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Time-resolved ARPES

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Ultrafast pump and probe beams with a finely-tuned delay time perform ARPES, photoemitting electrons which are captured by the spectrometer's detector.

How fast do electrons and lattice vibrations propagate in a solid? In what ways can we understand and control the remarkable properties of matter, emergent from complex ionic and electronic correlations, on the time-scales of their motion? How should we characterize and control matter away — especially far away — from equilibrium? We aim to answer these, and many other fascinating questions using ultrashort femtosecond (10-15 s) light pulses which act as an ultrafast, stroboscopic flashlight for electrons in solids. Our subgroup actively pioneers this exciting and rapidly developing field by applying trARPES (time- and angle-resolved photoemission spectroscopy) to study novel quantum materials [1].


Our Motivation

The central thrust of solid state physics is the investigation of how many-body systems with countless particles, interactions, correlations, and excitations organize such that order emerges. Ordered quantum states may be structured at a high enough degree that their description, understanding, and eventual technological application become possible.

Electronic, ionic, spin, and orbital degrees of freedom are largely decoupled in conventional materials, namely elemental metals or semiconductors. These subsystems are then separately treatable in most cases. Our resulting understanding of these conventional materials — even down to the quantum level of microscopic interactions — has reached such an impressive level that their usage has become indispensable to modern technological devices.

Our deep insight into conventional materials stands in stark contrast to strongly correlated electron materials, which encompass many families of compounds where electronic, ionic, spin, and orbital degrees of freedom are fundamentally entangled, and act on multiple length, energy, and time scales. Many material properties remain to be understood microscopically. Correlation effects are often manifest in broken-symmetry ground states which may lead to novel states of quantum matter. A classic example is the Peierls instability in quasi-one-dimensional atomic structures, where a spontaneous periodic lattice modulation causes a metal-to-insulator transition at low temperatures; that is, where interaction between electrons and ions induces a pronounced change of material properties.

Our Approach

Coherent phonons in Bi2Te3 excited and probed with time-resolved ARPES.

We contribute to this fascinating field of solid state research by investigating the microscopic nature of these interactions and couplings using ultrafast spectroscopy. Femtosecond time-resolved spectroscopy techniques are a new tool for the study of elementary scattering processes in complex materials. A salient example are materials featuring metal-to-insulator transitions, for which optical excitation may transiently close band gaps where the timescale of gap closing helps distinguish electronic and phononic processes.

The powerful tool of angle-resolved photoemission spectroscopy (ARPES) offers high-resolution energy and momentum information of the electronic band structure in thermal equilibrium. However, it does not reveal the scattering channels that underlie electronic band structure and its excited states.

Time- and angle-resolved photoemission spectroscopy (trARPES) thus augments and complements conventional ARPES by folding in femtosecond time-resolution. trARPES directly resolves elementary scattering processes by tracking the evolution of electronic band structure (a function of energy and electron momentum) through simultaneous measurement of spectral and dynamic information. It involves a pump-probe scheme, where a femtosecond infrared laser pulse excites the sample by electron-hole pair creation, and a subsequent UV pulse probes the transient response of its electronic structure after a time delay Δt.

Ultrafast changes of electronic structure studied with trARPES includes metal-to-insulator transitions, transient populations in the unoccupied part of the band structure, cooling of excited carriers due to electron-phonon coupling, and collective excitation modes such as coherent phonons. The wide range of microscopic processes accessible by trARPES promises new insights into non-equilibrium properties of correlated materials, in turn facilitating our understanding of its broken-symmetry ground states. Crucially, most broken-symmetry ground states are associated with particular collective boson modes that can modulate the electronic structure after intense, optical femtosecond excitation. Different energy scales of various interactions connect to different time scales of the decay of an excited state population in relaxation processes. This allows a direct connection between cooperative effects and details of the electronic band structure to be established. For example, in a charge density wave system we can identify couplings between coherent modes and electronic bands, allowing us to verify the amplitude mode. Time domain approaches in trARPES also resolve the coupling of collective modes that are otherwise difficult to do so (in the frequency domain, as in regular ARPES). These capabilities offer new ways to disentangle the interactions which lead to the emergence of order and correlations.

Our Methods

We use two complementary commercial Ti:Sapphire lasers in combination with a state-of-the-art ultrahigh vacuum system built around a Scienta R4000 hemispherical electron analyzer.

Our Spectra Physics Tsunami oscillator operates near a wavelength of 800 nm (1.5 eV) at a repetition rate of 76 MHz and generates 25 nJ pulse energy with a pulse duration of 50 fs. One part of its output is split off and frequency quadrupled to yield 200 nm (6 eV) UV probe pulses. The remaining fundamental excites the sample. The Tsunami's high repetition rate and low pulse energies make it ideal for studying weak perturbations by providing the high statistics (electron count) needed to detect minute changes in the electronic structure of samples.

Our second laser is a Coherent RegA with IR-OPA. It delivers much higher pulse energies in the μJ range, at a repetition rate in the hundreds of kHz. This laser system allows us to strongly perturb the sample and trigger cooperative phenomena such as coherent phonon excitations and ultrafast phase changes. The IR-OPA also enables pump photon energy to be tuned to relevant optical transitions in the range of 0.5⁠ – 1 eV.

Our Results

Dynamics of Charge Ordering

Ultrafast, momentum-dependent dynamics of the melting of the charge density wave state in TbTe3 monitored by trARPES. More information can be found in [2-3].

In collaboration with the group of Martin Wolf in Berlin, we studied the combined electron and phonon dynamics of the prototypical charge density wave system TbTe3  [2-3]. Ultrafast, momentum-dependent dynamics of the melting of its charge density wave state were tracked.

trARPES allowed us to observe the effects of collective excitations via their interaction with the electronic band structure. We resolved a momentum-dependent, anisotropic excitation: optical excitation results in a transient 'melting' of the charge ordered state which showed up as a time-dependent closing of the gap in the electronic band structure. Furthermore, we revealed the collective mode that coherently modulates electronic band structure through electron-phonon coupling. As trARPES allows us to simultaneously obtain the single electron spectral function and observe the real-time influence of collective modes on electronic bands, it uncovers the connection between them. We concluded that the collective vibrations observed resulted from the excitation of the amplitude mode of the charge density wave.

Our observation of the transient effects of the amplitude mode on the band structure, and documentation of the melting of the electronic CDW gap in real time is — to our knowledge — the first time that momentum-dependent dynamics were recorded with trARPES. Observing the amplitude mode, which is at the core of correlated charge density wave physics, is a major breakthrough in uncovering the mechanics of collective phenomena in solid state physics. Future experiments will investigate the influence of the amplitude mode in the superconducting phase of the high temperature superconducting cuprates. We believe that discovering a collective mode in these materials similar to the one we demonstrated in charge ordered systems would be a major breakthrough in understanding the underlying physics in these systems.

Electron-Phonon Coupling in Unconventional Superconductors

Coherent lock-in at the A1g phonon frequency. (A) Quantitative characterization of the displacement of Se atom (blue) and the corresponding correlated energy band shifts (orange and green) in the time domain, measured by combined techniques of trXRD and trARPES. (B) The phonon mode of FeSe (top) periodically modulates the electronic band energies (bottom).

The driving mechanism of unconventional superconductivity has been subject to long debate. The importance of electron-phonon coupling (EPC) to this complex phenomenon has recently been recognized in the cuprates [4].

By using trARPES, we can characterize EPC experimentally and sieve apart effects from different phonon modes. Ultrafast light-induced excitation of coherent phonon oscillations simultaneously modulates lattice and electronic properties at the same frequency. This enables a mode-specific investigation of EPC by associating electronic oscillation frequencies to known phonon frequencies.

Other time-resolved optical spectroscopies have observed coherent phonons in cuprate superconductors, yet their inability to also directly resolve electronic states limited the understanding of microscopic interactions. We reported the first trARPES study of coherent phonon oscillations in the optimally doped cuprate superconductor Bi2Sr2CaCu2O8+δ (Bi2212). We observed two dominant phonon modes at 3.9 and 5.6 THz, both involving CuO2 plane motion. Electrons near the Fermi level originate from the same CuO2 planes and strongly couple to these phonon modes. In contrast, coherent phonon modes involving mainly Bi and Sr motion have not been detected with trARPES. This highlights the mode-selective coupling of the coherent phonons to the band structure [5].

When combined with a time-resolved diffraction technique, trARPES also enables us to quantitatively study EPC strength. For example, we used both X-ray diffraction (XRD) and ARPES in the time domain to track the same light-induced coherent phonon in the iron-based superconductor FeSe, and linked electronic and lattice degrees of freedom. We effectively “locked-in” the frequency of the A1g phonon mode and extracted the electron-phonon deformation potential that quantified EPC strength. Comparison with theory indicated that EPC strength is strongly enhanced by the electron-electron correlations. This highlights the important interplay between electron-phonon and electron-electron interactions in FeSe and suggests that their combined effect is at play in superconductivity [6].

Electron Dynamics in Topological Insulators

For topological insulators, it is important in the context of potential spintronics applications to understand the interplay of spin-polarized surface electrons with non-spin-polarized bulk electrons. Our work revealed the coupling between bulk and surface electrons of the topological insulator Bi2Se3 directly in the time domain. We use trARPES to probe the dynamics of optically excited electrons directly in the electronic band structure. Our femtosecond 'movie' depicts how the excited electrons filled unoccupied bands but are prevented from relaxing immediately back to equilibrium due to the bulk band gap. These hot electrons accumulate at the bulk conduction band edge and act as a reservoir, which continues to populate the spin-polarized surface states for longer than 10 ps. This finding may pave the way for the development of ultrafast optical switches of spin-polarized conduction channels [7].

As seen in the example above, electron dynamics are strongly dependent on the band structure above the Fermi level. While standard ARPES is an excellent tool for probing occupied electronic states, it cannot be used to study electronic structure above the Fermi level. To overcome this limitation, we employed a technique known as two-photon photoemission spectroscopy (2PPE). This technique utilizes two ultrafast laser pulses to first populate, then photoemit from unoccupied electronic states. We have applied 2PPE to the topological insulator Bi2Se3 to obtain a complete picture of its electronic structure from the Fermi level all the way up to the vacuum level. We found that unoccupied states hosted a second, topologically protected Dirac surface state which resonantly excitable by 1.5 eV photons [8].

Resonant transitions of the photocurrents. (a) Difference between the populations of the unoccupied bands when excited by left and right circularly polarized light. (b) Three resonant optical transitions between occupied and unoccupied states of Bi2Se3 with a 3 eV excitation. Blue dashed lines mark the initial states upshifted by the resonant excitations. (c) Time-dependent contributions to the photocurrent from each of the resonant optical transitions in (b).

Knowledge of the unoccupied band structure of Bi2Se3 was instrumental to our investigations of photocurrents generated via circularly polarized optical excitations. These photocurrents can be measured in conventional transport configurations and are carried by topological surface states. Photon helicity controls photocurrent direction, making such systems amenable to usage in electronic applications. The spectroscopic signature of photocurrents in trARPES is an asymmetric electron population in momentum space. We found that in Bi2Se3, only resonant optical transitions led to such momentum-asymmetric electron populations and contributed to photocurrent generation. We also observed that different bands contributed to the net current in opposite directions. Our work provided a microscopic understanding of how photocurrents in topological materials may be controlled, and set the stage for further studies pointing towards spintronic applications [9].


[1] U. Bovensiepen and P. S. Kirchmann. Elementary relaxation processes investigated by femtosecond photoelectron spectroscopy of two-dimensional materials. Laser & Photonics Reviews 6, 589 (2012)

[2] F. Schmitt et al. Effect of the amplitude mode and the transient melting of the charge density wave on the electronic structure of TbTe3. Science 321, 1649 (2008)

[3] F. Schmitt et al. Ultrafast electron dynamics in the charge density wave material TbTe3. New J. Phys. 13, 063022 (2011)

[4] Y. He et al. Rapid change of superconductivity and electron-phonon coupling through critical doping in Bi-2212. Science 362, 6410 (2018)

[5] S.-L. Yang et al. Mode-selective coupling of coherent phonons to the Bi-2212 electronic band structure. Phys. Rev. Lett. 122, 176403 (2019)

[6] S. Gerber et al. Femtosecond electron-phonon lock-in by photoemission and x-ray free-electron laser. Science 357, 6346 (2017)

[7] J. A. Sobota et al. Ultrafast optical excitation of a persistent surface-state population in the topological insulator Bi2Se3. Phys. Rev. Lett. 108, 117403 (2012)

[8] Direct optical coupling to an unoccupied Dirac surface state in the topological insulator Bi2Se3. Phys. Rev. Lett. 111, 136802 (2013)

[9] H. Soifer et al. Band-Resolved Imaging of Photocurrent in a Topological Insulator. Phys. Rev. Lett. 122,167401 (2019)