Ultrafast Switching to a Stable Hidden Quantum State in an Electronic Crystal

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Science  11 Apr 2014:
Vol. 344, Issue 6180, pp. 177-180
DOI: 10.1126/science.1241591

Exposing a Hidden State

Shining intense laser light on a material can temporarily alter its properties. The effect usually subsides after a few picoseconds, unless the system is trapped in a metastable state, in which case the transient period may last as long as microseconds. Stojchevska et al. (p. 177) observed that, following exposure to a 35-femtosecond laser pulse, the layered dichalcogenide 1T-TaS2 entered a stable “hidden” state not present in the equilibrium phase diagram and stayed there indefinitely. The switch to the hidden state could be reversed by heat or a train of laser pulses. Because the switch alters the sample's conducting properties, the phenomenon might also lead to practical applications.


Hidden states of matter may be created if a system out of equilibrium follows a trajectory to a state that is inaccessible or does not exist under normal equilibrium conditions. We found such a hidden (H) electronic state in a layered dichalcogenide crystal of 1T-TaS2 (the trigonal phase of tantalum disulfide) reached as a result of a quench caused by a single 35-femtosecond laser pulse. In comparison to other states of the system, the H state exhibits a large drop of electrical resistance, strongly modified single-particle and collective-mode spectra, and a marked change of optical reflectivity. The H state is stable until a laser pulse, electrical current, or thermal erase procedure is applied, causing it to revert to the thermodynamic ground state.

In condensed matter systems, laser photoexcitation may temporarily destroy ground-state ordering; the system typically reverts to the ground state in a few picoseconds, unless it passes though a transient metastable state. Such metastable states have been shown to persist on time scales between 10−9 and 10−3 s (19) before returning to the ground state by a combination of thermal, electronic, and lattice relaxation processes (2). Stability of photoinduced states has been demonstrated in a manganite (6) and in chalcogenide glasses (10), where switching occurs between neighboring equilibrium thermodynamic states. Here, we report on bistable switching to a hidden (H), spontaneously ordered macroscopic quantum state whose properties are distinct from those of any other state in the equilibrium phase diagram. The hidden state transition (HST) occurs in a layered quasi–two-dimensional chalcogenide 1T-TaS2 crystal, which exhibits multiple competing ground states under equilibrium conditions. Near Tc0 = 550 K, 1T-TaS2 forms an incommensurate (IC) charge density wave (CDW) with an associated lattice distortion. Upon cooling, these modulations sharpen to form star-shaped polaron clusters (Fig. 1A). Their ordering is thought to be responsible for a variety of phases, causing a transition to a nearly commensurate (NC) state for T < Tc1 = 350 K, and a hysteretic first-order transition to a gapped commensurate (C) phase near Tc2 = 183 K. Upon heating, the system develops a triclinic (T) stripe-like ordered state around 223 K, which reverts to the NC state at T = 283 K (11). Further nearby equilibrium states are revealed upon application of external pressure (12) or doping (13), both of which make 1T-TaS2 superconducting.

Fig. 1 Resistivity switching of 1T-TaS2 by a 35-fs laser pulse at 800 nm.

(A) Temperature dependence of the four-probe resistance r(T) on temperature cycling; blue and green curves are measured on cooling and warming, respectively. The sketches show the lattice distortions associated with an individual polaron (top) and their ordering in the NC (high T) and C (low T) states. (B) The drop of r at 1.5 K after a single pulse with UW > UT, where UT is the threshold fluence (red arrow); the blue curve is the resistance measured on cooling. Upon heating, the resistance reverts between 60 and 100 K (black curve). Inset: Schematic of the sample and contacts.

To induce the HST, we use a single sub–35-fs write (W) pulse from an amplified Ti-sapphire laser at 800 nm with energy UW ≈ 1 mJ/cm2. After a HST is induced at 1.5 K, the four-probe resistance r(T) drops approximately three orders of magnitude and remains in this state indefinitely (verified up to 1 week) at this temperature (Fig. 1B). Upon heating, r(T) is approximately constant up to 60 K, whereupon it starts increasing; above TH ~ 100 K, it merges approximately with the virgin r(T) curve corresponding to the C state. The current-voltage characteristics remain linear throughout. Empirically we found that the H state can be completely erased (E) by a train of 104 50-ps pulses, each with energy UE ≈ 1 mJ/cm2. Alternatively, Joule heating can be used for erasure by passing a current of ~0.1 mA through the device (14). In both cases, the system reverts to the C state. Stable switching can also be achieved at intermediate temperatures up to T ~ 70 K (14). The effect is entirely reversible from cycle to cycle and from sample to sample, irrespective of the sample growth batch, and there appears to be no limit on the number of W-E cycles that can be performed. [See supplementary materials for experimental details on thermal protocols, including aging effects (15), and a description of the laser lithography used to manufacture the contacts.]

To gain insight into the microscopic nature of the hidden state, we investigated the single-particle and collective excitations by pump-probe spectroscopy, with the pump and probe pulse energies kept low (<10 μJ/cm2 and <1 μJ/cm2, respectively) to ensure minimal disturbance of either state. The sample reflectivity R(T) was simultaneously recorded by the probe beam. In Fig. 2, we show the transient reflectivity ΔR/R of 1T-TaS2. In the virgin C state, we observed oscillations due to the coherent excitation of the amplitude mode (AM) and phonons that were superimposed on a background from exponentially decaying single-particle (SP) excitations across the gap (16). The spectrum S(ω) obtained by Fourier transformation shows a strong AM at 2.46 THz and weaker phonon modes at 2.1, 2.18, 3.2, and 3.85 THz (Fig. 2B). The HST modified the ΔR/R (Fig. 2A) and the SP signal was substantially reduced. In the spectrum after the HST (Fig. 2B), the AM peak at 2.46 THz disappears in favor of a new mode at 2.39 THz; intensities of modes at 3.10 THz and 3.85 THz are reduced, and some additional spectral intensity appears between 2 and 2.5 THz. Upon heating, the spectrum of the H state remains unchanged until ~70 K; above 70 K, it gradually returns to the C state. Concurrent with the switching of the AM and phonons, we observed a switching of reflectivity R at 800 nm (Fig. 2D). All the observations display typical threshold behavior as a function of UW; below threshold fluence, the resistivity, AM frequency, and reflectivity revert to the C state values after the W pulse. Close to threshold fluence, the AM shows bimodal behavior (fig. S5D), which we interpret as incomplete switching. We observed no intermediate shift of the AM in different samples, indicating distinct two-phase behavior. The H state spectrum is quite different from the NC state spectrum (Fig. 2, A and B) or the T state spectrum (14), indicating that it is not related to the equilibrium states.

Fig. 2 Spectral signatures of the HST process.

(A) Transient reflectivity ΔR(t)/R of 1T-TaS2 in the virgin state (blue dashed line), after exposure to a 50-fs W pulse (red line), and after an E pulse (green line). Black line: data in the NC state at 220 K recorded upon cooling (offset for clarity). (B) The corresponding Fourier-transformed power spectra S(ω) using the same color notation. (C) Switching threshold fluence UT as a function of pulse length τW measured optically with pump-probe experiments. The red line is predicted by the model calculation (14). (D) Reflectivity at 800 nm recorded with the photodiode during a sequence of alternating W and E pulses. (The noise is from the laser.)

We emphasize some notable features of the HST: (i) After photoexcitation, the H state spontaneously orders below TH, as indicated by the narrowness of the AM peak and the fact that no partial frequency shift is observed even when incomplete switching is caused by near-threshold excitation. (ii) The switching occurs only with short pulses, and the threshold increases with increasing τW (Fig. 2C). (Note that the threshold can no longer be achieved with τW > 4 ps at any UW that we tried.) (iii) The H state is stable until erased or heated above ~70 K. Note that TH has no special importance under equilibrium conditions and is relevant only for describing the transition from the H state to the C state.

To understand these unusual phenomena, we first introduce a scenario for switching based on the current understanding of the electronic ordering in 1T-TaS2 (11, 15, 17, 19), and then describe a phenomenological model consistent with the data. The relevant electronic states of 1T-TaS2 in the C state that are within reach of our 1.5-eV laser photons are shown in Fig. 3C. They are formed predominantly from a single Ta d band, which is split into subbands by the formation of a CDW depicted in Fig. 1A. Six of these subbands are filled with 12 electrons per new large unit cell, forming a manifold of occupied states up to 0.4 eV below EF (Fig. 3C, in blue). The 13th leftover electron is localized on the central Ta atom, causing inward radial displacements of 12 neighbors in the shape of a star of David (9, 14, 16), thus forming a self-localized polaron. The 13th electron gives rise to a half-filled narrow metallic band straddling the Fermi level; this band is further split by the Coulomb interaction into upper and lower Hubbard bands (Fig. 3C, green) (18), whereby the upper band merges with the manifold of unoccupied subbands above EF while the lower one is ~0.2 eV below EF. This is well above the top of the valence band at –0.4 eV, which makes the C state a Mott insulator in the form of a polaronic crystal (12, 17, 18).

Fig. 3 Real-space CDW reordering, free energy, and change of electronic structure in the H state.

(A) Idealized diagram of polaron reordering after a laser pulse. (B) CDW free energy Fd as a function of nd. (C) Energy level diagram of the C state, based on (14, 15, 28). Occupied bands in blue are those from Ta atoms within each polaron in Fig. 1. The upper and lower Hubbard bands are shown in green. Photoexcitation, initial energy relaxation, and subsequent relaxation processes of the e and h are shown. ked, keh, and khd are the rates for transitions of electrons to defect states, electrons to hole states, and holes to defect states, respectively.

Photoexcitation initially creates equal numbers of electrons (e) and holes (h) by an interband transition, followed by rapid intraband thermalization via scattering within the e-h population and with the lattice, as well as transitions between different bands, reaching states near the Fermi level and melting the C order on a time scale on the order of 50 fs (2023). The maximum effective electronic temperature reached in the process is Te ~ 1000 K; the lattice reaches ~150 K within 3 to 5 ps, whereupon the electrons and lattice are in quasi-equilibrium. [See (14) for temperature measurements and model estimates.] However, the large asymmetry of the band structure in this compound (17) can also lead to a photodoping effect: The electrons and holes scatter and lose energy at different rates, leading to a transient imbalance of their respective populations, ne and nh, within less than 5 ps.

A photodoped hole in this system annihilates with the localized 13th electron; this process removes the charge at the center of the polaron, leaving a void in the place of the polaronic distortion. Because some of the 13th electrons have been annihilated by holes, not all ions in these regions are charge-compensated, and they have an excess charge. Yet these regions cannot conduct because the remaining 12 electrons are in filled states within the gap formed by the long-range CDW (Fig. 3C). The excess charge will be screened by the electrons, which are now transferred to the delocalized bands. At a sufficiently high concentration nv, these voids are expected to aggregate by diffusion into domain walls. The overall state becomes conducting via the band states released by the annihilated polarons, which, if ordered, would form a new ordered structure of polaron clusters separated by domain walls, as indicated schematically in Fig. 3A. We can also imagine that photoexcited electrons could squeeze into the structure in between the polarons, creating interstitials with a concentration ni (11). Together with voids with a concentration nv, the total “intrinsic defect” concentration nd = nv – ni may have either sign. Overall charge conservation nh + nv = ne + ni gives the imbalance of the current carriers, nd = ne nh.

The value of nd is related to deviations δq/π ≈ –nd of the CDW wave vector q with respect to the C state. Conventionally, photodoping is a transient effect, so once e-h symmetry is recovered, the voids and domain walls disappear and the C state is restored. However, if the voids can be stabilized by collectively ordering into a long-range ordered state, the final state is different from the original one. The free energy Fd(nd) appropriate for the formation of the charge-ordered state outlined above (19) needs to include the effect of repulsion between the domain walls and between their crossings (19, 25, 26), and should reproduce the first-order nature of the transition (19, 26). Values of Fd(nd) based on these considerations and existing models (19, 26) are plotted in Fig. 3B. The time dependencies of concentrations ne(t) and nh(t) are calculated in (14).

The model (14) is consistent with the main experimental observations, namely the appearance of a switching threshold for the W pulse fluence, its critical pulse-length dependence, the threshold temperature for the E cycle, the high conductance, and the remarkable stability of the H state. The switching is caused by relatively weak and short pulses, which—considering the large change in resistance and optical reflectivity—has potential for device applications. The effect will also stimulate the search for new generations of room-temperature nonvolatile memory elements in electronically ordered materials. As a memory element switchable by 35-fs pulses, our device is already comparable to the current speed record of 40 fs in magnetic materials (28).

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S10

Table S1

References (2955)

References and Notes

  1. See supplementary materials on Science Online.
  2. Acknowledgments: Supported by the Slovenian Research Agency, European restructuring funds (CENN Nanocenter), and European Research Council advanced grant TRAJECTORY. A European patent application PCT/SI2013/000056 has been submitted. We thank L. Forro, V. V. Kabanov, N. Kirova, P. Monceau, E. Tossatti, and E. Tutis for valuable discussions.

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