self-propelled colloids, Soft Matter 13, 8940 (2017).
- Q.-L. Lei, M. P. Ciamarra, and R. Ni, Nonequilibrium strongly hyperuniform fluids of circle active particles with large local density fluctuations, Sci. Adv. 5, eaau7423 (2019).
- S. Torquato, Hyperuniform states of matter, Phys. Rep. 745, 1 (2018).
- M. Henkel, H. Hinrichsen, and S. Lübeck, Non-Equilibrium Phase Transitions: Absorbing Phase Transitions (Springer, Dordrecht, 2008), Vol. 1.
- Y. Kuroda, T. Kawasaki, and K. Miyazaki, Long-range translational order and hyperuniformity in two-dimensional chiral active crystal, Phys. Rev. Res. 7, L012048 (2025).
- N. D. Mermin, Crystalline order in two dimensions, Phys. Rev. 176, 250 (1968).
- R. Hanai, Nonreciprocal frustration: Time crystalline order-by-disorder phenomenon and a spin-glass-like state, Phys. Rev. X 14, 011029 (2024).
- M. Kardar, Statistical Physics of Fields (Cambridge University Press, Cambridge, 2007).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/yntx-ss9r for details on simulation methods and system-size dependence.
- E. P. Bernard and W. Krauth, Two-step melting in two dimensions: First-order liquid-hexatic transition, Phys. Rev. Lett. 107, 155704 (2011).
- Z. Ma and R. Ni, Dynamical clustering interrupts motility-induced phase separation in chiral active Brownian particles, J. Chem. Phys. 156, 021102 (2022).
- A. Onuki, Phase Transition Dynamics (Cambridge University Press, Cambridge, 2007).
- Y. Kuroda, H. Matsuyama, T. Kawasaki, and K. Miyazaki, Anomalous fluctuations in homogeneous fluid phase of active Brownian particles, Phys. Rev. Res. 5, 013077 (2023).
- Y. Kuroda and K. Miyazaki, Microscopic theory for hyperuniformity in two-dimensional chiral active fluid, J. Stat. Mech. (2023) 103203.
- I. Guillamón, H. Suderow, A. Fernández-Pacheco, J. Sesé, R. Córdoba, J. M. De Teresa, M. R. Ibarra, and S. Vieira, Direct observation of melting in a two-dimensional superconducting vortex lattice, Nat. Phys. 5, 651 (2009).
- J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6, 1181 (1973).
- B. I. Halperin and D. R. Nelson, Theory of two-dimensional melting, Phys. Rev. Lett. 41, 121 (1978).
- A. P. Young, Melting and the vector Coulomb gas in two dimensions, Phys. Rev. B 19, 1855 (1979).
- K. J. Strandburg, Two-dimensional melting, Rev. Mod. Phys. 60, 161 (1988).
- J. Y. Lee and K. J. Strandburg, First-order melting transition of the hard-disk system, Phys. Rev. B 46, 11190 (1992).
- J. A. Zollweg and G. V. Chester, First-order melting transition of the hard-disk system, Phys. Rev. B 46, 11186 (1992).
- H. Weber, D. Marx, and K. Binder, Melting of two-dimensional solids: A Monte Carlo study, Phys. Rev. B 51, 14636 (1995).
- A. Jaster, The hexatic phase of the two-dimensional hard disks system, Phys. Lett. A 330, 120 (2004).
- C. H. Mak, Finite-size scaling of the hexatic phase in two-dimensional hard disks, Phys. Rev. E 73, 065104(R) (2006).
- K. Zahn, R. Lenke, and G. Maret, Two-stage melting of paramagnetic colloidal crystals in two dimensions, Phys. Rev. Lett. 82, 2721 (1999).
- Y. Peng, Z. Wang, A. M. Alsayed, A. G. Yodh, and Y. Han, Melting of colloidal monolayers with long-range repulsions, Phys. Rev. Lett. 104, 205703 (2010).
- K. Bagchi, H. C. Andersen, and W. Swope, Computer simulation study of the melting transition in two dimensions, Phys. Rev. Lett. 76, 255 (1996).
- X.-q. Shi, F. Cheng, and H. Chaté, Extreme spontaneous deformations of active crystals, Phys. Rev. Lett. 131, 108301 (2023).
- P. Digregorio, D. Levis, A. Suma, L. F. Cugliandolo, G. Gonnella, and I. Pagonabarraga, Full phase diagram of active Brownian disks: From melting to motility-induced phase separation, Phys. Rev. Lett. 121, 098003 (2018).
- Y.-W. Li and M. P. Ciamarra, Accurate determination of the translational correlation function of two-dimensional solids, Phys. Rev. E 100, 062606 (2019).
- S. C. Kapfer and W. Krauth, Two-dimensional melting: From liquid-hexatic coexistence to continuous transitions, Phys. Rev. Lett. 114, 035702 (2015).