Momentum-resolved linear dichroism in bilayer MoS2

Information about the symmetry and orbital character of electronic wave functions can be determined via photoemission selection rules that shape the measured intensity in an ARPES experiment. In a time-resolved ARPES experiment, the intensity contains additional information about inter-band excitations induced by an ultrafast laser pulse with tunable polarization. We take advantage of this capability to explore the polarization-dependent photoemission intensity in the transiently-populated conduction band of bilayer MoS2. We find a strong linear dichroism effect in the conduction band of bilayer MoS2. To support our experimental findings, we provide an effective model to evaluate the one-electron dipole matrix elements governing optical excitations and the photoemission process. In the case of single-layer MoS2, we find a significant masking of intensity outside the first Brillouin zone, which originates from an in-plane interference effect between photoelectrons emitted from the Mo orbitals. For the bilayer, an additional inter-layer interference effect leads to a distinctive modulation of intensity with photon energy. We then model the polarization-dependent photoemission intensity in the transiently-populated conduction band using the semiconductor Bloch equations. Our theoretical analysis reveals a strongly anisotropic momentum-dependence of the optical excitations due to intra-layer single-particle hopping, which explains the measured linear dichroism in bilayer MoS2.

Momentum-resolved linear dichroism in bilayer MoS2
Klara Volckaert, Habib Rostami, Deepnarayan Biswas, Igor Marković, Federico Andreatta, Charlotte E Sanders, Paulina Majchrzak, Cephise Cacho, Richard T Chapman, Adam Wyatt, Emma Springate, Daniel Lizzit, Luca Bignardi, Silvano Lizzit, Sanjoy K Mahatha, Marco Bianchi, Nicola Lanata, Phil DC King, Jill A Miwa, Alexander V Balatsky, Philip Hofmann, Søren Ulstrup, arXiv:1910.01848
Physical Review B: Rapid Communications, Accepted.

Layer and orbital interference effects in photoemission from transition metal dichalcogenides
Habib Rostami, Klara Volckaert, Nicola Lanata, Sanjoy K Mahatha, Charlotte E Sanders, Marco Bianchi, Daniel Lizzit, Luca Bignardi, Silvano Lizzit, Jill A Miwa, Alexander V Balatsky, Philip Hofmann, Søren Ulstrup, arXiv:1910.01882
Physical Review B, Accepted.

Odd-Frequency (Berezinskii) Pairing

Odd frequency superconductivity (OFSC) or Berezinskii pairing is a nontrivial manifestation of dynamical order, where the Cooper pair amplitude is odd in relative time. This possibility extends the conventionally allowed symmetries of the pair amplitudes. It is a rich and testing playground for the dynamics of quantum matter. Although bulk OFSC is yet to be identified, there are several proposals to realize such a system inmheterostructures, with broken translational symmetry, in a driven system with multiband superconductivity. Our group is currently working in several directions to identify the signatures of OFSC in the vicinity of paramagnetic impurities, Dirac semimetals, non-hermitian systems, amongst other candidate setups.

Odd-frequency superconductivity
Jacob Linder, Alexander V. Balatsky
Review of Modern Physics, Accepted.

Electron dynamics in a two-dimensional metal

Single layer tantalum disulphide is a genuine two-dimensional metal, which belongs to a class of transition metal dichalcogenides with strongly correlated electrons and therefore complex many-body interactions. It is currently unknown how the transition from the bulk to the single layer limit affects these interactions, and ultimately the electron dynamics. Here, we study the response of this two-dimensional metal in a van der Waals heterostructure with graphene to the generation of excited carriers by an optical laser pulse. Upon excitation, the elevated electronic temperature is accompanied by a substantial energy shift of the metallic band. These effects are explained by a combination of temperature-induced shifts of the chemical potential, as well as temperature-induced changes in static screening. These contributions are evaluated in a semi-empirical tight-binding model. We find that the shift resulting from a change in the chemical potential is dominant.

Transient hot electron dynamics in single-layer TaS2
Federico Andreatta, Habib Rostami, Antonija Grubišić Čabo, Marco Bianchi, Charlotte E. Sanders, Deepnarayan Biswas, Cephise Cacho, Alfred J. H. Jones, Richard T. Chapman, Emma Springate, Phil D. C. King, Jill A. Miwa, Alexander Balatsky, Søren Ulstrup, and Philip Hofmann
Physical Review B 99, 165421 (2019)

Spatially-resolved ARPES of van der Waals heterostructures

Two-dimensional materials can be stacked on top of each other like Lego bricks to form new materials where adjacent layers interact with each other by weak van der Waals forces. Such material systems are referred to as van der Waals heterostructures. Each layer possesses its own distinct electronic properties, however, the atomic registries and orientations between adjacent layers can give rise to a new, rich and complex electronic structure. These van der Waals heterostructures may consequently exhibit hybrid properties which could provide new functionality for nanoscale devices. We have recently explored heterobilayers comprised of two different two-dimensional materials, i.e. graphene and the transition metal dichalcogenide, tungsten disulphide, where we have been focusing on understanding the superlattice potential formed from a twist in the orientation between two layers of the stack using angle resolved photoemission spectroscopy with spatial resolution down to the nanoscale. While our focus on these van der Waals heterostructures has been primarily on interlayer interactions, we have been concurrently exploring the influence of lateral changes in the layers, and their subsequent influence on both quasiparticle band alignments and optical properties of the heterostructure.

Nanoscale mapping of quasiparticle band alignment
Søren Ulstrup, Cristina E Giusca, Jill A Miwa, Charlotte E Sanders, Alex Browning, Pavel Dudin, Cephise Cacho, Olga Kazakova, D Kurt Gaskill, Rachael L Myers-Ward, Tianyi Zhang, Mauricio Terrones, Philip Hofmann
Nature communications 10, 1 (2019)

Direct observation of minibands in twisted heterobilayers
Søren Ulstrup, Roland J Koch, Simranjeet Singh, Kathleen M McCreary, Berend T Jonker, Jeremy T Robinson, Chris Jozwiak, Eli Rotenberg, Aaron Bostwick, Jyoti Katoch, Jill A Miwa

Machine learning for large organic crystal structures

Machine learning has entered the field of quantum matter with applications covering quantum materials and the many-body problem. Interpretable and computationally-efficient machine learning models are able to capture the structure-property relationship in materials science.

Among others, we use the organic materials database developed within our group as a training set for our machine learning studies. The database hosts electronic and magnetic structures of about 25,000 3-dimensional organic crystals and provides a highly complex dataset to work on. Applying machine learning we intend to provide predictions towards novel functional materials based on the properties calculated within our training sets.

Band Gap Prediction for Large Organic Crystal Structures with Machine Learning
Bart Olsthoorn R. Matthias Geilhufe Stanislav S. Borysov Alexander V. Balatsky,
Advanced Quantum Technologies 2, 1900023 (2019)

Single-layer, single-orientation transition metal dichalcogenides

Semiconducting singe-layer transition metal dichalcogenides such as single-layer MoS2 and WS2 are thought to hold huge potential in (opto) electronic applications because of the so-called valley degree of freedom and the possibility to couple this to optical excitations. The concept of “valley-tronics” derived from this could be used to store or transmit quantum information. Alas, the possibility to exploit the distinct valley polarisation in a grown sample relies on the fact that the entire sample is grown in a single orientation, without the presence of the very common so-called mirror domains. In a collaboration between scientists in Italy and Aarhus, we have realised the growth of single layer MoS2 and WS2 in a single orientation and exploited this to study resulting effects of valley- and spin-polarisation in these materials. The single orientation is demonstrated in photoelectron diffraction experiments. It can be directly seen in the diffraction patterns in the figure, as these show a three-fold rather than a six-fold symmetry.

Novel single-layer vanadium sulphide phases, Fabian Arnold, Raluca-Maria Stan, Sanjoy K. Mahatha, H. E. Lund, Davide Curcio, Maciej Dendzik, Harsh Bana, Elisabetta Travaglia, Luca Bignardi, Paolo Lacovig, Daniel Lizzit, Zheshen Li, Marco Bianchi, Jill A. Miwa, Martin Bremholm, Silvano Lizzit, Philip Hofmann, C. E. Sanders, arxiv1803.07999
2D Materials 4, 0454009 (2018).

Suppression of Mirror Domains in the Epitaxial Growth of Single Layer WS2, Luca Bignardi, Daniel Lizzit, Harsh Bana, Elisabetta Travaglia, Paolo Lacovig, Charlotte E. Sanders, Maciej Dendzik, Matteo Michiardi, Marco Bianchi, Moritz Ewert, Lars Buß, Jens Falta, Jan Ingo Flege, Alessandro Baraldi, Rosanna Larciprete, Philip Hofmann, Silvano Lizzit, arxiv1806.04928
Physical Review Mat. 3, 014003 (2019).

Spin structure of K valleys in single-layer WS2 on Au(111), Philipp Eickholt, Charlotte Sanders, Maciej Dendzik, Luca Bignardi, Daniel Lizzit, Silvano Lizzit, Albert Bruix, Philip Hofmann, Markus Donath, arxiv1807.11235
Physical Review Letters 121, 136402 (2018).

Larger than 80% Valley Polarization of Free Carriers in Singly-Oriented Single Layer WS2 on Au(111), H. Beyer, G. Rohde, A. Grubišić Čabo, A. Stange, T. Jacobsen, L. Bignardi, D. Lizzit, P. Lacovig, C. E. Sanders, S. Lizzit, K. Rossnagel, P. Hofmann, M. Bauer, arxiv1907.10553, Physical Review Letters, in press.

Dark Matter Detection

Dirac materials have a wide range of applications and have even been proposed as a sensor material for dark matter particles. The energy range accessible by the small gap in massive Dirac cones provides the sensitivity to search in the sub-MeV mass scale. The small gap filters out the background thermal noise while still capturing excitations due to dark matter. Moreover, an anisotropic Dirac cone should show daily modulation of the dark matter signal due to the Earth’s rotation.

In our group, we have applied Materials Informatics in the search for new candidate sensor Dirac materials. We have identified the first organic candidate material, the Dirac-line semimetal (BEDT-TTF)⋅Br, with a small gap of 50 meV. Additionally, we have studied the role of impurities in the sensor and their effect on Dark matter detection.

Materials Informatics for Dark Matter Detection
R. Matthias Geilhufe Bart Olsthoorn Alfredo D. Ferella Timo Koski Felix Kahlhoefer Jan Conrad Alexander V. Balatsky
Physica Status Solidi Rapid Research Letters 12, 11 (2018)

Mass fluctuations and absorption rates in Dirac materials sensors
Bart Olsthoorn and Alexander V. Balatsky, arXiv:1909.10394v1

Novel single-layer vanadium sulphide phases

Most novel two-dimensional materials studied so far are extracted from existing “parent” materials that can be viewed as stacks of van der Waals bonded layers. The two-dimensional version is then simply one isolated such layer, e.g. graphene whose parent compound is graphite. It is an intriguing question if there are any truly new materials in two dimensions that do not have a bulk analogue. In this work, we have discovered several phases of two-dimensional vanadium sulphide. Some can be though as a simple layer extracted from a bulk VS2 crystal, but one phase is entirely new and has no known bulk analogue.

Novel single-layer vanadium sulphide phases, Fabian Arnold, Raluca-Maria Stan, Sanjoy K. Mahatha, H. E. Lund, Davide Curcio, Maciej Dendzik, Harsh Bana, Elisabetta Travaglia, Luca Bignardi, Paolo Lacovig, Daniel Lizzit, Zheshen Li, Marco Bianchi, Jill A. Miwa, Martin Bremholm, Silvano Lizzit, Philip Hofmann, C. E. Sanders, arxiv1803.07999
2D Materials 5, 045009 (2018).

Bosonic Dirac Matter

Dirac matter can also be composed of bosons and not just fermions as it is normally assumed. Bosons with spin (pseudo-spin) -momentum locking can equally be described by the Dirac equation. Photons, phonons, magnons etc, are examples of bosonic excitations occuring in nature. Magnons are spin waves in magnetically-ordered systems – ferromagnets or anti-ferromagnets, for example.

In our group, we study a case of occurrence of Dirac bosons in a nonequilibrium system of pumped interacting magnons in ferromagnets. Under pumping, magnons occupy high energy parts of the spectrum, and rescattering between magnons will redistribute them over the lower parts. This resembles processes corresponding to weak turbulence in flow dynamics. If the local spins of the ferromagnet occupy sites of the hexagonal lattice, for example what happens in a CrBr_{3} ferromagnet, the linear crossing points (Dirac points) will appear in the magnon spectrum, opening possibilities for studying Dirac magnons. We propose a situation when under rescattering pumped magnons occupy states close to the Dirac points. We study conditions of the Bose Einstein condensation of Dirac magnons in this case. Physical properties of such a condensate are going to be studied. The role of Dzyaloshinskii-Moriya interaction in physics of the Dirac BEC will be considered.

Dirac Magnons in Honeycomb Ferromagnets
Sergey S. Pershoguba, Saikat Banerjee, J. C. Lashley, Jihwey Park, Hans Ågren, Gabriel Aeppli, and Alexander V. Balatsky,
Physical Review X 8, 011010 (2018)

Magnetic excitations spectra on the Organic Materials Database (OMDB)

Materials with competing ground states and phases constitute a challenge for ab initio based modeling. A prominent example are magnetic materials. We have extended the Organic Materials Database (OMDB) [1] to include magnetic excitation properties. For inelastic neutron scattering we focus on the dynamical structure factor S(Q,ω) which contains information on the excitation modes of the material. The starting point is to consider magnetic materials within the OMDB. Using a ferromagnetic reference spin configuration, the magnetic Hamiltonian are obtained by using the infinitesimal rotation technique for calculation of Heisenberg exchange interactions.

For these magnetic Hamiltonians, quenching simulations down to zero temperature are performed in order to obtain the magnetic ground states. The magnetic excitation spectra are calculated by means of linear spin wave theory and atomistic spin dynamics simulations. The current dataset features collinear as well as noncollinear magnetic materials and has now been released on the OMDB. Representative results and the use of pattern matching algorithms to identify materials with desired properties are highlighted in [2].

Organic materials database: An open-access online database for data mining
Stanislav S. Borysov, R. Matthias Geilhufe, Alexander V. Balatsky
PLOS ONE 12, e0171501 (2017).

Spin wave excitations of magnetic metalorganic materials
Johan Hellsvik, Roberto Díaz Pérez, R. Matthias Geilhufe, Martin Månsson, Alexander V. Balatsky, arXiv:1907.01817v1

Transient excitonic condensate in pumped Dirac materials

Driven or non-equilibrium Dirac materials offer a new platform for investigation of collective instabilities. Recent pump-probe photoemission experiments on graphene and three-dimensional (3D) topological insulators (TIs) show the existence of a long-lived population inversion, a situation when photoexcited electrons and holes form two independent Fermi-Dirac distributions. Motivated by these results, we propose to search for transient excitonic instability in optically-excited DMs with population inversion. Optical pumping combined with the Dirac nature of the spectrum offers a knob for tuning the effective interaction between the photoexcited electrons and holes, and thus provides a way of reducing the critical coupling for excitonic instability. As a result, a transient condensate of electron-hole pairs could be achieved in a pumped DM while it is not attainable in equilibrium.

The key signature of the transient excitonic condensate are the energy gaps that open up at the non-equilibrium chemical potentials for electrons and holes, with the size of the gaps decreasing as the system returns to equilibrium (Fig.1). Among the existing DMs, the most promising candidates are (i) undoped suspended graphene, with gaps on the order of 10meV and a critical temperature of 70K, and (ii) 3D TIs with a single Dirac cone, where gaps of the order of few eV and critical temperatures of tens of K can be achieved. 3D TIs are particularly attractive due to prolonged lifetime of the population inversion. By tuning the material properties, it is possible to find new promising systems among 2D and 3D DMs.

Excitonic gap formation in pumped Dirac materials
Christopher Triola, Anna Pertsova, Robert S. Markiewicz, and Alexander V. Balatsky
Physical Review B 95, 205410 (2017).

Excitonic instability in optically pumped three-dimensional Dirac materials
Anna Pertsova and Alexander V. Balatsky
Physical Review B 97, 075109 (2018)

Light-Matter interactions in Dirac materials

The result of applying an external electromagnetic field on a medium manifests itself the creation of screening fields from within which consequently change the polarisation of the medium. The temporal dynamics of such polarisation fields then create electric currents. The relationship between the current and the external field is highly nontrivial in general, as it depends not only on the internal properties of the medium, but also on the excitation regime of the field. Low intensity fields tend to produce polarisations which scale linearly with the intensity and to generate currents oscillating at the same frequency as the external perturbation. Depending on the bond strength and intrinsic lattice symmetries, certain optical features may be enhanced or suppressed. If the field strength is increased and resonant with some characteristic internal frequency, the system responds non-linearly and creates currents with a nontrivial harmonic composition. This has obvious technological applications in the development of optoelectronic devices and sensors.

Dirac materials have unusual optical properties. For instance, graphene does not have a direct band gap between its two optically-active bands and can therefore show resonant behaviour when excited with any frequency, making it highly transparent in the monolayer setup. It also shows universal conductivity in the low field regime, independent of any system parameters. Besides, it is a strong source of third-harmonics.
In our group, we work on understanding features of novel interactions in Dirac and Weyl semimetals and the role of the carrier features in optical observables such as currents or time-dependent carrier densities.

Nonlinear optical effects of opening a gap in graphene
David N. Carvalho, Fabio Biancalana, and Andrea Marini
Physical Review B 97, 195123 (2018)

Theory of third-harmonic generation in graphene: A diagrammatic approach
Habib Rostami, Marco Polini
Physical Review B 93, 161411 (2016)

Ultrafast Band Structure Control of a Two-Dimensional Heterostructure

The band gap in a bulk semiconductor is a characteristic feature of the material and can usually not be modified without, for instance, massive chemical substitution. For a two-dimensional material this is quite different: It is well known that the band gap of two-dimensional semiconductors such as MoS2 or WS2 can be changed drastically, merely by placing these materials onto substrates with different dielectric properties. This is due to the screening properties of the substrate that have a strong effect on the electron-hole interaction in the two-dimensional material. In this paper we show that the band gap can also be modified by creating a dense population of excited electrons and holes using a femtosecond laser pulse. In this way, the change of screening happens in the material itself due to the excited carriers. This opens the possibility of applications in which the materials’ properties as such are modified on an ultrafast time scale.

Ultrafast Band Structure Control of a Two-Dimensional Heterostructure, Søren Ulstrup, Antonija Grubišić Čabo, Jill A. Miwa, Jonathon M. Riley, Signe S. Grønborg, Jens C. Johannsen, Cephise Cacho, Oliver Alexander, Richard T. Chapman, Emma Springate, Marco Bianchi, Maciej Dendzik, Jeppe V. Lauritsen, Phil D. C. King, and Philip Hofmann, arxiv1606.03555
ACS Nano 10, 6315 (2016).

Quasi one-dimensional metallic band dispersion in the commensurate charge density wave of 1T-TaS2

TaS2 in its 1T structural modification is a metallic transition metal dichalcogenide that has been studied for more than 40 years because of its many fascinating phase transitions at low temperatures. The new emerging phases are slightly different charge density waves of the electrons, along with a strong deformations of the lattice. The reason for these transitions are still subject to controversy, but both strong electron-lattice and strong electron-electron interactions are thought to be important. Until recently, 1T TaS2 was viewed as a stack of quasi independent TaS2 layers, held together by weak van der Waals forces, and it was tried to explain the charge density wave transitions in a simple two-dimensional picture. However, recent calculations have predicted a strong dispersion of an electronic band perpendicular to the TaS2 layers, i.e. electrons moving in that direction. In this work, we have been able to confirm this predicted dispersion experimentally, confirming that a quasi two-dimensional picture might not be sufficient to understand this complex material.

Quasi one-dimensional metallic band dispersion in the commensurate charge density
wave of 1T-TaS2, Arlette S. Ngankeu, Kevin Guilloy, Sanjoy K. Mahatha, Marco Bianchi, Charlotte E. Sanders, Kai Rossnagel, Jill Miwa and Philip Hofmann, arxiv1705.00455
Physical Review B 96, 195147 (2017).

Crystalline and electronic structure of single-layer TaS2

In its bulk form, TaS2 is a layered crystal similar to WS2 or MoS2, but with the important difference that TaS2 is a metal, not a semiconductor. It exists in two structural modifications and due to its metallic character, it is susceptible to different electronic instabilities such as charge density waves or superconductivity. In contrast to the semiconducting MoS2 or WS2, single layers of TaS2 cannot be peeled off by “the Scotch tape method” because the material is not air-stable. In this work, we report the first synthesis of single layer TaS2 and we investigate its electronic structure. It turns our, that the single layer is also metallic, but it does not undergo any instabilities down to the lowest temperatures we have investigated.

Crystalline and electronic structure of single-layer TaS2 Charlotte E. Sanders, Maciej Dendzik, Arlette S. Ngankeu, Andreas Eich, Albert Bruix, Marco Bianchi, Jill A. Miwa, Bjørk Hammer, Alexander A. Khajetoorians, Philip Hofmann, arxiv1606.05856
Physical Review B 94, 081404(R) (2016).