Main

The interactions of electronic, orbital, spin and nuclear degrees of freedom govern the emergence of symmetry-broken functional states in solids. Light allows for tilting the balance between distinct states and phases1,2 and enables control over the final states by precisely tuning the optical interaction (Fig. 1a, top). A prototypical scenario is given by the optical quench of an electronic density modulation and lattice distortion in charge-density-wave (CDW) materials3,4,5,6. In the prevalent case of a Peierls insulator7, the interplay of quasi-one-dimensional (quasi-1D) electronic states at the Fermi energy and the lattice instability lead to the opening of a bandgap (ΔCDW) and the formation of electronic valleys in a metal–insulator transition (Fig. 1a, bottom)8. Photodoping of occupied bonding and unoccupied antibonding states at the band edges, in turn, collapses the bandgap and transiently reverses the phase change9,10. Although such optical switching frequently occurs on femtosecond timescales, it is largely indiscriminate with respect to the induced electronic transitions. In particular, electronic states near the gap are generally populated indirectly via rapid relaxation from optically accessible higher-lying bands (Fig. 1b, top)3,11. The deposited energy per lifted carrier, therefore, far exceeds that required for a minimally invasive phase transformation, which leaves the system with substantial lattice and electronic heat. A valley-polarized population from excitation at the bandgap12, on the other hand, may largely prevent dissipation to promote a minimum-energy transition pathway (Fig. 1b, bottom). Moreover, close to the photon-energy threshold, the phase change is expected to become particularly susceptible to local variations in the real-space microstructure and domain distribution4,13.

Fig. 1: Optical surface electronic texture control via valley-selective photodoping.
figure 1

a, Top: schematic of the optical control parameters that drive selective surface domain switching. Bottom: the Peierls transition in a 1D atomic chain yields the formation of a periodic lattice distortion and CDW with a characteristic energy gap (ΔCDW). The electron density of valence (dark red) and conduction (light red) states exhibits a bonding and antibonding character with respect to the CDW along the chain direction. b, Top: light-induced electronic quench of the CDW phase. A population of states at the CDW gap, mediated by higher-lying surface bands (Multiband), is accompanied by electronic and lattice heating and yields a homogeneous phase change across the surface via delocalized energetic charge carriers. Bottom: direct bandgap excitation (Valley selective) minimizes dissipation, which manifests in domain-specific switching (red wires), with pronounced phase coexistence and local carrier confinement. c, Optical transition between the insulating (8 × 2) and metallic (4 × 1) phases of indium nanowires. d, Top: density-functional-theory-calculated electronic band structure of the Si(111) (8 × 2)–In phase (Methods). ΔΓ and ΔX denote the direct bandgaps, leading to the formation of energetic valleys in the band structure. Bottom: energy-integrated optical absorption. X-valley selectivity for low excitation energies and parallel polarization minimizes electronic heating and enables orientation-specific switching. Unspecific multiband absorption at higher excitation energies yields a delocalized hot-carrier distribution and homogeneous switching. The threshold energy is chosen to illustrate the transition between the regimes (see also Supplementary Fig. 1). k∥ is the momentum vector along the Brillouin-zone high-symmetry points with respect to the wire direction.

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Realizing such conditions, in this work, we use the valley-selective photodoping of strongly coupled electronic states to demonstrate control over the domains and texture of a quasi-1D Peierls insulator. Specifically, we exploit the anisotropic absorption of nanowire domains by tuning both photon energy and polarization to the transition matrix elements most strongly coupled to the structural transformation. The reduction in electronic excess energy facilitates a minimum-energy pathway to domain-specific switching and decreases thermal relaxation. This selection of the carrier energy allows for spatial control over the phase transition, from delocalized carriers and homogeneous switching at high photon energy to locally confined carriers and domain-specific switching close to resonant gap excitation. The photoinduced formation of metallic nanodomains surrounded by insulating nanodomains demonstrated here represents the controlled preparation of nanoscale electronic textures, suggesting avenues for optically engineered electronic percolation and quantum confinement in ‘Peierls heterostructures’.

Valley-specific excitation of Peierls-distorted atomic wires

Atomic wires formed by indium atoms on the (111) face of silicon14 are a prominent model system with near-ideal quasi-1D electronic properties. The corresponding surface reconstruction in a metallic (4 × 1) room-temperature phase is characterized by a parallel arrangement of atomic zigzag chains (Fig. 1c)15. Cooling below the critical temperature Tc = 125 K transforms the system into the insulating (8 × 2) hexagon phase in a triple-band Peierls transition16. A doubling of lattice periodicity is brought about by shear and rotary distortions, leading to the formation of interchain and intrachain covalent bonds within the coupled indium chains, respectively17. The phase change is equally reflected in the electronic band structure by the opening of bandgaps and concomitant formation of energetic valleys (Fig. 1d, top). Lateral shearing of zigzag chains causes a bandgap opening at the surface Brillouin-zone Γ point (ΔΓ)18, whereas the rotation-induced dimerization of outer indium atoms yields a bandgap at the X point (ΔX)17.

In particular, the formation of a supercooled metallic (4 × 1) phase can be triggered by light without reaching the phase transition temperature. In this process, optically generated electrons and holes rapidly scatter towards electronic states at the CDW gap, quenching the insulating bandgap and lifting the structural distortion on a 350-fs timescale9. Although the ultrafast transition involves a directed coherent nuclear motion driven by valley-specific couplings between carrier populations and well-defined unit-cell distortions10,17,19, the associated band structure dynamics were so far found to be independent of the incident photon energy11,20. However, the inherent anisotropy of bands at the insulating gap holds the potential for spatially distinct final-phase textures, which have not been explored21. We illustrate this anisotropy in the energy-integrated optical absorption of indium nanowires (Fig. 1d, bottom). At low photon energies, we find that absorption is largely limited to transitions in the X valley (at the insulating gap ΔX) and to a polarization parallel to the nanowire direction. By contrast, multiband absorption at higher excitation energies is unspecific towards strongly coupled states and exhibits a weaker perpendicular anisotropy.

Creating coexistent electronic phases by polarization-selective switching

We explore this regime experimentally by using ultrafast low-energy electron diffraction (ULEED) combined with wavelength- and polarization-controlled excitation (Methods and Extended Data Fig. 1). In short, ULEED uses the backscattering diffraction of electron pulses from surfaces to probe optically induced changes in the atomic-scale structure22,23,24,25. In the present system, we monitor the phase transformation via changes in the intensity of characteristic diffraction peaks. Specifically, at a base temperature of T = 60 K, indium nanowires in the (8 × 2) CDW phase undergo a pump-induced ultrafast transition into the metastable (4 × 1) structure, which is subsequently probed by a photoemitted electron pulse. After the pump pulse, we observe an intensity decrease and increase in the (8 × 2) and (4 × 1) diffraction features, respectively. We systematically trace the photon-energy-resolved intensity suppression of the (8 × 2) diffraction features at a fixed time delay (Δt = 40 ps) as a function of polarization, relative to the nanowire orientation (the analysed diffraction features are sketched in Extended Data Fig. 2). For this purpose, we differentiate two regimes of nanowire textures on the Si(111) surface: a single orientation, imposed by a linear step gradient on a 2°-miscut wafer (Fig. 2a) and rotational domains, formed naturally on the non-stepped surface (Fig. 3a) (domain-size range, 103–104 nm2 (ref. 26)). For a single orientation, we observe that the switching efficiency of the atomic wires is highly dependent on the incident electric-field polarization. At infrared (IR) driving wavelengths (Fig. 2b, left), the observed anisotropy aligns with the nanowire orientation, which specifically points towards direct absorption by quasi-1D electronic states close to the X point in the surface Brillouin zone (Fig. 1d, bottom). Here the coupling of the bonding and antibonding orbitals with respect to the CDW necessitates a polarization along the nanowire (Extended Data Fig. 3). This assignment is corroborated by the fingerprint of the involved electronic states, given by their preferential coupling to the vibrational rotation mode10,17,19. In consequence, optical excitation at the CDW gap yields a mode displacement that modulates the dimerization of indium atoms along the nanowire edges. Indeed, we observe an increased amplitude of the rotational mode in complementary coherent control experiments at IR wavelengths (Supplementary Note 1).

Fig. 2: Polarization and photon energy dependencies of the (8 × 2) to (4 × 1) switching efficiency.
figure 2

a, LEED image and real-space sketch of parallel-oriented indium atomic wires on a stepped Si wafer surface with a 2° miscut relative to the (111) plane. b, Polarization-dependent switching efficiency for increasing photon energy, at the maximum diffraction spot suppression (1 – I(8 × 2)Δt = 40 ps/I(8 × 2)Δt = −150 ps). The in-plane electric-field component is depicted relative to the nanowire direction. Incident fluences (from left to right): 1.04 mJ cm–2, 0.59 mJ cm–2, 0.62 mJ cm–2, 1.09 mJ cm–2 and 1.40 mJ cm–2.

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Fig. 3: Polarization-sensitive and charge-transfer-induced switching in a domain texture.
figure 3

a, Three-fold symmetric rotational domains on a flat Si(111) wafer surface. The LEED image comprises a superposition of domain-specific reflexes. b, Polarization-dependent switching of rotational domains. Δφ denotes the angle between the in-plane electric field and the nanowire orientation. c, Isotropic switching at near-IR wavelengths for all domain orientations in the entire fluence range. d, Transition between valley-selective to multiband excitation manifests in a loss of the intrinsic anisotropy (Fig. 2) due to the interdomain transfer of hot charge carriers. Incident fluences for 0.8 eV, 1.2 eV and 1.55 eV are 1.60 mJ cm–2, 1.40 mJ cm–2 and 2.03 mJ cm−2, respectively.

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In the near-IR regime, the anisotropy gradually reverses towards perpendicular polarization (Fig. 2b, right), where the population of electronic states at the CDW gap is largely mediated by higher-energy surface bands, spread across the entire surface Brillouin zone. This reversal is intuitively explained by the energy-dependent alternation of Bloch function symmetries, which necessitates a rotation to perpendicular anisotropy at higher transition energies (Supplementary Note 2)27. Our findings are qualitatively consistent with linear reflectance anisotropy21 and IR spectroscopy28 studies, suggesting an intrinsic anisotropy due to polarization-sensitive absorption with respect to the nanowire orientation in conjunction with a nonlinear phase transition efficiency as a function of excitation density (Fig. 3c).

Harnessing the measured intrinsic anisotropy, we next demonstrate real-space texture control in the rotational domain structure (Fig. 3a). Here the nanowire orientation is directly linked to the diffraction reflex angle in the LEED image, providing orientation-resolved access to the phase change within the domain texture. To illustrate the dependence of the switching efficiency with the in-plane electric-field component, the domain-specific anisotropy is depicted with respect to the individual nanowire orientation (Fig. 3b). For IR excitation, the polarization dependence agrees with the intrinsic anisotropy, that is, with that measured on a stepped surface, which demonstrates domain-specific absorption and switching. At shorter near-IR wavelengths, in stark contrast to the intrinsic anisotropy, we find a surprisingly isotropic response (Fig. 3d), which is independent of the excitation density (Fig. 3c). From these data, we conclude that the homogeneous global response of all the domains stems from the delocalizing transfer of energetic photoexcited charge carriers across domain boundaries, effectively eliminating the intrinsic domain response. The strong dependence on photon energy is further attributed to the increasing amount of optical excess energy in the electron system after the insulator–metal transition, allowing for higher mobility across potential barriers between metallic and neighbouring insulating domains. A direct observation of this charge-transfer-induced phase transition in future studies could involve time-resolved scanning tunnelling microscopy29,30 or time- and angle-resolved photoemission spectroscopy.

Suppressed ground-state relaxation from minimized thermal fluctuations

Beyond charge carrier confinement, we examine the implications of lattice heating from photon excess energy on the metastable state. Specifically, we track the temporal evolution of the (8 × 2) spot intensity at identical initial suppression on a stepped wafer and observe a prolonged recovery from near-IR to IR excitation (Fig. 4a). We ascribe this difference to photon-energy-dependent thermal fluctuations, driving the relaxation via over-the-barrier transitions (Fig. 4a, inset)31. This assignment is corroborated by a more pronounced suppression in (4 × 1) diffraction intensity at near-IR driving, due to a larger Debye–Waller effect at this excitation (Fig. 4b). The diffuse background intensity (Fig. 4c) provides further information on the degree of dynamic and structural disorders of the surface32. The photon-energy-dependent thermal fluctuations are reflected in different levels of the diffuse background throughout the delay range. In addition, however, both curves display a global reduction in the diffuse background below the value before excitation. We interpret this finding as direct evidence for a laser-induced ordering of the surface on the transition to the metastable (4 × 1) phase. Specifically, the annihilation of localized defects in the CDW lattice33,34 render this surface more long-range ordered. Besides a potential narrowing of the spot widths, which could not be resolved experimentally, the absence of such point-like defects in the (4 × 1) phase will also decrease diffuse scattering throughout the Brillouin zone. Our findings, thus, imply that valley-selective excitation approaches a minimum-energy pathway for the phase transition and leaves the system in a highly ordered state from which thermal relaxation is suppressed (Fig. 4d).

Fig. 4: Lattice heating and thermal relaxation of the metastable (4 × 1) phase, driven by optical excess energy.
figure 4

a, Integrated (8 × 2) diffraction spot intensity as function of pump–probe delay Δt at incident photon energies of 0.8 eV and 1.55 eV on a stepped wafer. The light polarization was chosen parallel and perpendicular to the nanowire orientation, respectively, corresponding to the maximum switching efficiency at fluences of F0.8 = 1.95 mJ cm−2 and F1.55 = 3.12 mJ cm−2. For identical intensity suppression, the relaxation into the (8 × 2) ground state accelerates with photon energy due to increasing thermal lattice fluctuations, following the phase transition (see the inset). b, Corresponding (4 × 1) diffraction spot intensity. Increased lattice heating at 1.55-eV excitation manifests in an intensity reduction due to the Debye–Waller effect (ΔIDBW). c, Pump-induced dynamic disorder increases the diffuse background intensity, counteracted by a reduction in the static disorder from enhanced phase homogeneity. d, Left: real-space sketch of indium atomic wires in the (8 × 2) phase, showing characteristic phase defects (alongside phase boundaries46), which cause diffuse background scattering. Right: the photoinduced (4 × 1) structure exhibits an increased phase homogeneity. Thermal lattice fluctuations cause an accelerated relaxation for increasing photon energy.

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Discussion and outlook

From these observations, an intuitive picture of the spatiotemporal phase-change dynamics in the regime of valley-selective versus multiband excitation emerges. IR photon absorption effectively confines charge carriers to rotational nanodomains, selected by the incident polarization. The population and depopulation of strongly coupled electronic states at the X valley collapses the bandgap (Fig. 1d, ΔX) in an insulator–metal transition within about 200 fs (ref. 11), localizing the low-energy photoexcited charges to the absorbing domain. As lattice fluctuations are suppressed, thermal ground-state recovery slows down on the nanosecond timescale25,35. On the other hand, near-IR absorption across the band structure yields a delocalized hot charge carrier distribution, homogeneous switching and pronounced lattice heating.

We believe that optically engineered phase textures expand the paradigm of light-induced phenomena and enable a polarization-sensitive control of functional states in real space. Therefore, motivated by our experimental findings, we theoretically explore a tangible implementation of ‘Peierls heterostructures’. Polarization-specific switching can yield optically controlled electronic properties in percolation networks (Extended Data Fig. 4 and Supplementary Note 3 provide the proposed device design). Although homogeneous switching results in a surface texture with isotropic conductivity, that is, an equal fraction of metallic nanowire orientations, domain-specific switching promises tunable anisotropy when the incident polarization and fluence are adjusted accordingly. Furthermore, a possible implementation of optically tailored electronic properties is given by the transient formation of isolated metallic grains at parallel polarization, resulting in the quantization of electronic states within the insulating bandgap (Extended Data Fig. 5 and Supplementary Note 2 show the tight-binding simulations of the the resulting local density of states).

In conclusion, our results demonstrate the quench of a Peierls insulator by means of valley-selective optical transitions that specifically address bonding and antibonding orbitals. In this way, we achieve deep subwavelength precision in an optically driven phase change and gain control over the real-space texture. Our results suggest an important role of optical excess energy in photoinduced phenomena with immediate ramifications for the ability to prepare and manipulate coexisting electronic phases. The inherent nature of Peierls physics at the core of this quasi-1D system implies a broader relevance to materials, where changes between electronic phases are instigated by distinct low-symmetry electronic states. As such, we believe that polarization-sensitive switching offers a versatile framework for patterning domain structures and controlling nanoengineered functionalities across various exotic electronic systems, such as correlated oxides4,13,31,36,37,38,39, Weyl semimetals40,41 and materials exhibiting electronic nematicity42,43,44,45. Hence, the optical preparation of electronic phase separation introduces an additional degree of freedom in light-induced switching.

Methods

Density functional theory calculations

We performed density functional theory simulations within the local density approximation47 as implemented in the Vienna ab initio simulation package48. The electronic structure is described by projector-augmented wave potentials49 with a plane-wave basis set limited to a cut-off energy of 250 eV. The surface was modelled using periodic boundary conditions and a slab with three bilayers of silicon. Si dangling bonds at the bottom layer were saturated with hydrogen. To determine the ground-state electronic structure, a 2 × 8 × 1 Monkhorst–Pack mesh was used to sample the Brillouin zone of the Si(111)–(8 × 2)In structure, corresponding to 256 k points in the Si(111)–(1 × 1) surface unit cell. The band structure calculations were performed using 40 (10) k points along the Γ–X (X–M) direction.

The orbital character of the bonding and antibonding states (Extended Data Fig. 3) was determined by integrating the electronic density of states along the X–M direction and across the topmost four valence bands and lowest four conduction bands, respectively. The resulting densities are plotted in Extended Data Fig. 3 at an isovalue of 0.033 e− Å−3.

Consistent with the numerical approach outlined elsewhere21, the oscillator strength was calculated in independent particle approximation from the squared transition matrix elements (∥Mif∥2) between all the occupied (i) and unoccupied (f) surface bands within the Brillouin zone along the depicted high-symmetry points at parallel and perpendicular polarizations with respect to the wire direction. To this end, we considered 240 occupied and 120 empty bands. The calculated values at all the momenta are energy integrated and normalized to the overall maximum.

Ultrafast LEED and optical setup

Ultrafast LEED is a technique for the investigation of structural dynamics at solid-state surfaces by means of an optical pump and electron probe scheme (Extended Data Fig. 1)22,23,24,25. It combines the high surface sensitivity of photoemitted low-energy electrons in backscattering geometry with ultrafast optical excitation to follow the evolution of non-equilibrium surface structures .

The demonstrated high temporal and momentum resolutions are achieved using a custom-built laser-driven electron gun consisting of a nanometric tungsten tip as well as four metal electrodes (outer diameter, 2 mm). Ultrashort electron pulses are generated from localized two-photon photoemission by illuminating the tip apex with femtosecond laser pulses (central wavelength, λc = 400 nm; pulse duration, τp = 45 fs; pulse energy, Ep = 30 nJ) at a repetition rate of 100 kHz. The small diameter of the electron gun allows for a small sample distance without blocking the backscattered electrons, resulting in pulse durations down to 16 ps. Detected electrons are amplified and recorded by a combination of a chevron microchannel plate, a phosphor screen and a scientific complementary metal–oxide–semiconductor camera.

In the described experiments, the surface is excited using a wavelength-tunable optical pump pulse from an optical parametric amplifier (λc = 800 nm, 1,240 nm, 1,550 nm and 2,066 nm; ℏω = 1.55 eV, 1.0 eV, 0.8 eV and 0.6 eV; Δτ = 232 fs) or with a fixed pulse wavelength from a Yb:YAG amplifier system (λc = 1,030 nm, ℏω = 1.2 eV and Δτ = 212 fs). The surface is probed by a photoemitted 80-eV electron pulse with a beam diameter of ~80 × 80 μm2 (full-width at half-maximum).

Sample preparation

All the experiments in this work have been conducted under ultrahigh-vacuum conditions (base pressure, p < 2 × 10−10 mbar), thereby minimizing the effect of adsorbate-related (8 × 2) ground-state recrystallization from the supercooled (4 × 1) phase50. The silicon substrate (phosphorus-doped wafers with resistivity R = 0.6–2 Ω cm), showing only a single-wire orientation, was miscut by 2° towards the [–1 –1 2] direction to create a high surface step density. The oriented steps effectively confine the atomic indium wires along one crystallographic direction. On the other hand, wafers cut along the (111) face of silicon exhibit much larger terraces, where all the three crystallographically equivalent orientations are equally found. All the samples were cleaned by flash annealing at 1,350 °C for 5 s via direct-current heating. Subsequently, 1.2 monolayers of indium were deposited onto the resulting Si(111) (7 × 7) surface reconstruction at room temperature and annealed at T = 400 °C for 300 s. The resulting Si(111) (4 × 1)–In phase was inspected in our ultrafast LEED setup and subsequently cooled to a base temperature of T = 60 K using an integrated continuous-flow helium cryostat. The phase transition between the high-temperature (4 × 1) and low-temperature (8 × 2) phases was observed at a temperature of 125 K.