Janus State: Duality in Condensed Systems
- Janus state is a term for configurations with two inequivalent faces created by controlled asymmetry, as seen in 2D materials, optical traps, and magnetic systems.
- It encompasses both static (e.g., inversion-symmetry–broken monolayers) and dynamic (e.g., field-driven particle orientation) states, resulting in novel functional behaviors.
- This duality underpins phenomena such as enhanced Stark effects, skyrmionic textures, and polarization-selective photonic modes, unifying diverse physical applications.
Searching arXiv for the supplied Janus-state papers to ground the article in the cited literature. Searching arXiv for "Janus state" and key related papers. Janus state is a domain-dependent technical term for a configuration whose two “faces” are inequivalent. The expression is used in the same broad sense as the Roman god Janus: two sides, channels, components, or constituent states differ in composition, symmetry, topology, orientation, or statistics. In condensed matter, it commonly denotes a structurally asymmetric monolayer with chemically different top and bottom surfaces; in soft matter and optical manipulation, a stable orientational state of a two-hemisphere particle; in magnetism, a remanent texture selected by asymmetric geometry or exchange bias; in photonics, a single resonant state whose upward and downward radiation channels carry different polarization topologies; and in quantum optics, a coherent superposition of two squeezed states whose interference creates distinct statistical “faces” (Lu et al., 2024, Gao et al., 2020, Philipp et al., 2021, Dong et al., 14 May 2026, Azizi, 12 Aug 2025).
1. Semantic core and range of usage
The unifying feature of Janus-state terminology is controlled inequivalence. In all of the cited usages, the relevant object or state is not merely anisotropic; it possesses a specifically two-sided character. What changes from field to field is the carrier of that duality: chemical termination in a monolayer, refractive-index contrast across a sphere, exchange-biased versus unbiased remanence, topological charge in opposite radiation half-spaces, or interference between two bosonic components.
| Domain | Meaning of “Janus state” | Representative paper |
|---|---|---|
| 2D materials | Structurally asymmetric monolayer with different atomic species on opposite sides | (Lu et al., 2024) |
| Optical trapping | Stable orientational configuration of a trapped spherical Janus particle | (Gao et al., 2020) |
| Magnetic particles | Remanent magnetic texture of a hemispherical cap particle | (Philipp et al., 2021) |
| 2D magnetism | Symmetry-broken monolayer enabling DMI, cycloids, and skyrmions | (Xu et al., 2019) |
| Photonic BICs | BIC-derived state with different upward/downward polarization topology | (Dong et al., 14 May 2026) |
| Quantum optics | Superposition of two squeezed vacua or squeezed coherent states | (Azizi, 16 Mar 2026) |
A second distinction is between cases where “Janus” names the state itself and cases where it names the underlying asymmetric unit. In "Angular Trapping of Spherical Janus Particles" the Janus state is explicitly the stable angular configuration of the trapped particle (Gao et al., 2020). In "Multifaceted dynamics of Janus oscillator networks" the formal term is instead “Janus oscillator,” and the relevant states are the collective asynchronous, phase-locked, chimera, and hysteretic regimes generated by that two-faced unit (Nicolaou et al., 2018).
A third distinction is between static and operational meanings. Some Janus states are equilibrium or metastable structures, such as a Janus monolayer or a remanent onion state. Others are field-selected operating states, such as a polarization-controlled trap orientation, a nonequilibrium self-diffusiophoretic motor state, or a chiral quasi-BIC. This suggests that the term denotes a symmetry logic more than a single ontology.
2. Structurally asymmetric Janus states in two-dimensional materials
In 2D materials, Janus-state language is most directly structural. "Symmetry-breaking-induced giant Stark effect in 2D Janus materials" defines the Janus state as a structurally asymmetric 2D monolayer created by breaking the out-of-plane mirror symmetry of a parent symmetric monolayer (Lu et al., 2024). The model system starts from symmetric SnSb with an A-B-B-A four-atom-layer stacking and generates six Janus group IV-V monolayers by one-sided Ge and As substitution: GeSbAs, SnSbAs, GeSnSb, GeSnAs, SbSn-GeAs, and SbGe-SnAs. The broken vertical mirror symmetry produces an intrinsic dipole moment, an internal electrostatic potential gradient, and spatial separation of the valence-band maximum and conduction-band minimum. For the Janus monolayers, the dipole moments per unit cell are about $0.034$–$0.113$ D. The Stark response becomes giant and approximately linear: when the vertical electric field varies from to $0.30$ V/Å, SnSbAs shows a band-gap change up to $134$ meV, whereas symmetric SnSb changes by only 0 meV, about 1 times smaller. The paper relates this to the conventional Stark expression
2
and its generalized form with an induced field 3, with 4. The key microscopic quantity is the VBM-CBM charge-center separation 5, generally larger than 6 Å in the Janus monolayers but smaller than 7 Å in SnSb over the studied field range.
In "Antiferromagnetic and Electric Polarized States in Two-Dimensional Janus Semiconductor Fe8Cl9I0", the Janus state again originates in top-bottom chemical inequivalence, now between Cl and I faces (Zhang et al., 2020). The monolayer belongs to the 1 (No. 157) space group; Fe atoms are sandwiched between a Cl layer and an I layer, and each primitive cell contains one formula unit. The paper reports negative formation energy 2 eV per primitive cell, a reaction energy difference of 3 eV for 4, a phonon spectrum without imaginary modes, and ab initio MD at 5 K for 6 ps preserving the honeycomb structure. The optimized lattice constant is 7 Å and the Young’s modulus is 8 N/m. Because Cl and I have different electronegativities, Bader analysis gives 9 transferred to each I and 0 to each Cl from Fe, yielding an out-of-plane electric polarization of about 1 eÅ and a piezoelectric coefficient of about 2 pm/V. Magnetically, the zero-strain ground state is zigzag AFM with 3, but tensile strain drives four states in sequence: AFM with 4, AFM with 5, FM with 6, and FM with 7. The AFM-to-FM transition occurs around 8 tensile strain, and another magnetization-direction change occurs near 9.
The Janus concept is extended further in "Multiple magnetic states, valley electronics, and topological phase transitions in two-dimensional Janus XYZH" (Tian et al., 28 Feb 2025). These monolayers have composition $0.034$0, $0.034$1, $0.034$2, $0.034$3, with four sublayers arranged as $0.034$4 in space group $0.034$5 (No. 156). The paper proposes $0.034$6 stable ferromagnetic semiconductor monolayers, all showing spontaneous valley polarization and anomalous valley Hall response. For ScBrSH, the valley splitting is $0.034$7 meV, and under strain the system passes through a half-valley metal near $0.034$8 and a QAH phase between $0.034$9 and $0.113$0, with Chern number $0.113$1 and Hall conductance $0.113$2. Here the Janus state is not only polar but valley-active and topological.
Across these examples, the structural Janus state is best understood as built-in inversion-symmetry breaking across the layer thickness. A plausible implication is that the central material functionality is often pre-encoded at zero field: internal potential gradients, charge transfer, SOC asymmetry, and layer-selective orbital rehybridization exist before any external tuning is applied.
3. Magnetic Janus states: remanence, chirality, and layer-coupled topology
In magnetic systems, Janus-state language often shifts from structural asymmetry to the magnetic configuration selected by that asymmetry. "Magnetic Skyrmion State in Janus Monolayers of Chromium Trihalides Cr(I,X)$0.113$3" uses Janus engineering to break inversion symmetry in chromium trihalides by putting I on one side and Br or Cl on the other (Xu et al., 2019). The broken inversion symmetry makes first-neighbor Dzyaloshinskii-Moriya interaction symmetry-allowed. The reported DMI values are $0.113$4 meV with $0.113$5 for Cr(I,Br)$0.113$6, $0.113$7 meV with $0.113$8 for Cr(I,Cl)$0.113$9, and 0 for pristine CrI1. Magnetic anisotropy also changes: 2 meV/Cr for CrI3, 4 meV/Cr for Cr(I,Br)5, and 6 meV/Cr for Cr(I,Cl)7. Parallel tempering Monte Carlo and conjugate-gradient relaxation identify intrinsic skyrmionic states in Cr(I,Br)8, with single- and multi-skyrmion states 9, $0.30$0, and $0.30$1, whereas Cr(I,Cl)$0.30$2 requires an out-of-plane field: skyrmions become metastable between roughly $0.30$3 T and $0.30$4 T, with a stable metastable $0.30$5 skyrmion at $0.30$6 T.
A distinct magnetic usage appears in "Magnetic hysteresis of individual Janus particles with hemispherical exchange-biased caps" (Philipp et al., 2021). Here the particle is Janus because only one hemisphere of a silica sphere is coated with magnetic material. Dynamic cantilever magnetometry on individual particles, combined with micromagnetic simulations, shows that the remanent Janus state depends decisively on exchange bias. For the ferromagnetic Janus particle with Cu/CoFe/Si cap, the global vortex state is energetically favored at remanence and is $0.30$7 attojoules lower in energy than the onion state; the remanent moment is nearly extinguished, $0.30$8. For the exchange-biased particle with Cu/Ir$0.30$9Mn0/CoFe/Si cap, simulations fit the data with 1 kJ/m2, the vortex is not a stable remanent state, and the onion state is stabilized with 3 to 4. The easy axis lies in the equatorial plane and the hard axis along the pole axis, consistent with dominant uniaxial shape anisotropy.
The bilayer part of the XYZH study adds a layer-coupled magnetic and topological Janus-state hierarchy (Tian et al., 28 Feb 2025). For ScBrSH bilayers, all six examined stackings favor interlayer AFM over interlayer FM. In the AA family, AA-1 and AA-2 lack mirror symmetry along 5 and carry out-of-plane ferroelectric polarization 6 pC/m with a switching barrier of 7 meV. These states exhibit layer polarization anomalous valley Hall response, with valence-band valley polarization of about 8 meV and valley Berry curvature around 9 Å$134$0. Under tensile strain the bilayer enters a QLSH phase around $134$1, interpreted as the superposition of two QAH monolayers with opposite chiralities, and twisting by $134$2 induces altermagnetism.
These magnetic cases show that a Janus state need not be defined by net polarity alone. It may instead denote a chiral-exchange-enabled spin texture, a remanent metastable manifold selected by unidirectional anisotropy, or a layer-antagonistic topological phase in which opposite magnetic sectors are locked to opposite layers or valleys.
4. Particle-scale orientational, interfacial, and nonequilibrium Janus states
At the particle and interface scale, Janus states are frequently operational states selected by external fields or maintained gradients. In "Angular Trapping of Spherical Janus Particles", the Janus state is the stable rotational configuration of a PS/PMMA sphere in a linearly polarized laser trap (Gao et al., 2020). The particle has five degrees of freedom, three translational and two rotational, with orientation described by elevation angle $134$3 and azimuth angle $134$4 of a virtual normal to the hemispherical interface pointing toward the PMMA side. The stable states are
$134$5
and
$134$6
Thus the interface plane is parallel to the plane formed by beam propagation and polarization, and the particle center is displaced by about $134$7 along $134$8 so that the trap center lies inside the higher-index PS hemisphere. The restoring torque has the form $134$9, giving a twofold angular symmetry. When the polarization rotates by angle 00, the stable states rotate one-to-one with it, and experiments report interface-angle tracking with a standard deviation of about 01–02.
"Dynamics of Janus motors with microscopically reversible kinetics" uses the term differently: the Janus state is the operating state of a motor with catalytic and noncatalytic hemispheres (Huang et al., 2018). At equilibrium the system may remain chemically active, but it has no sustained net flux and therefore no propulsion. The nonequilibrium steady state is established by fluxes of chemical species maintaining chemical affinity, and propulsion emerges only then. The microscopic reaction model
03
is constructed to satisfy detailed balance through
04
The work also reports quantitative agreement between fluctuating thermodynamics and microscopic simulation for the drift velocity, with a theoretical estimate 05 and simulation 06. Here the Janus state is explicitly a nonequilibrium operating condition rather than a static structure.
A third mesoscale usage appears in "Droplet impact dynamics on Janus-textured heated substrates" (Huang et al., 2022). The substrate has a denser region with spacing 07 and a sparser region with 08, so the droplet experiences lateral asymmetry in wettability, heat transfer, vapor generation, and capillarity. The simulations identify three boiling states: contact boiling, transition boiling, and film boiling. Droplets in contact boiling migrate toward the denser region, while in film boiling at low Weber number they move toward the sparser region, in agreement with the experiments of Zhang et al. cited in that paper. The motion is attributed to unbalanced Young’s force, vapor pressure difference, and thermophoretic force. This is a state-dependent Janus effect: the preferred direction reverses when the boiling regime changes.
These examples illustrate a recurrent pattern. The Janus state is often the stable compromise of a field-driven optimization problem: optical energy reduction in a trap, entropy production under chemical fluxes, or interfacial-force balance during boiling impact. The asymmetry is designed into the object or substrate, but the state is selected dynamically.
5. Photonic Janus states and Janus bound states in the continuum
In photonics, Janus-state terminology acquires a topological meaning. "Tunable high-09 Janus-to-chiral bound states in the continuum in bilayer PhCs" defines a Janus state as a single BIC-derived resonant state whose upward and downward radiation channels carry different polarization topologies (Dong et al., 14 May 2026). The starting point is a symmetry-protected 10-point BIC. Interlayer displacement 11 breaks out-of-plane mirror symmetry 12, decouples upward and downward radiation, and creates the Janus BIC while preserving the true 13-point BIC. A subsequent diagonal in-plane displacement 14 reconstructs the polarization singularities and yields a Janus-chiral BIC. The momentum-space topological charge is
15
with 16. In the Janus regime, one radiation channel can carry a different effective charge from the other; after further in-plane perturbation, the upward channel can have 17 while the downward channel retains 18. The normalized Stokes parameter
19
shows opposite circular-polarization tendency in the two channels. For quasi-BIC realizations, the resonance wavelength is tunable from about 20 to 21 nm by 22 and from about 23 to 24 nm by 25; CD exceeds 26, and with conductivity tuning it becomes switchable and exceeds 27. Near-field optical chirality and multipole decomposition identify a spin-selective magnetic-dipole resonance as the dominant microscopic mechanism.
"Janus bound states in the continuum in structurally symmetric photonic crystals" shows that the same Janus principle can be realized without geometrical asymmetry (Zuo et al., 6 May 2025). The bilayer photonic crystal slab preserves geometric 28 symmetry but allows independent refractive indices 29 and 30, creating optical asymmetry. In the symmetric case 31, the system supports a symmetry-protected BIC at 32 with 33 and an off-34 Friedrich-Wintgen BIC with 35. With detuning 36, the off-37 vortex splits into two C points with half-integer charge 38, and the upward and downward C points shift in opposite directions. At 39, the paper reports opposite net charges near 40: upward 41, downward 42. The structural parameters are explicitly given as 43 nm, 44, ellipticity ratio 45, layer thickness 46 nm, and total thickness 47 nm.
Photonic Janus states therefore differ from chemical Janus states in a fundamental way. The “two faces” are not different surfaces in a compositional sense, but different far-field topologies of the same mode viewed from opposite half-spaces. This suggests a more abstract Janus semantics: asymmetry may reside in the radiation channels rather than in the material body.
6. Janus states in collective dynamics, lattice statistics, and quantum optics
In nonlinear dynamics, the Janus concept appears at the level of the dynamical unit. "Multifaceted dynamics of Janus oscillator networks" defines a Janus oscillator as a pair of phase oscillators with distinct natural frequencies, typically 48 and 49, coupled internally by 50 and externally by 51 (Nicolaou et al., 2018). The ring dynamics are
52
53
The paper does not define a separate formal “Janus state,” but the two-faced unit generates asynchronous states, twisted and uniform phase-locked states, traveling and intermittent chimeras, explosive synchronization, asymmetry-induced synchronization, and inverted synchronization transitions. The cited thresholds are 54, 55, a chimera interval roughly 56, and a heterogeneity threshold around 57 beyond which explosive synchronization disappears.
"Bethe-lattice calculations for the phase diagram of a two-state Janus gas" places the Janus notion into equilibrium statistical mechanics (Liarte et al., 2014). Each particle has one of two orientation classes, 58 or 59, corresponding to opposite Janus-surface orientations. Directional interactions are encoded by pair energies 60, and the Bethe-lattice thermodynamics reduce to a nonlinear density map 61. Fixed points correspond to homogeneous phases, and stable 2-cycles correspond to modulated period-2 phases. The key combination
62
determines the phase topology: 63 gives first-order coexistence between two homogeneous densities, while 64 gives a continuous transition into a cycle-2 modulated phase. In this usage, the Janus state is a discrete orientation state that propagates into macroscopic phase structure through directional interactions.
Quantum-optical Janus states are yet another generalization. "Displaced Janus States: Tunable Non-Gaussianity and Exact Higher-Order Coherences for Quantum Advantage" defines the displaced Janus state as
65
a coherent superposition of two squeezed coherent states with the same displacement 66 but different squeezing parameters (Azizi, 12 Aug 2025). Exact arbitrary-order coherence functions are obtained through generalized squeezing polynomials. The state can interpolate between extreme bunching and strong antibunching or multiphoton suppression; in the antisymmetric small-squeezing limit with 67, the paper gives
68
It also reports Wigner negativity and, in the displaced 69-like limit, 70 for displacement-phase sensing, while arguing that nonlinear Gaussian parameter encoding can reach Heisenberg scaling.
"Quantum Fisher information and quadrature squeezing in Janus superpositions of squeezed vacua" then sharpens the metrological interpretation (Azizi, 16 Mar 2026). Here the Janus state is the simpler superposition
71
The paper proves that under a fair fixed-mean-photon-number comparison, no genuine Janus advantage exists for principal second-moment squeezing: the single squeezed vacuum remains optimal. By contrast, within a fixed two-state span, Janus interference can beat either constituent in a laboratory quadrature variance and in number-generated phase QFI. At fixed observed squeezing 72, the Janus state can substantially enhance quadratic-generator QFI beyond the pure-Gaussian squeezed-vacuum benchmark. For phase sensing at fixed 73, the Janus state beats the squeezed vacuum when
74
These dynamic, statistical, and quantum usages show the widest semantic spread of the term. In some cases Janus labels a two-component unit with opposed tendencies; in others it labels a superposition whose interference reshapes higher moments. The common structure is still two-facedness, but the “faces” may now be dynamical branches, orientation classes, or competing quantum-statistical regimes.
Janus state is therefore best treated as a cross-disciplinary family of concepts rather than a single definition. Its invariant content is the coexistence of two inequivalent faces within one object, mode, or superposition. What changes across fields is the mathematical carrier of that duality: broken mirror symmetry and internal dipoles in 2D materials, remanent magnetic textures in curved caps, stable orientations in optical traps, nonequilibrium flux-maintained propulsion, direction-dependent topological charge in BIC photonics, discrete orientation sectors in lattice models, and interference-controlled higher moments in bosonic superpositions. This breadth explains both the utility and the ambiguity of the term: “Janus state” is precise only within a specified physical context, but across contexts it consistently marks a controlled asymmetry that generates new functionality.
