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Time-Resolved ARPES

How fast can electrons and atoms move in a solid? How can we understand and control the remarkable properties of matter that emerge from complex correlations of atomic and electronic constituents on the time-scales of this motion? How can we characterize and control matter away - especially far away - from equilibrium? We are working on answering these and many other fascinating questions using ultrashort femtosecond (10-15 s) light pulses that serve as an ultrafast stroboscopic flashlight for electrons in a solid. Our subgroup is actively pioneering this exciting and rapidly developing field by applying trARPES to study novel quantum materials [1].

Contents

· Motivation

· Approach

· Methods

· Results

    · Dynamics of Charge Ordering

    · Electron-Phonon Coupling in Unconventional Superconductors

    · Electron Dynamics in Topological Insulators

· Publications

Our Motivation

One deeply intriguing aspect of solid state physics is how many-body systems with countless particles, interactions, correlations and excitations organize such that order emerges. These ordered quantum states may even organize to such a high degree that a description, understanding and technological application are actually possible.

Electronic, ionic, spin, and orbital degrees of freedom are largely decoupled in conventional materials like elemental metals or semiconductors. Consequently, these subsystems may be treated separately in most cases and our resulting understanding of such conventional materials - even on the quantum level of microscopic interactions - has reached an impressive level that we exploit in modern technological devices every day.

This deep insight of conventional materials is in stark contrast to the situation for so-called strongly correlated electron materials that summarize many families of compounds where electronic, ionic, spin, and orbital degrees of freedom are fundamentally entangled and are acting on multiple length, energy and time scales. Consequently, many material properties remain to be understood microscopically. Such correlation effects are often manifested in broken-symmetry ground states that may lead to interesting and novel states of quantum matter. A classic example for such effects is the Peierls-instability of a quasi-one-dimensional atomic structure. Here, a spontaneous periodic lattice modulation can cause a metal-to-insulator transition at low temperatures, where the coupling of electrons and ions is responsible for a pronounced change of numerous material properties.

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

Our Approach

We aim at contributing 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 investigation of elementary scattering processes in such complex materials. For example, in a material with a metal-to-insulator transition, optical excitation can transiently close band gaps where the timescale of the gap closing is indicative of electronically or vibrationally driven 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, fails to provide direct access to the underlying scattering channels in the electronic band structure and associated excited states.

Time- and angle-resolved photoemission spectroscopy (trARPES) extends and complements conventional ARPES by adding femtosecond time-resolution. trARPES resolves elementary scattering processes directly in the electronic band structure as function of energy and electron momentum due to simultaneous measurement of the spectral and dynamic information. In such a pump-probe scheme, a femtosecond infrared laser pulse excites the sample by electron-hole pair creation and a subsequent UV pulse probes the transient electronic structure after a time delay Δt.

In detail, ultrafast changes of the occupied electronic structure including metal-to-insulator transitions, transient populations in the unoccupied part of the band structure, cooling of excited carriers due electron-phonon coupling, and collective excitation modes such as coherent phonons are studied with trARPES. The wide range of microscopic processes accessible with trARPES promises new insights into non-equilibrium properties of correlated materials, which in turn facilitates our understanding of the underlying broken-symmetry ground states. trARPES grants new perspectives, where different energy scales of different interactions connect to different time scales of the decay of an excited state population its energy relaxation processes. Importantly, most broken-symmetry ground states are associated with particular collective boson modes that can modulate the electronic structure after intense, optical femtosecond excitation. This allows establishing a direct connection of cooperative effects with details of the electronic band structure. For example, in a charge density wave system we can identify which coherent modes couple to which electronic band and can thus identify the amplitude mode. The time domain approacess in trARPES can also resolve the coupling of collective modes that are hard to resolve in frequency domain as in regular ARPES. These new capabilities open unprecedented options for disentangling interactions leading to emergence of order and correlations.

Our Methods

In our trARPES laboratory at Stanford University we are using two complementary commercial Ti::Sa 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 800 nm (1.5 eV) wavelength at a repetition rate of 76 MHz and generates 25 nJ pulse energy with a pulse duration of 50 fs. One part of the output of the oscillator is frequency quadrupled to yield 200 nm (6 eV) UV probe pulses and the remaining fundamental excites the sample. The high repetition rate and low pulse energies make this system ideal for studies of weak perturbations with the high statistics required for detection of minute changes in the electronic structure of the sample.

Our second laser is a Coherent RegA with IR-OPA that delivers much higher pulse energies in the μJ range at a repetition rate of 100's of kHz. This laser system allows us to strongly perturb the sample and thereby trigger cooperative phenomena like coherent phonon excitation and ultrafast phase changes. Moreover, the IR-OPA enables tuning of the pump photon energy 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, Berlin, Germany we studied the combined electron and phonon dynamics of the prototypical charge density wave system TbTe3. 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 and thus in a time-dependent closing of the gap in the electronic band structure. Furthermore, we revealed the collective mode that coherently modulates the electronic band structure due to electron-phonon coupling. Since trARPES allows us to obtain the single particle spectral function and simultaneously observe the influence of collective modes on the electronic bands in real time it clearly reveals their connection. Thus, we were able to conclude that the observed collective vibrations are a result of 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. In fact, we think that discovering a collective mode in these materials similar to the one we demonstrated observable in charge ordered systems could mean 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 the subject of a long debate. The importance of electron-phonon coupling (EPC) in this complex phenomenon has recently been recognized in the cuprates [4].

By using trARPES, we can characterize the EPC experimentally and separate the effects from different phonon modes. Ultrafast light-induced excitation of coherent phonon oscillations simultaneously modulates the 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.

For cuprate superconductors, time-resolved optical spectroscopies have observed coherent phonons, yet the inability to directly resolve electronic states limits the understanding of microscopic interactions. We reported the first trARPES study of the coherent phonon oscillations in optimally doped cuprate superconductor Bi2212. We observed two dominant phonon modes at 3.9 and 5.6 THz, both involving the CuO2 plane motion. The 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 motions have not been detected with trARPES. This highlights the mode-selective coupling of the coherent phonons to the band structure. More information can be found in  [5].

trARPES also enables us to quantitatively study the EPC strength when combined with a time-resolved diffraction technique. For example, we used both X-ray diffraction (XRD) and ARPES in the time domain to track the same light-induced coherent phonon in iron selenide (FeSe), hence linking electronic and lattice degrees of freedom. We effectively “locked-in” the frequency of this A1g phonon mode and extracted the electron-phonon deformation potential which quantifies the EPC. Comparison with theory indicates that the EPC strength is strongly enhanced by the electron-electron correlations. This highlights the importance of the interplay between electron-phonon and electron-electron interactions in FeSe and suggests that their combined effect is at play in superconductivity. More information can be found in  [6].

Electron Dynamics in Topological Insulators

For topological insulators, it is important to understand the interplay of spin-polarized surface electrons with non-spin-polarized bulk electrons, which is critical for potential spintronics applications. Our work reveals 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 material's electronic band structure. Our femtosecond 'movie' depicts how the excited electrons fill 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 >10 ps. This finding may pave the way for development of ultrafast optical switches of spin-polarized conduction channels. More information can be found in  [7].

As seen in the example above, the electron dynamics are strongly dependent on the band structure above the Fermi level. While 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 employ a technique known as two-photon photoemission spectroscopy (2PPE). This technique utilizes two ultrafast laser pulses to first populate and then subsequently photoemit from unoccupied electronic states. We have applied 2PPE to the topological insulator Bi2Se3 to obtain a complete picture of the electronic structure from the Fermi level up to the vacuum level. We found that the unoccupied states host a second, topologically protected Dirac surface state which can be resonantly excited by 1.5 eV photons. More information can be found in  [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).

The knowledge of the unoccupied band structure was instrumental in our investigations of the photocurrents generated via circularly polarized optical excitations in Bi2Se3. These photocurrents can be measured in conventional transport configurations and are carried by topological surface states. The light helicity controls the photocurrent direction, making such systems interesting for 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 lead to such momentum-asymmetric electron populations and therefore contribute to photocurrent generation. We also observed that different bands contribute to the net current in opposite directions. Our work provides a microscopic understanding of how to control photocurrents in topological materials and sets the stage for further studies leading toward spintronic applications. More information can be found in  [9].

Publications

[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)