arXiv subjects

Mark Oliver Goerbig

Publications and source records attributed to Mark Oliver Goerbig.

10 recordsLinked to original sources

arXiv2021

Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry

Linear crossing of energy bands occur in a wide variety of materials. In this paper we address the question of the quantization of the Berry winding characterizing the topology of these crossings in dimension $D=2$. Based on the historical example of $2$-bands crossing occuring in graphene, we propose to relate these Berry windings to the topological Chern number of a $D=3$ dimensional extension of these crossings. This dimensional embedding is obtained through a choice of a gap-opening potential. We show that the presence of an (emergent) $\mathcal{PT}$ symmetry, local in momentum and antiunitary, allows us to relate $D=3$ Chern numbers to $D=2$ Berry windings quantized as multiple of $π$. We illustrate this quantization mechanism on a variety of three-band crossings.

cond-mat.mes-hall↗

arXiv2021

Charge density waves and their transitions in anisotropic quantum Hall systems

In recent experiments, external anisotropy has been a useful tool to tune different phases and study their competitions. In this paper, we look at the quantum Hall charge density wave states in the $N=2$ Landau level. Without anisotropy, there are two first-order phase transitions between the Wigner crystal, the $2$-electron bubble phase, and the stripe phase. By adding mass anisotropy, our analytical and numerical studies show that the $2$-electron bubble phase disappears and the stripe phase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystals that may be observed experimentally is unveiled after the bubble phase gets out. Upon increase of the anisotropy, the energy of the phases at the transitions becomes progressively smooth as a function of the filling. We conclude that all first-order phase transitions are replaced by continuous phase transitions, providing a possible realisation of continuous quantum crystalline phase transitions.

cond-mat.str-el↗

arXiv2021

SU(4) spin waves in the $ν=\pm1$ quantum Hall ferromagnet in graphene

We study generalized spin waves in graphene under a strong magnetic field when the Landau-level filling factor is $ν=\pm 1$. In this case, the ground state is a particular SU(4) quantum Hall ferromagnet, in which not only the physical spin is fully polarized but also the pseudo-spin associated with the valley degree of freedom. The nature of the ground state and the spin-valley polarization depend on explicit symmetry breaking terms that are also reflected in the generalised spin-wave spectrum. In addition to pure spin waves, one encounters valley-pseudo-spin waves as well as more exotic entanglement waves that have a mixed spin-valley character. Most saliently, the SU(4) symmetry-breaking terms do not only yield gaps in the spectra, but under certain circumstances, namely in the case of residual ground-state symmetries, render the originally quadratic (in the wave vector) spin-wave dispersion linear.

cond-mat.mes-hall↗

arXiv2020

Skyrmion zoo in graphene at charge neutrality in a strong magnetic field

As a consequence of the approximate spin-valley symmetry in graphene, the ground state of electrons in graphene at charge neutrality is a particular SU(4) quantum-Hall ferromagnet to minimize their exchange energy. If only the Coulomb interaction is taken into account, this ferromagnet can appeal either to the spin degree of freedom or equivalently to the valley pseudo-spin degree of freedom. This freedom in choice is then limited by subleading energy scales that explicitly break the SU(4) symmetry, the simplest of which is given by the Zeeman effect that orients the spin in the direction of the magnetic field. In addition, there are also valley symmetry breaking terms that can arise from short-range interactions or electron-phonon couplings. Here, we build upon the phase diagram, which has been obtained by Kharitonov [Phys. Rev. B \textbf{85}, 155439 (2012)], in order to identify the different skyrmions that are compatible with these types of quantum-Hall ferromagnets. Similarly to the ferromagnets, the skyrmions at charge neutrality are described by the $\text{Gr}(2,4)$ Grassmannian at the center, which allows us to construct the skyrmion spinors. The different skyrmion types are then obtained by minimizing their energy within a variational approach, with respect to the remaining free parameters that are not fixed by the requirement that the skyrmion at large distances from their center must be compatible with the ferromagnetic background. We show that the different skyrmion types have a clear signature in the local, sublattice-resolved, spin magnetization, which is in principle accessible in scanning-tunneling microscopy and spectroscopy.

cond-mat.mes-hall↗

arXiv2020

Dynamical conductivity of the Fermi arc and the Volkov-Pankratov states on the surface of Weyl semimetals

Weyl semimetals are known to host massless surface states called Fermi arcs. These Fermi arcs are the manifestation of the bulk-edge correspondence in topological matter and thus are analogous to the topological chiral surface states of topological insulators. It has been shown that the latter, depending on the smoothness of the surface, host massive Volkov-Pankratov(VP) states that coexist with the chiral ones. Here, we investigate these VP states in the framework of Weyl semimetals, namely their density of states and magneto-optical response. We find the selection rules corresponding to optical transitions which lead to anisotropic responses to external fields. In the presence of a magnetic field parallel to the interface, the selection rules and hence the poles of the response functions are mixed.

cond-mat.mes-hall↗

arXiv2018

Hamiltonian theory for Quantum Hall systems in a tilted magnetic field: robustness of activation gaps

We use the Hamiltonian theory developed by Shankar and Murthy to study a quantum Hall system in a tilted magnetic field. With a finite width of the system in the $z$ direction, the parallel component of the magnetic field introduces anisotropy into the effective two-dimensional interactions. The effects of such anisotropy can be effectively captured by the recently proposed generalized pseudo-potentials. We find that the off-diagonal components of the pseudo-potentials lead to mixing of composite fermions Landau levels, which is a perturbation to the picture of $p$ filled Landau levels in composite-fermion theory. By changing the internal geometry of the composite fermions, such a perturbation can be minimized and one can find the corresponding activation gaps for different tilting angles, and we calculate the associated optimal metric. Our results show that the activation gap is remarkably robust against the in-plane magnetic field in the lowest Landau level.

cond-mat.str-el↗

arXiv2018

Model Prediction of Self-Rotating Excitons in Two-Dimensional Transition-Metal Dichalcogenides

Using the quasiclassical concept of Berry curvature we demonstrate that a Dirac exciton - a pair of Dirac quasiparticles bound by Coulomb interactions - inevitably possesses an intrinsic angular momentum making the exciton effectively self-rotating. The model is applied to excitons in two-dimensional transition metal dichalcogenides, in which the charge carriers are known to be described by a Dirac-like Hamiltonian. We show that the topological self-rotation strongly modifies the exciton spectrum and, as a consequence, resolves the puzzle of the overestimated two-dimensional polarizability employed to fit earlier spectroscopic measurements.

cond-mat.mes-hall↗

arXiv2017

Exciton spectrum in two-dimensional transition metal dichalcogenides: The role of Diracness

The physics of excitons, electron-hole pairs that are bound together by their mutual Coulomb attraction, can to great extent be understood in the framework of the quantum-mechanical hydrogen model. This model has recently been challenged by spectroscopic measurements on two-dimensional transition-metal dichalchogenides that unveil strong deviations from a hydrogenic spectrum. Here, we show that this deviation is due to the particular relativistic character of electrons in this class of materials. Indeed, their electrons are no longer described in terms of a Schroedinger but a massive Dirac equation that intimately links electrons to holes. Dirac excitons therefore inherit a relativistic quantum spin-1/2 that contributes to the angular momentum and thus the exciton spectrum. Most saliently, the level spacing is strongly reduced as compared to the hydrogen model, in agreement with spectroscopic measurements and ab-initio calculations.

cond-mat.mes-hall↗

arXiv2016

Optical Absorption by Dirac Excitons in Single-Layer Transition-Metal Dichalcogenides

We develop an analytically solvable model able to qualitatively explain nonhydrogenic exciton spectra observed recently in two-dimensional (2d) semiconducting transition metal dichalcogenides. Our exciton Hamiltonian explicitly includes additional angular momentum associated with the pseudospin degree of freedom unavoidable in 2d semiconducting materials with honeycomb structure. We claim that this is the key ingredient for understanding the nonhydrogenic exciton spectra that was missing so far.

cond-mat.mes-hall↗

arXiv2013

Non-trivial Surface-band Dispersion on Bi(111)

We performed angle-resolved photoelectron spectroscopy of the Bi(111) surface to demonstrate that this surface support edge states of non-trivial topology. Along the $\barΓ\bar{M}$-direction of the surface Brillouin zone, a surface-state band disperses from the projected bulk valence bands at $\barΓ$ to the conduction bands at $\bar{M}$ continuously, indicating the non-trivial topological order of three-dimensional Bi bands. We ascribe this finding to the absence of band inversion at the $L$ point of the bulk Bi Brillouin zone. According to our analysis, a modification of tight-binding parameters can account for the non-trivial band structure of Bi without any other significant change on other physical properties.

cond-mat.mtrl-sci↗