the tungsten tip. This leads to emission of the pulsed electron beam from the front facet only, and thus greatly enhances the beam coherence in comparison to thermionic emitters (Fig.2.1D to F).
Considering brightness limitations, most imaging, diffraction and spectroscopy applications that are possible with an unmodified microscope can be performed at the Göttingen UTEM as well (Fig.2.6).
The versatility of the Göttingen UTEM is also reflected by the diverse applications benefiting from the high-coherence pulsed beam (66). An early quantum optics experiment (and later follow-ups) investigated the inelastic interaction of the free electrons with optical near-fields (147,148,152–154). While this kind of electron-photon interaction does not fundamentally require a pulsed electron beam, the necessary optical near-field strengths could initially only be achieved in pulsed schemes (155). Meanwhile, the use of optical resonators for the near-field confinement has opened up perspectives for continuous-beam interactions as well (156,157). By temporally scanning optical and electron pulses across each other to obtain an electron-photon cross-correlation, the effect is routinely used to determine the electron pulse duration as reported in Ref. (66) and used in Chapter5.
The femtosecond temporal resolution of the Göttingen UTEM has been harnessed by another set of experiments imaging optically driven (102) and current-driven magnetization dynamics (103,104) on the nanoscale. Finally, the observation and analysis of strain waves in a single-crystalline graphite film has been demonstrated, which contributes to the field of ultrafast structural dynamics (158). This field is of central importance to the present thesis and will be reviewed in the following section.
2.8 Ultrafast imaging of structural and electronic dynamics
While the UTEM quantum optics experiments certainly opened up novel experimental per-spectives, investigations of electronic, structural and magnetic properties look back at a long tradition of conventional TEM investigations of the same or similar materials. However, by adding femtosecond time resolution, completely new insights into the couplings between the different degrees of freedom are obtained. The purpose of this section is to summarize a number of central experiments investigating ultrafast material dynamics using UTEM.
One advantage of the UTEM approach over related stroboscopic techniques is the availability of a number of contrast methods that allow for access to different degrees of freedom of the specimen in the same experimental setting. In some widely investigated materials, such as vanadium dioxide (VO2) and different TMDCs (Chapter3), electron-lattice coupling and strong
correlation effects lead to physical phenomena that can only be fully understood by investigating both, the structural and electronic contributions. These phenomena include, for example, metal-insulator phase transitions (MITs) (159) and the formation of charge-density waves (CDWs) (160).
Ultrafast EELS, for example, can be used to gain insights into the electronic component of material dynamics as demonstrated for graphite, both in the low-loss and high-loss regimes (161–
164). High-loss EELS spectra allow to investigate the dynamics of chemical bonds on ultrafast time scales, while the electronic, magnetic and optical properties of materials are controlled by low-energy excitations (165,166). Both types of observations are rather challenging: The low inelastic scattering cross-section for loss energies>100 eV, on the one hand, leads to long integration times in low-dose ultrafast experiments. On the other hand, the finite width of the ZLP in TEMs without a monochromator covers relevant low-loss features such as the dynamics of band gaps in MITs.
Another way to obtain information about the transient electronic properties of materials exploits the inelastic electron-photon interaction. It has been shown in the past that spatial mapping of energy sidebands allows for imaging of plasmonic fields in metallic nanostructures (photon-induced near-field electron microscopy or PINEM) (166,167). The intensity of the optical near-field depends on the dielectric function of the material—a property that undergoes a pronounced change in a MIT and that can thus serve as a source of image contrast, as exemplified using VO2nanowires (168).
The structural component of the MIT in VO2has been investigated in a number of diffraction experiments using UTEM (131,169), dedicated UED setups (24,64,170–173) and x-rays (174, 175). Diffraction experiments have the distinct advantage over all-optical experiments that even minute structural changes, such as the formation of vanadium dimers in the MIT (which is equivalent to the formation of a CDW along the vanadium chains), lead to the emergence or disappearance of distinct diffraction orders corresponding to the changes in crystal symmetry.
These are spatially separated from other diffraction orders in the diffraction pattern, such that—
given reasonably low inelastic scattering background intensity and detectors with sufficiently high DQE—even very weak changes can be observed and analyzed. The intensity of the vanishing diffraction orders can be considered an order parameter of the structural phase transition (24).
While UED experiments can also be conducted using UTEM devices (28,131,134,163, 169,176–178), pioneering works have proven that the strength of UTEM lies in the nanometer spatial resolution it contributes to structural dynamics investigations (56,57,131,169). The stroboscopic UTEM images in Fig.2.7A demonstrate the change of contrast in a polycrystalline
2.8 Ultrafast imaging of structural and electronic dynamics
A B
Figure 2.7: Ultrafast TEM images and diffraction patterns of VO2.(A) Images of the polycrystalline specimen in the monoclinic (M) room-temperature phase (left) and in the rutile (R) high-temperature phase (right) (before and after time-zero). The scale bar length is 100 nm. (B) Diffraction patterns corresponding to the M and R phases (left) compared to theoretical ring positions (center). Raw diffraction patterns of both phases are shown as well (right). The higher symmetry of the R phase leads to the disappearance of a number of diffraction orders that are prominent in the dimerized M phase. Reprinted from Ref. (131). Copyright 2006 National Academy of Sciences.
VO2 specimen before and after optical excitation. While the overall shape of the individual crystallites remains unaffected by the phase transition, transient features can be observed within.
Due to a strong contribution of diffracted beams that are not sensitive to the structural changes, these features carry rather low contrast. Simultaneously, the changes between the diffraction patterns observed in the monoclinic (M) room-temperature and the rutile (R) high-temperature phase are quite obvious (Fig.2.7B).
This emphasizes the necessity of contrast enhancement techniques in the real-space imaging of structural dynamics using UTEM, as first demonstrated by the example of an organometallic nanoparticle undergoing a spin-crossover phase transition (58). Structural strain in the particle is released during the transition, causing a change in morphology (Fig.2.8D). This leads to local changes in diffracted intensities that reflect the new lattice orientation. Using an individual circular aperture, a diffraction spot in the BFP can be selected (red circle in Fig.2.8C) to obtain DF images of the phase transition dynamics (Fig.2.8B). In this very specific case, an intense diffraction order with strong sensitivity to the crystal deformation was selected such that the corresponding BF images show a complementary spatial intensity distribution (Fig.2.8A).
Diffraction contrast as showcased in Figs.2.7and2.8represents a typical contrast mechanism in real-space UTEM images (56–62). When carefully evaluated, the obtained BF and DF images also allow for quantitative insights into the structural dynamics. This includes the observation of acoustic phonon modes in BF images, as demonstrated using graphite (56) and in a number of recent works on the TMDCs TaS2, WSe2 and MoS2 (59–61). Using this approach, the propagation of individual phonon wavefronts can be analyzed in space and time (Fig.2.9).
Figure 2.8: Single-nanoparticle morphology dynamics. (A) BF images of a nanoparticle at three different temporal delays. (B) Corresponding DF images obtained by selecting the(1 1 0)diffraction order using a circular objective aperture in the BFP. (C) Diffraction pattern of the single nanoparticle slightly tilted away from the[0 0 1]zone axis. The(1 1 0)reflection and diffraction peaks of the graphite substrate are encircled in red and gray, respectively. (D) Side view of the nanoparticle. Before time-zero, the particle is in a strained, diamagnetic low-spin (LS) state. After excitation, the particle transitions into a high-spin (HS) state which releases the strain. Reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer Nature,Nature Chemistry, Ref. (58), Copyright 2013 Nature Publishing Group.
Figure 2.9: Imaging of acoustic phonon propagation in multilayer 1T-TaS2.(A) BF reference image of the specimen at time-zero (𝑡ref=0 ps), and difference images of the observable dynamics. The red star indicates the propagation of an individual phonon wavefront. (B) Space-time plot extracted from a region of interest parallel to the red arrow in A. An average phonon velocity of 4.2(2) nm/ps can be extracted from the tilted bands.
Reprinted with permission from Ref. (61). Copyright 2020 American Chemical Society.
2.8 Ultrafast imaging of structural and electronic dynamics
Furthermore, the nanosecond morphological dynamics of a free-standing black phosphorus membrane has recently been modeled on the basis of structural mechanics simulations and DF images from two different diffraction orders. Due to a high degree of in-plane anisotropy, these two sets of DF images encode very different dynamics along zig-zag and armchair directions of the material (62). For a full reconstruction of the transient strain distribution in graphite, a convergent-beam scanning diffraction technique has proven successful. By scanning a focused beam along the specimen, all relevant diffraction orders can be recorded at once in order to reconstruct the local specimen deformation and visualize propagating strain waves (158).
Beyond these examples of the imaging of morphological dynamics, the real-space mapping of order parameters using UTEM remains to be demonstrated. Typically, the corresponding features are rather weak, as seen in the MIT in VO2(Fig.2.7B) or superstructures caused by the presence of CDWs (section3.2). The convergence angle of the beam in scanning diffraction techniques further expands the low-intensity spots to discs in reciprocal space, making them hard to separate from the background even with current direct detection technology. If convergence angles are too large, overlapping superstructure orders further complicate the evaluation of the individual convergent-beam diffraction patterns (see also section6.2.6).
When using DF imaging instead to investigate a single-crystalline specimen, one is typically constrained to using an individual circular aperture to tailor the image contrast. Accordingly, intensity of symmetry-equivalent spots also encoding order parameter information is discarded.
Taken together with the already weak intensity of these spots and typical beam currents of pulsed electron sources, a sufficient signal level in ultrafast DF images was challenging to achieve prior to the developments reported in Chapter5.
Chapter 3 Properties of transition metal dichalcogenides
Transition metal dichalcogenides (TMDC) are a class of materials that has been the subject of extensive scientific research since the 1970s. These compounds are described by the chemical formula MX2with a transition metal M and a chalcogen X, and form lattice structures consist-ing of quasi-two-dimensional, covalent X – M – X trilayers as shown in Fig.3.1A and B. The individual trilayers are bound by weak van-der-Waals interactions between chalcogens along the out-of-plane𝑐-axis (179).
As a whole, the TMDC class of materials exhibits an enormous wealth of exotic physical properties due to their unique combination of a quasi-two-dimensional crystal structure, strong spin-orbit and electron-lattice coupling and the occurrence of direct band gaps. External stimuli such as temperature, pressure or electrostatic doping can be used to further tune the material properties (180). Additionally, the properties of TMDCs can be significantly influenced by intercalation, i.e., the introduction of foreign atoms between the layers of the crystal (11,181).
One member of this group is the semiconducting MoS2, which has long been used as a solid lubricant because of the weak interlayer bond (185). Apart from this more practical application, a number of materials in the TMDC family has stimulated scientific interest due to the appearance of correlated phenomena, such as superconductivity and the formation of CDWs in metallic TMDC representatives, e.g. in TaS2and NbSe2(12,186,187).
Following the example of the exfoliation of graphene monolayers from graphite (188), mono-layers of TMDCs can be obtained from bulk crystals using the same technique (105). As seen in graphene, TMDC monolayers can exhibit new physical properties not present in their bulk ancestors. MoS2 and WSe2, for example, are indirect-band-gap semiconductors in their bulk form, and become direct-band-gap semiconductors when thinned down to a monolayer (6,189, 190). This could enable their use in transistors and optoelectronic devices (6,191,192).
A B
C 1T polytype D 2Ha polytype E 2 × 2 intercalated 2Ha polytype
Perspective rendering of 1T-polytype layers Top view of 1T polytype
Transition metal Chalcogen Intercalant atom
c
c c
a
a a
Figure 3.1: Crystal structure of TMDC polytypes.(A) Perspective rendering of three1𝑇-polytype X – M – X trilayers. The transition metal atoms M are drawn in turquoise, while the chalcogen atoms X are yellow. (B) Top view of the three trilayers shown in A. The hexagonal arrangement of transition metal and chalcogen atoms is visible. (C) Side view of the structure of a1𝑇-polytype material (space group𝑃3𝑚1). The in-plane lattice constant𝑎and the out-of-plane lattice constant𝑐are indicated. The octahedral coordination of the transition metal atom is visualized by gray polygons. (D) Side view of the structure of a2𝐻𝑎-polytype material (𝑃63/𝑚𝑚𝑐).
The lattice constant𝑐is doubled compared to C, and each unit cell contains two transition metal atoms. Gray polygons visualize the trigonal-prismatic coordination of the transition metal. (E) Side view of the structure of an intercalated2𝐻𝑎polytype (𝑃63/𝑚𝑚𝑐). Here, the specific case of an2 × 2in-plane long-range ordering is shown, thus doubling the lattice constant𝑎in comparison to D. The intercalant atom (magenta) is located within the octahedral interstitial site between the2𝐻layers. The presented atom positions are that of 1T-TaS2(A to C), 2H-TaS2(D) and Mn0.25TaS2(E) from Refs. (182–184), but are representative for other TMDCs adopting the same or similar structures.
Additionally, properties depend on the polytype of the TMDC material, the most common of which are1𝑇and2𝐻. While1𝑇-polytype TMDCs exhibit a trigonal symmetry with one trilayer per unit cell along the crystallographic𝑐-axis (Fig.3.1C),2𝐻-polytype TMDCs display a double unit cell size in𝑐-direction and hexagonal symmetry (Fig.3.1D4). The transition metal atoms in 1𝑇and2𝐻materials are in octahedral and trigonal-prismatic coordination, respectively (179).
Thinning a2𝐻-polytype material down to a monolayer thus breaks inversion symmetry and
4It should be noted that the trilayer stacking in the2𝐻𝑏polytype of MoS2and WSe2deviates from the2𝐻𝑎 stacking shown in Fig.3.1D. However, space group and unit cell size are unaffected. See Ref. (5) for more details, and Ref. (181) for the nomenclature.
Chapter 3 Properties of transition metal dichalcogenides
A
B
C
Figure 3.2: Coherent manipulation of valley pseudospin in WSe2.(A) Schematic of the excitation of a coherent superposition of𝐾and𝐾′excitons using a linearly polarized optical pulse (left). The fixed phase relationship between the𝐾and𝐾′valleys is shown by the pseudospin vector in a Bloch sphere (right). (B) Consecutive interaction with a circularly polarized below-band-gap optical control pulse lifts the valley energy degeneracy by ℏΔ𝜔due to the optical Stark effect and introduces a phase differenceΔ𝜙 ∝ Δ𝜔Δ𝑡between the excitons in the 𝐾and𝐾′valleys, whereΔ𝑡is the duration of the control pulse (left). As a result, the pseudospin is rotated by Δ𝜙(right). (C) When detecting the time-integrated photoluminescence emerging from the material as a function of temporal delay𝜏between excitation and control pulse, the normalized Stokes parameter𝑆2characterizes its polarization direction (𝑆2 = 0: no pseudospin rotation;𝑆2 = ±1: pseudospin rotated by± 𝜋/2). The signal is reversed when switching the helicity of the control pulse (blue and red markers). The decay in∣𝑆2∣ with increasing delay time indicates an intervalley decoherence time of 350 fs. Reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer Nature,Nature Physics, Ref. (23), Copyright 2016 Nature Publishing Group.
leads, together with strong spin-orbit coupling (193), to a valley-selective circular dichroism in monolayer MoS2and WSe2. The emerging valley degree of freedom shares some similarities with the electron spin, opening up a completely new field ofvalleytronics(6,192,194–197).
Valley physics allows for intriguing schemes of optical control over charge carriers, as shown by the occurrence of an anomalous Hall effect. Thisvalley Hall effectis enabled by effective magnetic fields with opposite sign experienced by carriers in the𝐾and𝐾′valleys of the material, and can be controlled by creating a valley polarization using circularly polarized light (198).
Furthermore, it has been shown that a coherent superposition between𝐾and𝐾′ excitons can be manipulated by the helicity of optical pulses with photon energies below the band gap of the material (Fig.3.2). The properties of the emerging photoluminescence help to understand valley relaxation and decoherence mechanisms, paving the way for the use of the valley degree of freedom as an information carrier (23,199).
The consequences of the loss of inversion symmetry are just one example of how the quasi-two-dimensionality of TMDCs leads to the occurrence of exotic phenomena. This thesis presents
two studies on materials whose functionality is also enabled by dimensionality: intercalation of3𝑑transition metals between the layers of a 2H-TaS2host lattice gives rise to ferromagnetic phases at low temperatures (Chapter 4), and the low-dimensional Fermi surface of 1T-TaS2 offers ideal conditions for the emergence of a number of different CDW phases (Chapter5). In the following sections, the relevant physical basics and material properties are outlined and put into context with previous works on these materials.
3.1 Charge-density wave formation and metal-insulator transitions
Various TMDCs in general, and 1T-TaS2 specifically, exhibit one or more CDW phases. In the presence of a CDW, the spatial electron density is modulated to form a standing-wave pattern. A periodic lattice distortion (PLD) accompanies the CDW due to strong electron-phonon interactions, forming a superlattice that is either commensurate (C) or incommensurate (IC) with the underlying structural lattice.
The instability of a one-dimensional chain of atoms to the formation of a CDW was first predicted by Rudolph Peierls (160,200). Starting from the undistorted chain in Fig.3.3A and following the descriptions in Ref. (201), the energy gain connected to CDW/PLD formation in this system can be demonstrated. Assuming a pure sinusoidal modulation of the electron density 𝜌( ⃗𝑟) = 𝜌0( ⃗𝑟) [1 + 𝜌1cos(2𝜋 ⃗𝑄 ⋅ ⃗𝑟 + 𝜑)] , (3.1) where𝜌0 is the electron density of the undistorted state, and𝜌1,𝑄⃗and𝜑 are the amplitude, wave vector and phase of the modulation, respectively. The movement of the atoms due to the coupled PLD can by described by
⃗
𝑢( ⃗𝑟) = ⃗𝐴 sin(2𝜋 ⃗𝑄 ⋅ ⃗𝑟 + 𝜑). (3.2) The norm of the amplitude𝐴⃗is generally small in comparison to the lattice constant𝑎. Both modulations are schematically depicted in the top panel of Fig. 3.3B. From the model, we obtain the following stability criterion for CDW/PLD formation via a statically displaced phonon mode ⃗𝑘in a weak-coupling limit:
4𝑔2𝑘⃗
ℏ𝜔𝑘⃗ > 1
𝜒( ⃗𝑘). (3.3)
Here,𝑔𝑘⃗ is the electron-phonon coupling constant,𝜔𝑘⃗ is the phonon frequency, and𝜒( ⃗𝑘)is the electronic susceptibility. For a Peierls instability to occur, a large coupling constant and
3.1 Charge-density wave formation and metal-insulator transitions
Figure 3.3: Peierls instability in a one-dimensional chain of atoms. (A) Schematic view of the undistorted chain of atoms (yellow) with lattice constant𝑎and isotropic electron density𝜌( ⃗𝑟)(blue). The conduction band (orange) is half-filled up to the Fermi energy𝐸F. (B) Below the transition temperature𝑇C, both electron density and atom positions are modulated. The periodicity of the CDW/PLD state is2𝑎. Gaps ofΔopen at the Fermi energy, resulting in a filled valence band and an empty conduction band. Adapted from Ref. (160).
a large susceptibility are required at the CDW wave vector 𝑄 = ⃗𝑘. For the one-dimensional⃗ chain, these conditions are fulfilled at 2 ⃗𝑘F, where F⃗𝑘 is the Fermi wave vector. With falling temperatures,𝜒(2 ⃗𝑘F, 𝑇 )diverges which causes a renormalization of phonon frequencies around
⃗𝑄 = 2 ⃗𝑘F. This Kohn anomaly leads to a complete softening of the phonon mode ⃗𝑄(i.e., the renormalized phonon frequency𝜔̃𝑄⃗ approaches zero) and a second-order phase transition at the CDW transition temperature𝑇C. The CDW wavelength is given by𝜆 = 1/2 ⃗𝑘F (160,201).
In the presence of the CDW/PLD, the Brillouin zone edges of the superstructure coincide with the Fermi points at± ⃗𝑘F, opening an energy gap at the Fermi energy𝐸F (Fig.3.3B, bottom). The gap sizeΔis related to the PLD amplitude𝐴𝑄⃗ ⃗, the coupling constant𝑔𝑄⃗, the unrenormalized phonon frequency𝜔𝑄⃗and the ionic mass𝑀of the atom species:
Δ = 2∣ ⃗𝐴𝑄⃗∣ 𝑔𝑄⃗√2𝑀𝜔𝑄⃗
ℏ . (3.4)
The lower branch of the energy dispersion is completely occupied while the upper branch is unoccupied. The CDW/PLD formation in a linear chain therefore results in the occurrence of
The lower branch of the energy dispersion is completely occupied while the upper branch is unoccupied. The CDW/PLD formation in a linear chain therefore results in the occurrence of