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@PHDTHESIS{Hofmann:1048443,
      author       = {Hofmann, Jonathan Karl},
      othercontributors = {Voigtländer, Bert and Morgenstern, Markus},
      title        = {{E}lectrical anisotropy and shear-resistant topology in the
                      quasi one-dimensional van-der-{W}aals material
                      α-{B}i$_{4}${B}r$_{4}$},
      school       = {RWTH Aachen},
      type         = {Dissertation},
      publisher    = {RWTH Aachen University},
      reportid     = {FZJ-2025-04649},
      pages        = {pages 1 Online-Ressource : Illustrationen},
      year         = {2025},
      note         = {Dissertation, RWTH Aachen, 2025},
      abstract     = {The quasi-one-dimensional van-der-Waals material α-Bi4Br4
                      crystallizes in a monoclinic crystal structure consisting of
                      covalently bonded Bi4Br4 chains parallel to the lattice
                      vector b. The van-der-Waals interaction connects these
                      chains to form 2D layers. These layers are then stacked in
                      c-direction. α-Bi4Br4 features AB stacking. In contrast to
                      well-known van-der-Waals materials such as WTe2 or MoS2,
                      α-Bi4Br4 features two van-der-Waals gaps. A monolayer of
                      α-Bi4Br4 is a quantum spin Hall insulator. α-Bi4Br4 bulk
                      crystals readily cleaves to expose the (001) surface.
                      Furthermore, flakes of α-Bi4Br4 showing the same surface
                      can be prepared by mechanical exfoliation. Electrical
                      transport measurements are preformed using a four-tip
                      scanning tunnelling microscope (STM) to investigate the
                      anisotropy of the resistivity of α-Bi4Br4. A four-tip STM
                      integrates four individual STMs into a tight unit, to enable
                      transport measurements on surfaces. The piezo drives of the
                      individual STMs allow flexible tip configurations to be set
                      up as needed for a transport measurement. Furthermore, a
                      four-tip STM still can image the surface by scanning a
                      single tip and perform scanning tunnelling microscopy. Due
                      to the small resistances measured here, the exact
                      calibration of the voltage measurement in the four-tip STM
                      became a major issue for the measurement. This calibration
                      is therefore addressed in chapter 3. Chapter 5 presents a
                      modified surface structure of the α-Bi4Br4(001) surface.
                      Atomically resolved STM images show that the parallel Bi4Br4
                      chains exhibit a mutual shift different from the one
                      expected for this surface. Density functional theory
                      calculations by Mingqian Zheng and Jin-Jian Zhou indicate
                      that a monolayer of this new structure is also a quantum
                      spin Hall insulator. The modified structure arises due to
                      shear stress which is able to shift the parallel chains with
                      respect to each other because neighbouring chains are only
                      connected by weak van-der-Waals forces. Two different
                      methods to disentangle the resistivity tensor ρ of
                      α-Bi4Br4 are implemented: In chapter 6, the in-plane
                      anisotropy is first measured on the (001) surface of a bulk
                      α-Bi4Br4 crystal. For this, two measurements of the
                      resistance in a square tip configuration are used. Then, the
                      value of resistivity in b-direction is determined using a
                      distance-dependent measurement on a thin flake. Assuming
                      that the influence of the off-diagonal element of the
                      resistivity tensor can be neglected, an in-plane anisotropy
                      of A= $ρ_{a}$ / $ρ_{b}$ = 6.4(5) is obtained at room
                      temperature. Furthermore, the anisotropy normal to the ab
                      plane is found to be $A_{z}$ = $ρ_{z}$ / $ρ_{b}$ = 1300.
                      Thus, the resistivity in b-direction, parallel to the
                      chains, is the smallest, as expected from the crystal
                      structure. At 77 K, A = 5.0(3) and $A_{z}$ = 6500 were
                      measured. Chapter 7 demonstrates an alternative approach to
                      disentangle the three elements on the main diagonal of the
                      resistivity tensor ρ when the off-diagonal element is
                      neglected. Here, the tips are positioned in the corners of a
                      large, rectangular flake. The anisotropy can then be
                      obtained by the Bierwagen-Simon method. While it is possible
                      to demonstrate the disentanglement of the three components
                      of the resistivity tensor, the in-plane anisotropy A
                      measured with the second method was substantially smaller
                      than the result obtained before. The origin of this
                      discrepancy is traced back to imperfections of the flake.},
      keywords     = {Hochschulschrift (Other) / Rastertunnelmikroskopie ;
                      scanning tunneling microscopy ;
                      Vierspitzen-Rastertunnelmikroskopie ; four-tip scanning
                      tunneling microscopy ; Ladungstransport ; charge transport ;
                      topologische Isolatoren ; topological insulators ;
                      quasi-one-dimensional crystals ; quasi-eindimensionale
                      Kristalle ; higher-order topological insulators ;
                      Anisotropie ; anisotropy ; Resistivitätstensor ;
                      resistivity tensor (Other)},
      cin          = {PGI-3},
      cid          = {I:(DE-Juel1)PGI-3-20110106},
      pnm          = {5213 - Quantum Nanoscience (POF4-521)},
      pid          = {G:(DE-HGF)POF4-5213},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2025-06556},
      url          = {https://juser.fz-juelich.de/record/1048443},
}