Cavity -mediated thermal control of metal -to-insulator transition in 1T-TaS 2 Giacomo Jarc12 Shahla Yasmin Mathengattil12 Angela Montanaro123 Francesca Giusti12 Enrico

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Cavity-mediated thermal control of metal-to-insulator transition

in 1T-TaS2

Giacomo Jarc1,2, Shahla Yasmin Mathengattil1,2, Angela Montanaro1,2,3, Francesca Giusti1,2, Enrico

Maria Rigoni1,2, Rudi Sergo2, Francesca Fassioli3,4, Stephan Winnerl5, Simone Dal Zilio6, Dragan

Mihailovic7, Peter Prelovšek7, Martin Eckstein8, and Daniele Fausti1,2,3.

1Department of Physics, Università degli Studi di Trieste, 34127 Trieste, Italy

2Elettra Sincrotrone Trieste S.C.p.A., 34127 Basovizza Trieste, Italy

3Department of Physics, University of Erlangen-Nürnberg, 91058 Erlangen, Germany

4International School for Advanced Studies (SISSA), Via Bonomea 265, I-34136 Trieste, Italy

5Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf,

Bautzner Landstrasse 400, 01328, Dresden, Germany

6CNR-IOM TASC Laboratory, Trieste 34139, Italy

7Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia

8Institute of Theoretical Physics, University of Hamburg, Notkestrasse 9, 22607 Hamburg, Germany

Correspondence: daniele.fausti@elettra.eu

Placing quantum materials into optical cavities provides a unique platform for controlling

quantum cooperative properties of matter, via both weak and strong light-matter coupling

[1,2]. Here we report the experimental evidence of reversible cavity control of a metal-to-

insulator phase transition in a correlated solid-state material. We embed the charge density

wave material 1T-TaS2 into cryogenic tunable terahertz cavities [3] and show that a switch

between conductive and insulating behaviors, associated with a large change in the sample

temperature, is obtained by mechanically tuning the distance between the cavity mirrors and

their alignment. The large thermal modification observed is indicative of a Purcell-like scenario

in which the spectral profile of the cavity modifies the energy exchange between the material

and the external electromagnetic field. Our findings provide opportunities for controlling the

thermodynamics and macroscopic transport properties of quantum materials by engineering

their electromagnetic environment.

MAIN

Optical driving with ultrashort pulses has been extensively used to dynamically control the properties

of complex quantum materials [4-9]. Yet, several theoretical proposals indicate that the control of

materials functionalities can be obtained by modifying their electromagnetic environment,

embedding the materials into optical cavities, even in absence of a driving field [1,2]. Predictions

range from enhanced superconductivity through cavity-mediated electron pairing [10-15], cavity

control of the competing order between charge density wave and superconducting phases [16], cavity

control of excitons [17], enhanced ferroelectricity [18-20], and cavity control of magnetic orders [21].

Experimentally, it has been demonstrated that vacuum fields in the strong coupling regime [1] can

change material functionalities as, for example, the magneto-transport in two-dimensional materials

[22], the topological protection of the integer quantum Hall effect [23], or the ferromagnetic order in

unconventional superconductors [24].

Cavity control of phase transformations in complex systems can be achieved via distinct physical

mechanisms. On the one hand, the selective coupling of the cavity modes to the excitations of a given

phase can renormalize its free energy with respect to that of other ones, thereby modifying the

temperature at which the phase transition occurs. On the other hand, a cavity can reshape the exchange

of energy between a material and the thermal reservoir of photons in which the material is immersed

[25]. By engineering the density of states of the electromagnetic environment at the sample position

through tunable optical cavities, it is therefore possible to modify the sample’s absorption and

emission [26-29], and, in turn its temperature (Tint). Fig. 1A illustrates the two aforementioned cavity-

mediated mechanisms.

In this work, we investigate the metal-to-insulator phase transition in the transition metal

dichalcogenide 1T-TaS2 embedded in low-energy terahertz (THz) and sub-THz cryogenic cavities

(Fig. 1A). 1T-TaS2 exhibits a temperature-dependent charge order that originates from the

competition of Coulomb repulsion, lattice strain, interlayer hopping, and Fermi surface nesting [30-

32]. At ambient temperature, 1T-TaS2 is in a nearly commensurate charge density wave (NC-CDW)

phase with metallic character, featuring hexagonal-shaped polaron domains [30,33,34] forming a

David’s star pattern [35-37] (Fig. 1C). By lowering the temperature below ~ 180 K, a transition to an

insulating commensurate charge density wave (C-CDW) state occurs [31,38]. We note that the free

energy landscape of 1T-TaS2 is much more complicated than the simple sketch in Fig. 1A: the phase

Fig. 1: Mechanisms of cavity control of quantum material states and THz characterization of 1T-TaS2 metal-to-

insulator transition. A. Schematic of a material embedded in the middle of a tunable optical cavity with controllable

fundamental frequency 𝜔𝑐 and alignment. Coupling of the material’s excitations with the cavity mode can act on the

thermodynamics of the sample within two different scenarios. On the one hand, it can renormalize the free energy of one

material phase with respect to the other (bottom left panel). On the other hand, as a function of 𝜔𝑐 the cavity can reshape

the emission and absorption of the material, subsequently rescaling its local temperature Tint(𝜔𝑐) with respect to the

temperature measured on the sample support (Text). B. THz linear transmission spectra in free space at different

temperatures across 1T-TaS2 metal-to-insulator transition (temperature scans performed by cooling (upper panel) and

heating (lower panel)). To highlight the phase transition, each spectrum has been subtracted from the 280 K THz

transmission. C. Temperature dependence of the integrated low frequency transmission (0.2 THz <  < 1.5 THz), marking

the metal-to-insulator transition and its hysteresis. In the insets the time domain THz fields are shown for the metallic and

the insulating phases, together with the illustration of the in-plane lattice modulations characteristic of the insulating C-

CDW phase and of the metallic NC-CDW phase.

transitions in 1T-TaS2 are multiple and sensitive to the thermal history of the sample. Upon heating

from the C-CDW phase, an additional intermediate trigonal (T) phase with in-plane charge stripes

occurs at around 220 K and persists up to around 280 K, when the NC-CDW is re-established [39].

THz spectroscopy is a powerful tool for tracking the metal-to-insulator transition since it is able to

measure contactless the quasi-static dielectric response associated to the presence of conductive

charges characteristic of a metallic state (see Methods and Ref. [3] for further details on the

experimental set-up). Here we employ broadband time-domain THz spectroscopy to track the charge

order in the sample for different cavity settings. We demonstrate that a bidirectional switch between

the metallic and insulating phase can be obtained by tuning the cavity length and by adjusting the

alignment of its mirrors while keeping the cryogenic temperature of the sample support and mirrors

fixed.

It is important to highlight that a simultaneous measurement of the actual sample’s temperature inside

the cavity (Tint) and THz transmission is not viable. At a practical level, the placement of a physical

thermometer within the cavity would absorb the THz pulses and make the transmission measurements

unfeasible. At a fundamental level, any object placed within the optical cavity will perturb the cavity

environment and therefore the response of the light-matter assembly. For this reason, we have

designed an experimental protocol in which for the THz characterization we measure the temperature

on the cold-finger support of the sample outside of the cavity, denoted by Text (Fig. 1A). This protocol

allows us to identify an effective critical temperature Tceff for the phase transition which is defined as

the temperature of the support at which the phase transition is observed. In a separate measurement

campaign, we place a micrometric thermocouple, and we measure for different experimental

configurations the temperature at the sample position (with and without the sample) which we denote

as Tint, while simultaneously monitoring the external temperature Text.

THZ SPECTROSCOPY OF 1T-TaS2

Figure 1B shows the THz linear transmission of 1T-TaS2 in free space upon heating and cooling as a

function of the temperature of the sample support (Text). This captures the first-order transition

between the NC-CDW metallic phase and the C-CDW insulating phase. The phase transition results

in: i) an increase of the low frequency transmission (0.2 THz <  < 1.5 THz) below the effective

critical temperature, which is consistent with a transition to an insulating behavior (Drude-like

response of free carriers vanishes in the insulating phase [40,41]); and ii) the emergence below Tceff

of infrared-active optical phonons at 1.58 THz, 2.04 THz and 2.35 THz, which are screened by the

free carriers and therefore not visible in the metallic phase (Fig. 1C, insets, report time-domain THz

traces representative for the two phases). We will use the temperature dependence of the integrated

low-frequency transmission (0.2 THz <  < 1.5 THz) as a marker which tracks the charge order

dynamics in 1T-TaS2 and hence the metal-to-insulator phase transition (Fig. 1C). The low frequency

transmission is directly mapped into the evolution of the Drude optical conductivity 1()

representative of the free carriers response (Supplementary Information). Analogous transition

temperatures can be obtained by tracking the temperature dependence of the transmission at the

phonon frequency (Methods). The temperature dependence of the integrated low-frequency

transmission (0.2 THz <  < 1.5 THz) for the material in free space is shown in Fig. 1C. The

difference between the results obtained upon heating and cooling the sample in free space marks the

hysteresis associated to the first-order phase transition. The phase transition in free space upon heating

occurs at Text = 181 K and at 143 K upon cooling from the metallic phase. Note that the smooth

transition observed can be ascribed to the presence of intrinsic inhomogeneities and strain in the

system, which may smear out the first-order transition [42-44] (Methods). The effective critical

temperature Tceff measured in our set-up differs from the literature value [31] by about 35 K. This

discrepancy is attributed to the difference between the internal temperature of the sample (Tint) and

the temperature of the cryostat’s cold finger (Text), as a consequence of the small thermal conductivity

of the silicon nitride membranes holding the 1T-TaS2 sample [3]. A finite-elements simulation of the

membrane’s thermal profile is in quantitative agreement with the measured temperature shift (details

in the Methods section).

CHARACTERIZATION OF 1T-TaS2 IN CRYOGENIC THz FABRY PÉROT CAVITIES

Figure 2 presents the THz linear transmission as a function of the sample holder temperature (cooling

in Fig. 2A, and heating in Fig. 2B) of 1T-TaS2 in free space and embedded in the center of an optical

cavity with resonant frequency 𝜔𝑐 = 11.5 GHz and quality factor 𝑄∼ 4 (Methods). The placement

of the sample in such a cavity results in a modification of Tceff for the metal-to-insulator transition,

which is observed at 136 K on heating and at 109 K on cooling. The modification of Tceff depends

also on the thermal cycle. Indeed, a change of Tceff of 44 K is observed if the critical temperature is

approached from the insulating state (heating), while a shift of 33 K is obtained starting from the

metallic phase (cooling), resulting in a shrinking of the hysteresis of about 11 K. We highlight that

Tceff is independent from the input intensity of the THz field, which, therefore, acts only as a probe

and does not introduce a detectable thermal load on the sample (see Supplementary Fig. S15 for

measurements with different THz field strengths).

Next, we varied the cavity geometry and measure Tceff as a function of the alignment of the cavity

mirrors. We quantify the cavity misalignment as the sum of the misalignment angles of the two cavity

mirrors  with respect to the parallel mirrors configuration. The temperature dependence of the low-

frequency THz transmission (0.2 THz <  < 1.5 THz integration range) at different mirror alignments

is shown in Fig 3A for the temperature scans performed by heating and cooling the cold-finger sample

holder. Misaligning the mirrors modifies Tceff, which approaches the free space value when the cavity

is highly misaligned (Fig. 3A). In the inset of Fig. 3A, we show that a switch between the metallic

Fig. 2: Renormalization of the effective critical temperature of the metal-to-insulator phase transition within the

cavity. A, B. Temperature-dependent THz transmission upon cooling (A) and heating (B) for a sample held in free space

(left) and one placed in the middle of the 11.5 GHz cavity (right). C. Comparison between the hysteresis in free space

and within the 11.5 GHz cavity plotted as the integrated cavity transmission in the range 0.2 THz <  < 1.5 THz. The

free-space data have been arbitrarily translated along the horizontal axis to overlap with the cavity integrated transmission.

In the cavity, a renormalization of the effective critical temperature of 44 K (33 K) towards lower temperatures is

measured upon heating (cooling) the sample. This results in a shrinking of the effective phase-transition hysteresis of 11

K within the cavity.

and the dielectric linear response is obtained at fixed Text by solely changing the cavity alignment.

As any misalignment of the cavity mirrors reduces the photon lifetime within the cavity (and hence

the quality factor), the sensitivity of Tceff not only to the presence of the cavity but also to the mirrors

alignment, is suggestive of a cavity-mediated effect. This is further supported by the fact that

misaligning the cavity mirrors not only changes the effective critical temperature, but also increases

the effective hysteresis of the metal-to-insulator transition towards its free space value.

Figure 3B reports the THz transmission as a function of the cavity fundamental frequency at a fixed

cold-finger temperature (Text = 150 K). The results reveal that the cavity-mediated change of Tceff

overcomes the free space hysteresis, thus enabling a reversible touchless control of the metal-to-

insulator phase transition. Upon reducing the distance between the mirrors, we detected the phase

Fig. 3: Dependence of the effective critical temperature on the cavity geometry. A. Dependence of the effective metal-

to-insulator phase transition as a function of the cavity alignment for the 11.5 GHz cavity. The hysteresis is plotted for

each misalignment angle  as the integrated low frequency transmission (0.2 THz <  < 1.5 THz). In the inset panel, the

THz fields detected at the output of the coupled 11.5 GHz cavity at fixed temperature (Text = 154 K) as a function of the

mirrors alignment. Transition from the dielectric to the metallic behavior is detected passing from the misaligned to the

aligned configuration. B. Reversible cavity control of the metal-to-insulator transition at fixed temperature (Text = 150

K). The hysteresis as a function of the cavity fundamental mode is plotted as the evolution of the integrated low frequency

THz transmission (0.2 THz <  < 1.5 THz). The insets show the evolution of the time domain THz fields transmitted for

different values of the cavity frequency ranging from 50.0 GHz to 11.5 GHz (opening cavity case) and from 11.5 GHz to

50.0 GHz (closing cavity case), demonstrating the reversible switching between the two phases.

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Cavity-mediatedthermalcontrolofmetal-to-insulatortransitionin1T-TaS2GiacomoJarc1,2,ShahlaYasminMathengattil1,2,AngelaMontanaro1,2,3,FrancescaGiusti1,2,EnricoMariaRigoni1,2,RudiSergo2,FrancescaFassioli3,4,StephanWinnerl5,SimoneDalZilio6,DraganMihailovic7,PeterPrelovšek7,MartinEckstein8,andDanieleFaus...

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