Ultrafast triggering of insulator-metal transition in two-dimensional VSe 2
Deepnarayan Biswas, Alfred J. H. Jones, Paulina Majchrzak, Byoung Ki Choi, Tsung-Han Lee, Klara Volckaert, Jiagui Feng, Igor Marković, Federico Andreatta, Chang-Jong Kang, Hyuk Jin Kim, In Hak Lee, Chris Jozwiak, Eli Rotenberg, Aaron Bostwick, Charlotte E. Sanders, Yu Zhang, Gabriel Karras, Richard T. Chapman, Adam S. Wyatt, Emma Springate, Jill A. Miwa, Philip Hofmann, Phil D. C. King, Young Jun Chang, Nicola Lanata, Søren Ulstrup
UUltrafast triggering of insulator-metal transition intwo-dimensional VSe Deepnarayan Biswas, Alfred J. H. Jones, Paulina Majchrzak,
1, 2
Byoung Ki Choi, Tsung-Han Lee, Klara Volckaert, Jiagui Feng,
5, 6
Igor Markovi´c,
5, 7
FedericoAndreatta, Chang-Jong Kang, Hyuk Jin Kim, In Hak Lee, Chris Jozwiak, EliRotenberg, Aaron Bostwick, Charlotte E. Sanders, Yu Zhang, Gabriel Karras, Richard T. Chapman, Adam S. Wyatt, Emma Springate, Jill A. Miwa, PhilipHofmann, Phil D. C. King, Young Jun Chang, Nicola Lanata, and Søren Ulstrup Department of Physics and Astronomy,Interdisciplinary Nanoscience Center,Aarhus University, 8000 Aarhus C, Denmark Central Laser Facility, STFC Rutherford Appleton Laboratory,Harwell 0X11 0QX, United Kingdom Department of Physics, University of Seoul, Seoul 02504, Republic of Korea Department of Physics and Astronomy,Rutgers University, Piscataway, New Jersey 08856, USA SUPA, School of Physics and Astronomy,University of St Andrews, St Andrews KY16 9SS, United Kingdom Suzhou Institute of Nano-Tech. and Nanobionics (SINANO),CAS, 398 Ruoshui Road, SEID, SIP, Suzhou, 215123, China Max Planck Institute for Chemical Physics of Solids,N¨othnitzer Straße 40, 01187 Dresden, Germany Advanced Light Source, E. O. Lawrence BerkeleyNational Laboratory, Berkeley, California 94720, USA a r X i v : . [ c ond - m a t . m t r l - s c i ] J u l ssembling transition metal dichalcogenides (TMDCs) at the two-dimensional(2D) limit is a promising approach for tailoring emerging states of matter suchas superconductivity or charge density waves (CDWs) [1–5]. Single-layer (SL)VSe stands out in this regard because it exhibits a strongly enhanced CDWtransition with a higher transition temperature compared to the bulk in additionto an insulating phase with an anisotropic gap at the Fermi level [6–10], caus-ing a suppression of anticipated 2D ferromagnetism in the material [7, 11–13].Here, we investigate the interplay of electronic and lattice degrees of freedomthat underpin these electronic phases in SL VSe using ultrafast pump-probephotoemission spectroscopy. In the insulating state, we observe a light-inducedclosure of the energy gap on a timescale of 480 fs, which we disentangle from theensuing hot carrier dynamics. Our work thereby reveals that the phase tran-sition in SL VSe is driven by electron-lattice coupling and demonstrates thepotential for controlling electronic phases in 2D materials with light. Switching between a normal and an unconventional phase of a material using an ultrafastlaser pulse provides an opportunity to probe fundamental interactions and determine howthey concur in driving the phase transition [14]. This procedure has been employed intime- and angle-resolved photoemission spectroscopy (TR-ARPES) experiments to observeenergy-, momentum- and time-dependent melting of CDW and Mott insulator phases inbulk TMDCs [15–19] and uncover Cooper pair recombination rates in high-temperaturesuperconductors [20, 21]. The timescales on which the electronic system evolves followingexcitation provide detailed insights into the hierarchy of interactions underpinning the phasetransition. For example, electronic degrees of freedom typically respond on timescales in therange of 10 −
100 fs [16, 22], whereas processes involving lattice degrees of freedom occur ontimescales longer than 100 fs [23, 24].We apply TR-ARPES in order to investigate the microscopic origin of the insulator-metaltransition in SL VSe grown on bilayer (BL) graphene [6, 7]. Before discussing the results ofpump-probe experiments, we start by clarifying the electronic structure of the material andcharacterize the phase transition in static conditions. Above the critical temperature T c , thematerial assumes the 1T structural modification where the V and Se atoms are coordinatedin an octahedral geometry as shown in Fig. 1(a). The dispersion of this phase is calculatedusing density functional theory (DFT) and presented together with an ARPES spectrum2 RPES + DFT a DMFT ( U = 6 eV) Simulation b c df BL grapheneV SeARPES Simulation E - E F ( e V ) -0.3 0.0
20 K 206 K I n t en s i t y ( a r b . un i t ) E - E F (eV)DataSimulation ∆ ( m e V ) T s (K) e g h k F T c
135 KSimulation M Γ K k || (Å -1 ) ( M)(M ) M Γ K-3-2-10 M Γ K170 KV 3 d Se 4 p Å -1 Γ MK maxmin-0.20.00.2-0.20.00.2 -0.5 0.0 0.520 K206 K k F E - E F ( e V ) -0.5 0.0 Δ = 0 Δ = 60 meV 2 Δ k || (Å -1 ) 0.2 Å -1 Å -1 FIG. 1:
Electronic structure and temperature dependent phase transition in SL VSe .a, Schematic of 1T structure of SL VSe . b, ARPES data collected at 170 K in the ¯M-¯Γ- ¯K direction.The dashed red lines correspond to the calculated DFT dispersion (the raw data without DFTbands is shown in Supplementary Fig. S3). c, DMFT spectrum for U = BZ with contours sketching the Fermi surface at 170 K. d, Numerical simulation of the2D ARPES intensity optimized to the data in ( b ). e, ARPES spectra and corresponding simulationalong ¯M-¯Γ for the given sample temperatures (see Supplementary Video 1 and Supplementary Fig.S3). The dashed lines represent the simulated dispersion including many-body effects. f, Simulationof photoemission intensity with the Fermi-Dirac function removed for the given values of the gapparameter ∆ . g, Comparison of EDCs at k F for sample temperatures of 206 and 20 K. The cutswere obtained from the data (markers) and simulation (curves) in e . Tick marks indicate EDC peakpositions, demonstrating a shift away from E F with decreasing sample temperature. h, Extractedvalues (markers) of ∆ from spectra obtained at several sample temperatures along with a fit (blackcurve) to a mean-field expression describing the phase transition. The fitted value of T c is shownvia a dashed vertical line. along the high symmetry ¯M-¯Γ- ¯K direction in Fig. 1(b). The shallow states around E F arecomposed of V 3 d orbitals while the dispersive subbands at higher binding energies derive3rom Se 4 p orbitals (see Supplementary Fig. S1). The increased broadening of V 3 d stateswith energy below E F and the enhanced effective masses compared to the DFT dispersionare the telltale signs of correlation effects. Indeed, we find that these effects are capturedin our dynamical mean-field theory (DMFT) calculations for a relatively large Hubbardinteraction strength U as shown in Fig. 1(c) for U = I ( k, ω ) = ∣ M ( k, ω )∣ A ( k, ω ) n FD ( ω ) [25]. Here, A ( k, ω ) is the spectral function, M ( k, ω ) incorporatesthe single-electron dipole matrix elements that govern the selection rules of the photoemis-sion process and n FD = ( e ( ω − µ )/ k B T e + ) − is the Fermi-Dirac (FD) distribution functionwith chemical potential µ and electronic temperature T e . By combining the bare dispersionobtained from DFT with the electronic self-energy, Σ , deduced from the DFT and LDA +DMFT calculation, we are able to construct the spectral function of SL VSe , as describedin further details in the Methods. A numerical simulation of I ( k, ω ) with self-energy andmatrix elements adjusted to give an optimum description of the measured 2D image of thephotoemission intensity is shown in Fig. 1(d), providing a basic model to interpret ARPESspectra of SL VSe in the following discussion.We focus on measurements along the ¯M-¯Γ high symmetry direction in order to track theopening of a gap in the Fermi surface segment shown in the Brillouin zone (BZ) sketch inFig. 1(c), which occurs when the sample is cooled below T c [6, 10]. A detailed view of thiscut is presented for sample temperatures T s of 206 and 20 K around the Fermi crossing k F in Fig. 1(e). A significant T s -dependent change of the V 3 d dispersion is seen via the purpleand blue dashed curves that have been extracted using our 2D simulation of the intensity(see transition in Supplementary Video 1). The change of dispersion is linked to the gapopening described in terms of the parameter ∆ , which is demonstrated in the simulationwith the FD function removed in Fig. 1(f). For ∆ = E F , however, theintensity around the band maximum is not seen in the ARPES data because these states areunoccupied. As ∆ assumes a finite value, a gap of 2 ∆ opens, leading to increased spectralweight around ¯Γ below E F . The presence of such a gap is further corroborated by a shift ofthe peak away from E F in energy distribution curve (EDC) cuts at k F as T s is lowered, whichis demonstrated in Fig. 1(g). The complete T s -dependence of ∆ is determined by fittingthe 2D ARPES intensity measured at several temperatures, leading to the phase diagram in4 M-2-101 t = 60 fs EDCs at k F I n t en s i t y ( a r b . u . ) a b c de f posneg0 ΓM t = 2000 fs E - E F ( e V ) ΓM-2-101 t < 0 ΓM t = 60 fs ΓM t = 2000 fsminmax k F V 3 d Se 4 p E - E F ( e V ) ΓM-2-101 t = 60 fs ΓM t = 2000 fs E - E F ( e V ) E - E F (eV) Insulating Metallic
InsulatingMetallic
60 fs2000 fs< 0
FIG. 2:
Optical excitation of SL VSe . a - c, ARPES spectra of V 3 d and Se 4 p bands (seearrows in c ) revealing the response of the electronic structure a before ( t < b at the peak( t =
60 fs) and c at a long delay ( t = d, EDCs extracted alongthe vertical line at k F shown in a - c for the corresponding time delays. The top panel displays datafor the metallic phase ( T s =
200 K) while the bottom panel presents EDCs for the insulating phase( T s =
88 K). The intensity is plotted on a logarithmic scale. The dashed lines are exponentialfunction fits to the tail of the EDCs. e, Intensity difference for the metallic phase obtained bysubtracting the equilibrium spectrum in a from the excited state spectra at the given time delaysin b - c . f, Similar difference spectra as shown in e measured for the insulating phase. Fig. 1(h). The critical temperature found using this method is 135 ± to anoptical excitation. Measurements performed with sample temperatures of 200 K and 88 Kare compared in order to track the dynamics in both the metallic and insulating phases.TR-ARPES snapshots are shown along ¯M-¯Γ in Figs. 2(a)-(c) for excitation of the metallicphase using a pump pulse with an energy of 1.56 eV, temporal width of 30 fs and a fluencearound 5 mJ/cm at a time delay t before the optical excitation ( t < t =
60 fs) and at a longer delay ( t = d states around E F (see panel (b)), whichdoes not fully recover at longer delays (see panel (c)). The raw ( ω, k, t ) -dependent intensitymeasured under the same conditions for the insulating phase appears similar on a superficialview (see Supplementary Fig. S3 for a comparison). A comparison of EDCs at k F , shownon a logarithmic intensity scale in Fig. 2(d), reveals exponential tails with a t -dependentslope indicating the generation of hot carriers with an elevated electronic temperature inboth phases.A stronger indication for the spectral changes following excitation is obtained by calcu-lating the difference in photoemission intensity by subtracting a spectrum determined inequilibrium conditions before the arrival of the pump pulse from the spectrum measuredat a given delay time as shown for the two phases in Figs. 2(e)-(f) and SupplementaryVideo 2. A highly complex ω - and k -dependence of intensity depletion and increase is seen.Surprisingly, we observe strong difference signals persisting at long delays ( t = d and Se 4 p states with excitedholes (electrons) signified by the blue (red) regions of the spectra. However, the intensityis simultaneously affected by a change of the FD distribution due to the elevated electronictemperature T e , a t -dependence of the quasiparticle scattering rate Γ that manifests itselfas increased broadening of the bands [26, 27], and the possibility of a t -dependent ∆ in theinsulating phase. Using our model of the photoemission intensity presented in Fig. 1(d)we fit T e , Γ and ∆ such that our simulated intensity gives an optimum description of theARPES intensity at all measured time delays, noting that ∆ = : static II: dynamic III: metastablemetallicinsulating τ m = 308 fs τ i = 304 fs Δ T e ( K ) t (fs) Δ ( m e V ) t (fs) τ ∆ = 480 fsmetallicinsulating E - E F ( e V ) ΓMI: static II: dynamic III: metastable-101 gap closing a b
FIG. 3:
Dynamics of hot carriers and phase transition. a,
Time-dependent change of elec-tronic temperature determined by fitting the full ( ω, k ) -dependence of the photoemission intensityat each measured time delay in the metallic (open purple circles) and insulating (filled blue circles)phases. The full curves are fits to a function consisting of an exponential rise followed by an expo-nential decay with the given time constants τ m ( i ) for the decay in the metallic (insulating) phase.The shaded areas correspond to three distinct periods of the time-dependent response labeled as(I) static, (II) dynamic and (III) metastable. b, Time-dependence of ∆ . The solid curve is a fitto an exponential decay with a time constant of τ ∆ =
480 fs. The inset presents the intensitydifference between a fitted spectrum for the insulating state at equilibrium and a spectrum for themetastable metallic state, incorporating a change of ∆ from 54 meV to zero. The shaded regionsaround the data points in a - b represent the uncertainity associated with the analysis. that thermalization occurs via electron-electron interactions on a faster timescale than wecan resolve ( <
40 fs) [28].The change of electronic temperature extracted from this analysis is presented in Fig.3(a), revealing a qualitatively similar t -dependence in the two phases that can be dividedaccording to (I) a static period before excitation, (II) a dynamic period with a sharp riseof T e during excitation followed by an initial fast relaxation and (III) a metastable periodwhere the system remains out of equilibrium and does not relax on the timescale of ourmeasurement. The transient increase in electronic temperature is caused by ultrafast energytransfer from the laser pulse to the electrons in the V 3 d states. Energy is then transferred7rom electrons to the lattice leading to a decay of T e on a timescale of ≈
300 fs. Bothinsulating and metallic phases subsequently reach a stable elevated electronic temperaturecompared to equilibrium, indicating that electron and lattice subsystems have reached athermal equilibrium with a temperature larger than T c .Figure 3(b) presents the extracted t -dependence of ∆ from the TR-ARPES measurementof the insulating phase, revealing a transient closure of the gap during the dynamic period(region II), leaving the system in a metastable metallic phase (region III). The intensitydifference between the fitted spectrum in this metastable metallic state and the insulatingstate in equilibrium (region I) essentially reproduces the measured behavior, as seen bycomparing the inset in Fig. 3(b) with the difference spectrum at t = ∆ is essentialfor its simulation. The timescale where ∆ goes to zero is comparable to the time it takes theelectronic system to transfer energy to the lattice as seen in region II in Fig. 3(a). As thelattice is thermally excited it obtains sufficient energy to rearrange atoms and trigger theinsulator-metal transition, which is clocked to the time constant τ ∆ =
480 fs obtained froman exponential fit. This is on the order of quenching times observed for strong electron-latticecoupling CDWs in bulk TMDCs and significantly slower than the timescales associated withmelting of Mott gaps driven by electron-electron interactions [22].The appearance of a metastable state is strongly indicative of a slow reconfigurationof the thermally excited lattice, possibly involving the distorted ( √ ×
2) and ( √ × √ [6–8, 13]. This situation bears astriking resemblance to VO where an ultrafast excitation transforms an insulating phasewith a monoclinic structure to a metallic phase with a rutile structure [14, 29, 30]. Suchdynamics in SL VSe may be resolved in future studies utilizing ultrafast probes of thelattice structure.In conclusion, we have tracked the spectral function of SL VSe across an ultrafastinsulator-metal transition triggered by an intense optical excitation. The spectroscopic sig-natures of hot carrier dynamics and phase transition could be disentangled, revealing thatelectron-lattice energy exchange drives the transition in the first few hundreds of femtosec-onds following excitation and leads to a metastable metallic state. Such a situation is not8nly intriguing for the application of 2D materials in electronic memory devices, but thecoupling between electron and lattice degrees of freedom is also of fundamental interest forunderstanding the interplay of CDW physics and magnetism in 2D. ACKNOWLEDGEMENT
We thank Phil Rice, Alistair Cox and David Rose for technical support during theArtemis beamtime. We gratefully acknowledge funding from VILLUM FONDEN throughthe Young Investigator Program (Grant. No. 15375) and the Centre of Excellence forDirac Materials (Grant. No. 11744), the Danish Council for Independent Research, NaturalSciences under the Sapere Aude program (Grant Nos. DFF-9064-00057B and DFF-6108-00409) and the Aarhus University Research Foundation. This work is also supported byNational Research Foundation (NRF) grants funded by the Korean government (nos. NRF-2020R1A2C200373211 and 2019K1A3A7A09033389) and by the International Max PlanckResearch School for Chemistry and Physics of Quantum Materials (IMPRS-CPQM). Theauthors also acknowledge The Royal Society and The Leverhulme Trust. Access to theArtemis Facility was funded by STFC. The Advanced Light Source is supported by the Di-rector, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energyunder Contract No. DE-AC02-05CH11231.
COMPETING INTERESTS
The authors declare that they have no competing financial interests.
ADDITIONAL INFORMATION
Supplementary Information and two Supplementary Videos accompany this paper.
Correspondence and requests for materials should be addressed to S. U. ([email protected]). 9
ETHODS
Sample preparation.
SL VSe samples were grown on BL graphene on 6H-SiC(0001)using molecular beam epitaxy (MBE) with a base pressures better than 2 ⋅ − Torr.The sample measured to produce the data in Fig. 1(b) was grown at the University of StAndrews, UK. The remaining spectra were collected on samples grown at the Universityof Seoul, Republic of Korea. To obtain the BL graphene on SiC, the SiC substrates wereoutgassed at 650 ◦ C for a few hours and then annealed three times up to 1300 ◦ C for2 min. The formation of BL graphene was verified by reflection high-energy electrondiffraction (RHEED) and low-energy electron diffraction (LEED). High-purity V (99.8%)and Se (99.999%) were simultaneously evaporated while the substrate was kept at 250 ◦ C.The growth process was monitored with in situ RHEED. The growth rate was fixed at5 min per Se-V-Se layer. After growth, the sample was annealed at 450 ◦ C for 30 min. A100 nm Se film was deposited at room temperature to protect the sample while transferringthrough air. This Se capping layer was removed by annealing the sample at 300 ◦ C forseveral hours in the UHV analysis chamber before photoemission experiments. No no-ticeable change in sample quality was observed due to the capping and de-capping procedure.
Static ARPES experiments.
The ARPES spectrum shown in Fig. 1(b) was collectedusing a high-intensity He lamp ( hν = 21.2 eV, p-polarization) and a SPECS Phoibos 225hemispherical electron analyzer at University of St Andrews, UK. Here, samples weredirectly transferred from the attached MBE growth chamber to the ARPES chamber.The remaining static measurements were performed in the microARPES end-station (basepressure of ∼ ⋅ − Torr) at the MAESTRO facility at beamline 7.0.2 of the AdvancedLight Source, Lawrence Berkeley National Laboratory. The ARPES system was equippedwith a Scienta R4000 electron analyzer. We used a photon energy of 48 eV for T s -dependentscans. The total energy and angular resolution of our experiments were better than 20 meVand 0 . ◦ , respectively. TR-ARPES experiments.
The Materials Science end station of the Artemis facilityat Rutherford Appleton Laboratory was used for TR-ARPES measurements. Synchronizedinfrared (IR) pump and extreme ultraviolet (EUV) probe beams were generated from a10i:Sapphire laser system at 12 mJ, 1 kHz, with a 30 fs pulse length and a central wavelengthof 795 nm. The output of the laser was split: a small fraction of the energy was useddirectly to pump the sample at 1.56 eV, with fine control of the fluence achieved usinga half waveplate and a thin film polariser, while 2 mJ pulse energy was used to preparethe probe beam by high-harmonic generation. The laser was focused into a thin Ar gascell to generate a comb of odd harmonics in the EUV. The 19th harmonic at 29.6 eV wasselected, using a time-preserving monochromator [31]. The two beam polarisations wereorthogonal: the pump beam was s-polarised while the probe beam was p-polarised. Theend station is equipped with a SPECS Phoibos 100 hemispherical electron energy analyser.Experiments were performed in the wide-angle mode, with a slit size of 1 mm. The timeand angular resolution of the experiments were 46 fs and 0.3 ◦ , respectively. The optimumenergy resolution was 250 meV, as determined through our simulations of the photoemissionintensity. Energy resolution is limited by analyzer energy resolution (about 190 meV),EUV probe pulse broadening (about 100 meV), and space charge effects (about 130 meV).Temperatures from 88 to 220 K were reached using an open-cycle liquid He cryostat. Theory.
The LDA+DMFT calculations were performed at a temperature of T s =
200 K,assuming a Hund’s rule coupling J = . U from 5 to 9 eV. We utilized the DMFT package for theelectronic structure calculations of Ref. [32] interfaced with the local density approximation(LDA) functional implemented in Wien2k [33] and we adopted the fully-localized-limitscheme for the double-counting functional [34]. All simulations have been performed with10000 k -points and Rkmax = Simulation of ARPES intensity.
The photoemission intensity is described by theexpression I ( k , ω ) = ∣ M n ( k , ω )∣ A n ( k , ω ) n F D ( ω, T e ) , (1)as explained in the main text. The subscript n is the band index. The spectral function is11ritten as [25, 26, 40], A n ( k , ω ) = − π − Σ ′′ n ( k , ω )( ω − (cid:15) k n − Σ ′ n ( k , ω )) + Σ ′′ n ( k , ω ) , (2)where (cid:15) k n is the non-interacting band dispersion or bare band, which we describe using theDFT dispersion as an input. Σ ′ n and Σ ′′ n are the real and imaginary parts of the electronicself energy Σ n , respectively. In our simulation the correlation effects in the V 3 d states,including the gap opening of the dispersion, are included in Σ n through the expression (seeSupplementary Section 1 for further details) Σ n ( k , ω ) = Σ − − ZZ ω − i ΓZ + ∆ / Zω + Z ( (cid:15) k n + Σ ) + iΓ . (3)Here Σ is a constant energy shift of the states, Z is the quasiparticle residue, Γ is quasi-particle scattering rate, ∆ is the gap parameter and Γ is a constant related to the changein the scattering rate due to the presence of a gap. We also used a parameter, labeled ∆ E s ,to describe any rigid shift of all the bands including E F . Such a shift may arise due toan external electric field associated with vacuum space charge or surface photo voltage [41].Finally, the ARPES intensity is obtained by convoluting the photoemission intensity I ( k , ω ) by two Gaussians representing the energy ( R ω ) and momentum ( R k ) resolution broadeningof the instrument, I ARP ES = I ( k , ω ) ∗ R ω ∗ R k . (4)We expand M n ( k , ω ) in second order polynomial terms of both ω and k [26]. The Se 4 p states at higher binding energies are well-described by the DFT bands and using a scatteringrate that is merely expressed in terms of first order polynomials of ω and k . The parametersdescribing M n ( k , ω ) , Σ n and n F D are found in static conditions by performing a 2D fit ofthe simulated intensity to the ARPES spectra. We find that a satisfactory fit is obtainedusing a quasiparticle residue Z in the range of 0.52 to 0.54. For the fits of the TR-ARPESdata we account for the time dependent changes of FD distribution and spectral function byallowing a variation of T e , ∆E s and the self-energy through the scattering rate ( Γ ) and thegap parameter ∆ . We allow for a slight adjustment of the energy- and momentum-positionof the bands to ensure consistency between measured and fitted spectra. The resultingparameters of the fit to the TR-ARPES data are given in Fig. 3 and Supplementary Fig.S5. 12 upplementary Section 1: Form of the self energy in ARPES simulations -3-2-101-3-2-101 E - E F ( e V ) E - E F ( e V ) M Γ K Γ M Γ K Γ M Γ K Γ M Γ K Γ VSeV: d z2 V: d x2-y2 + d xy V: d xz + d yz DFT ad b ce f -1 0 -0.2 0.0DOS (arb. unit) Σ' (eV) Σ" (eV) g maxmin U = 6 eV d z d x -y + d xy d xz + d yz Total V d FIG. 4:
Theoretical calculations and band character. a - c, DFT calculated bands. Thecontribution from V and Se atoms are represented by yellow and violet color. The marker sizecorresponds to the V d z , d x + y + d xy and d xz + d yz orbital characters. d , LDA + DMFT calculatedband structure ( U = J = . e , Densityof states corresponding to LDA + DMFT calculated band structure, shown in (d) . f - g, Energydependence of the f real and g imaginary parts of the electronic self energy, respectively. The following mathematical form of the self energy was utilized in our simulations forinterpreting the ARPES data, within an energy window of ∼ Σ n ( k , ω ) = Σ loc ( ω ) − i ΓZ + ∆ / Zω + Z ( (cid:15) k n + Σ ) + iΓ . (5)Here k is the momentum, ω is the energy, (cid:15) k n is a generic band eigenvalue, Γ is scatteringrate, ∆ is the gap parameter, Γ is a constant related to the change in scattering rate dueto ∆ and Σ loc is the momentum-independent (local) component of the self-energy: Σ loc ( ω ) = Σ − − ZZ ω , (6)13
ABLE I: Quasiparticle weights of V 3 d orbitals for different values of U , at J = . U d z d x + y + d xy d xz + d yz which we approximated assuming a linear structure characterized by the quasiparticle residue Z and a constant energy shift Σ .To explain the physical reasons underlying Eq. (5) we note that the correspondingmomentum-resolved single-particle Green’s function is represented as follows: G n ( k , ω ) = ω − (cid:15) k n − Σ n ( ω, k ) = Zω − (cid:15) ∗ k n + Γ − ∆ ω + (cid:15) k n + iΓ , (7)where (cid:15) ∗ k n = Z ( (cid:15) k n + Σ ) . (8)In fact, the last expression in Eq. (7) has the same mathematical structure of the phenomeno-logical self-energy previously used for fitting ARPES data in the presence of a superconduct-ing or charge density wave (CDW) gap [8, 42]. Therefore, in this work, Eq. (5) is designedto represent the CDW effects on a band structure consisting of pre-existing quasi-particleexcitations renormalized by electron correlations.
Note that in Eq. (6) we assumed that Σ loc ( ω ) acts as a number rather than a matrix.However, in general, the self-energy correction Σ loc ( ω ) shall be expected to be significantonly for the V 3 d degrees of freedom. Furthermore, considering the symmetry of our system,the d z , d x + y + d xy and d xz + d yz components of the self-energy are not a-priori equal, asthey belong to distinct irreducible representations of the point symmetry group of the Vatoms. On the other hand, Eq. (6) is a meaningful approximation provided that, for energies ω within ∼ d electrons.2) The self-energy is approximately orbital-independent.14 E - E F ( e V ) M Γ K Γ M Γ K Γ M Γ K Γ U = 5 eV U = 7 eV U = 8 eV a b c maxmin DFT
FIG. 5:
Behavior of LDA+DMFT bands as a function of U . a-c, LDA+DMFT bandstructures calculated using the given values of screened on-site Coulomb interaction strength U , at J = .
3) The momentum-independent local component Σ loc of the self-energy is approximatelyreal and linear with respect to the frequency.Here we use DFT and LDA+DMFT calculations to prove that these hypotheses are, infact, approximately applicable to our system. We show the DFT calculated bands resolvedwith respect to their orbital character in Fig. 4(a)-(c). These calculations indicate that thebands have mostly V 3 d character near the Fermi level. Specifically, the spectral weightis dominated by the d z , d x + y + d xy contributions. Fig. 4(d) illustrates the LDA+DMFTband structure obtained for a screened Hubbard interaction strength U = J = . d character. Finally, as shown in Fig. 4(f) and (g), the self-energy is approximately linearand similar for all of the V 3 d orbitals for energies ∣ ω ∣ ≲ . Z α = (cid:187)(cid:187)(cid:187)(cid:187)(cid:187)(cid:187)(cid:187)(cid:187)(cid:187) − ∂Σ ′ α ∂ω (cid:187)(cid:187)(cid:187)(cid:187)(cid:187)(cid:187)(cid:187)(cid:187)(cid:187) − , (9)see Table 1, which are all ≳ .
5, in agreement with our simulation (in the range 0.52 to0.54).In Fig. 5 we show the LDA+DMFT bands for three different values of the Hubbardinteraction strength U . The bands are found to be very similar for these U values. Thisindicates that our theoretical predictions are robust.15 upplementary Section 2: Raw ARPES spectra in metallic and insulating phase -3-2-10 k F k F E - E F ( e V ) M Γ K M Γ Kmaxmin
Metallic Insulating a b -2-101-2-101 t = -500 fs E - E F ( e V ) E - E F ( e V ) M Γ M Γ t = 60 fs t = 2000 fs t = 500 fsM Γ M Γ metallicinsulating c T S = 170 K T S = 10 K FIG. 6:
Comparison of ARPES spectra. a-b,
Static ARPES spectra for metallic and insulatingphase. c, TR-ARPES spectra at the given time delays for metallic (top) and insulating (bottom)phase.
Fig. 6(a) and (b) show static ARPES spectra for both metallic and insulating phases. Thedispersion of the top V 3 d band is different close to k F due to the formation of the energy gapin the insulating phase. Figure 6(c) presents TR-ARPES snapshots of the spectral changesin these two scenarios before and after optical excitation.16 upplementary Section 3: Simulation of ARPES spectra -2-101-2-101-2-101 E - E F ( e V ) Data Simulation | Rel. error (ɛ) | E - E F ( e V ) M Γ M Γ M Γ E - E F ( e V ) t = -500 fs t = 60 fs t = 2000 fs abc N u m be r o f p i x e l s ( % ) Cumulative error distribution def N u m be r o f p i x e l s ( % ) N u m be r o f p i x e l s ( % ) N ( ɛ ) ɛ N ( ɛ ) ɛ N ( ɛ ) ɛ|ɛ| FIG. 7:
Quality of simulation. a-c,
TR-ARPES specta for T s =
200 K at the given time delays(left column). Simulated spectra and the corresponding unsigned relative errors ( ε = (simulation-data)/data) are shown in the middle and right columns, respectively. d - f, Cumulative distributionof ∣ ε ∣ for the corresponding time-delays in the same row in a - c for the energy range -2.5 eV to E F .The inserts present the distribution of ε . The green dashed lines in d - f correspond to ∣ ε ∣ = . As mentioned in the methods section of the main text, the ARPES intensity can beexpressed as, I ARP ES = [∣ M n ( k , ω )∣ A n ( k , ω ) n F D ( ω )] ∗ R ω ∗ R k . (10)The energy and momentum resolution functions ( R ω and R k ) are known from instru-ment calibration and remain fixed for a given measurement. Furthermore, in static ARPESmeasurements we use that T e = T s and µ = E F such that n F D is fully specified. The param-17 (fs) a b -30-15015 200010000 metallicinsulating ∆ Γ V d ( m e V ) t (fs)100500 200010000 metallicinsulating τ m = 400 fs τ i = 316 fs Δ E s ( m e V ) -101 E - E F ( e V ) InsulatingMetallic c d e f t = 60 fs t = 2000 fs t = 60 fs t = 2000 fsΔ T e = 1600 K Δ T e = 400 K Δ T e = 1050 K gap closingΔ T e = 100 Kno gap no gap gapped M Γ posneg0 M ΓM ΓM Γ
FIG. 8:
Resulting parameters from fits of t -dependent photoemission intensity. a, Thechange in the scattering rate ( Γ ) of V 3 d states for both insulating ( T s =
88 K) and metallic ( T s =
200 K) phase. The solid curves show fits to a fast exponential rise followed by an exponential decaywith the given time constants. b, The corresponding rigid energy shift of the spectra, ∆ E s . c-d, Difference between the fitted equilibrium spectra and the fitted spectra at the given time delays(60 fs and 2000 fs) for the metallic phase. e-f,
Corresponding difference spectra for the insulatingphase. eters describing M n ( k , ω ) and Σ n ( k , ω ) are obtained by performing a 2D fit of a simulated ( ω, k ) -dependent intensity to the corresponding ARPES spectrum. Since the values of Z and ∆ at a given T s are intrinsic properties of the V 3 d states that are independent of mea-surement configuration, we apply the values obtained from the static ARPES simulations todescribe the TR-ARPES spectra. The parameters describing M n ( k , ω ) are related to thephotoemission setup, however, we use the assumption that M n ( k , ω ) is independent of timesuch that the matrix element is always determined in the equilibrium part of the TR-ARPESmeasurements. Data points acquired for t < −
100 fs are described using a single optimizedspectrum, as the system is in equilibrium. The parameters of this optimized spectrum are18sed as input for the fit of the TR-ARPES data points acquired at the remaining time delaypoints.In Figs. 7(a)-(c) we show the TR-ARPES spectra, simulated spectra and the correspond-ing unsigned relative error ( ∣ ε ∣ ) at t = −
500 fs, 60 fs and 2000 fs for the metallic phase( T s =
200 K). The associated cumulative distribution of ∣ ε ∣ is given in Figs. 7(d)-(f). Asthe actual intensity for the pixels above E F is very small, irrespective of the simulationquality, the relative error for these pixels are high. We have therefore selected the energyrange from -2.5 eV to E F for our error analysis. All fitted pixels that fall below a margin setby ∣ ε ∣ = . ≈
92% of the pixels for all the three time delays. The symmetricdistribution of the relative error (see inserts in Figs. 7(d)-(f)) with respect to ε = Γ ) associated with the V 3 d band and the energy shift (∆ E s ) which accompany theparameters T e and ∆ shown in Fig. 3 of the main text. Figs. S5(c)-(f) present the intensitydifference calculated by subtracting the fitted equilibrium spectra from the fitted spectra at t =
60 fs and t = upplementary Section 4: Reproducibility of intensity difference signals -2-101-2-101 E - E F ( e V ) E - E F ( e V ) M Γ M Γ M Γ M Γ T s = 88 K T s = 118 K T s = 166 K T s = 200 K t =
60 fs t = ab Insulating Metallic posneg0
Sample I Sample I Sample IISample II
FIG. 9:
Reproducibility of the response to optical excitation. a,
Difference spectra at t =
60 fs for sample temperature 88 K (sample II), 118 K (sample I), 166 K (sample I) and 200K (sample II). b, Corresponding difference spectra at t = ( ω, k ) -region of the spectra most strongly affected by the phase transition. We have performed consistency checks of the observed intensity difference by repeatingthe measurements discussed in the main manuscript for sample temperatures T s of 88 K,118 K, 166 K and 200 K and for two independent SL VSe samples, verifying that thespectral signatures are robust for the two phases across T c =
135 K. Figure 9 summarizesthese results by presenting the corresponding intensity difference spectra. [1] X. Xi, L. Zhao, Z. Wang, H. Berger, L. Forr´o, J. Shan, and K. Mak, Nat. Nanotechnol. ,765 (2015).[2] M. Ugeda, A. Bradley, Y. Zhang, S. Onishi, Y. Chen, W. Ruan, O. Claudia, H. Ryu, M. Ed-monds, H. Tsai, et al., Nat. Phys. , 92 (2016).
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