arXiv subjects

Mark O. Goerbig

Publications and source records attributed to Mark O. Goerbig.

At least 19 recordsLinked to original sources

arXiv2025

Quantized and nonquantized Hall response in topological Hatsugai-Kohmoto systems

We explore the robustness of Hall conductivity quantization in several insulating systems, exhibiting one scenario where the quantization is not preserved. Specifically, we apply the Kubo formula to topological models with the Hatsugai-Kohmoto interaction. Starting from the many-body degeneracy induced by this interaction in the topological Kane-Mele model, we consider Zeeman fields to select specific states within the ground-state manifold that reveal a non-quantized Hall response, precisely for the case with a Zeeman field diagonal in the bands of the Kane-Mele model. From a physical point of view, this term may mimic a ferromagnetic order that arises naturally when couplings beyond the Hatsugai-Kohmoto interaction are taken into account.

cond-mat.mes-hall↗

arXiv2024

Beating Fabry-Pérot interference pattern in a magnonic scattering junction in the graphene quantum Hall ferromagnet

At filling factor $ν=0,\pm1$, the ground state of graphene is a particular SU(4) ferromagnet which hosts a rich phase diagram along with several spin, pseudospin or "entanglement" magnon modes. Motivated by recent experiments, we study a $ν=-1|0|-1$ Fabry-Pérot magnonic junction. If the ground state at $ν=0$ is spin polarized, there exist two spin modes which interfere and create a beating pattern, while pseudospin modes are reflected. The same scenario occurs for pseudospin magnon if the $ν=0$ ground state is pseudospin polarized. The observation of such an interference pattern would provide information on the low-energy anisotropies and thus on the ground state.

cond-mat.mes-hall↗

arXiv2024

Helical trilayer graphene in magnetic field: Chern mosaic and higher Chern number ideal flat bands

Helical trilayer graphene (hTG) exhibits a supermoiré pattern with large domains centered around stacking points ABA and BAB, where two well-separated low-energy bands appear with different total Chern numbers at each valley, forming a Chern mosaic pattern. In the chiral limit, the low-energy bands become exactly flat at zero energy for magic-angle twists. Here we investigate these zero-energy flat bands and their topological properties in the presence of a perpendicular magnetic field. We show that hTG retains the precise flatness of the zero-energy bands, even at finite magnetic fields. We find topological phase transitions at fields corresponding to unit and half magnetic flux leading to an emergence of higher Chern number flat bands. Consequently the Chern mosaic gets modified for finite magnetic fields. We further find the analytical forms of zero-energy wave functions and identify a set of hidden wave functions, which gives crucial insights into both the topological transitions and enhancement of Chern numbers across them. We also find topological transitions away from the chiral limit with finite corrugations and at different magic angles.

cond-mat.mes-hall↗

arXiv2024

Normal state quantum geometry and superconducting domes in (111) oxide interfaces

We theoretically investigate the influence of the normal state quantum geometry on the superconducting phase in (111) oriented oxide interfaces and discuss some of the implications for the $\text{LaAlO}_3/\text{SrTiO}_3$ (LAO/STO) heterostructure. From a tight-binding modeling of the interface, we derive a two-band low-energy model, allowing us to analytically compute the quantum geometry and giving us access to the superfluid weight, as well as to showcase the role of two particular relevant energy scales. One is given by the trigonal crystal field which stems from the local trigonal symmetry at the interface, and the other one is due to orbital mixing at the interface. Our calculations indicate that the variation of the superfluid weight with the chemical potential $μ$ is controlled by the quantum geometry in the low-$μ$ limit where it presents a dome. At higher values of $μ$ the conventional contribution dominates. In order to make quantitative comparisons between our results and experimental findings, we rely on an experimentally observed global reduction of the superfluid weight that we apply to both the conventional and geometric contributions. Furthermore, an experimentally measured non-monotonic variation of $μ$ with the gate voltage $V_g$ is taken into account and yields a two-dome scenario for the superconducting critical temperature as a function of $V_g$. The observed dome in the low-$V_g$ regime is explained by the non-monotonic evolution of a dominant conventional part of the superfluid density. In contrast, the expected second dome at larger values of $V_g$ limit would be due to a dominant quantum-geometric contribution.

cond-mat.supr-con↗

arXiv2024

Role of the Berry curvature on BCS-type superconductivity in two-dimensional materials

We theoretically investigate how the Berry curvature, which arises in multi-band structures when the electrons can be described by an effective single-band Hamiltonian, affects the superconducting properties of two-dimensional electronic systems. Generically the Berry curvature is coupled to electric fields beyond those created by the periodic crystal potential. A potential source of such electric fields, which vary slowly on the lattice scale, is the mutual interaction between the electrons. We show that the Berry curvature provides additional terms in the Hamiltonian describing interacting electrons within a single band. When these terms are taken into account in the framework of the usual BCS weak-coupling treatment of a generic attractive interaction that allows for the formation of Cooper pairs, the coupling constant is modified. In pure singlet and triplet superconductors, we find that the Berry curvature generally lowers the coupling constant and thus the superconducting gap and the critical temperature as a function of doping. From an experimental point of view, a measured deviation from the expected BCS critical temperature upon doping, e.g. in doped two-dimensional transition-metal dichalcogenides, may unveil the strength of the Berry curvature.

cond-mat.mes-hall↗

arXiv2023

Topological interface states -- a possible path towards a Landau-level laser in the THz regime

Volkov-Pankratov surface bands arise in smooth topological interfaces, i.e. interfaces between a topological and a trivial insulator, in addition to the chiral surface state imposed by the bulk-surface correspondence of topological materials. These two-dimensional bands become Landau-quantized if a magnetic field is applied perpendicular to the interface. I show that the energy scales, which are typically in the 10-100 meV range, can be controlled both by the perpendicular magnetic field and the interface width. The latter can still be varied with the help of a magnetic-field component in the interface. The Landau levels of the different Volkov-Pankratov bands are optically coupled, and their arrangement may allow one to obtain population inversion by resonant optical pumping. This could serve as the elementary brick of a multi-level laser based on Landau levels. Moreover, the photons are absorbed and emitted either parallel or perpendicular to the magnetic field, respectively in the Voigt and Faraday geometry, depending on the Volkov-Pankratov bands and Landau levels involved in the optical transitions.

cond-mat.mes-hall↗

arXiv2023

Cascade of multi-electron bubble phases in monolayer graphene at high Landau level filling

The phase diagram of an interacting two-dimensional electron system in a high magnetic field is enriched by the varying form of the effective Coulomb interaction, which depends strongly on the Landau level index. While the fractional quantum Hall states that dominate in the lower energy Landau levels have been explored experimentally in a variety of two-dimensional systems, much less work has been done to explore electron solids owing to their subtle transport signatures and extreme sensitivity to disorder. Here we use chemical potential measurements to map the phase diagram of electron solid states in $N=2$, $N=3$, and $N=4$ Landau levels in monolayer graphene. Direct comparison between our data and theoretical calculations reveals a cascade of density-tuned phase transitions between electron bubble phases up to two, three or four electrons per bubble in the N=2, 3 and 4 Landau levels respectively. Finite temperature measurements are consistent with melting of the solids for T$\approx$1K.

cond-mat.mes-hall↗

arXiv2022

From the Integer to the Fractional Quantum Hall Effect in Graphene

The fractional quantum Hall effect is a very particular manifestation of electronic correlations in two-dimensional systems in a strong perpendicular magnetic field. It arises as a consequence of a strong Coulomb repulsion between electrons in the same Landau level that conspires with a particular chirality of the electronic states. This chirality is inherited from the classical cyclotron motion, i.e. a particular sense of electronic rotation due to the orientation of the magnetic field. The specificity of the FQHE in graphene consists of a four-fold spin-valley degeneracy inherited from the electronic bands in the vicinity of the Fermi level. The relevant Coulomb interaction respects this SU(4) symmetry, and one is therefore confronted with a generic four-component fractional quantum Hall effect, as well as with other correlated four-component phases, such as spin-valley ferromagnetic states. The present article aims at a -- mainly theoretical -- discussion of these exotic phases, in comparison with experimental evidence for them.

cond-mat.mes-hall↗

arXiv2021

Surface plasmonics of Weyl semimetals

Smooth interfaces of topological systems are known to host massive surface states along with the topologically protected chiral one. We show that in Weyl semimetals these massive states, along with the chiral Fermi arc, strongly alter the form of the Fermi-arc plasmon, Most saliently, they yield further collective plasmonic modes that are absent in a conventional interfaces. The plasmon modes are completely anisotropic as a consequence of the underlying anisotropy in the surface model and expected to have a clear-cut experimental signature, e.g. in electron-energy loss spectroscopy.

cond-mat.mes-hall↗

arXiv2020

Volkov-Pankratov states in topological superconductors

We study the in-gap states that appear at the boundaries of both 1D and 2D topological superconductors. While the massless Majorana quasiparticles are guaranteed to arise by the bulk-edge correspondence, we find that they could be accompanied by massive Volkov-Pankratov (VP) states which are present only when the interface is sufficiently smooth. These predictions can be tested in an s-wave superconductor with Rashba spin-orbit coupling placed on top of a magnetic domain wall. We calculate the spin-resolved local density of states of the VP states about the band inversion generated by a magnetic domain wall and find that they are oppositely spin-polarized on either side of the topological phase boundary. We also demonstrate that the spatial position, energy-level spacing, and spin polarization of the VP states can be modified by the introduction of in-plane electric fields.

cond-mat.supr-con↗

arXiv2018

Competing Fractional Quantum Hall and Electron Solid Phases in Graphene

We report experimental observation of the reentrant integer quantum Hall effect in graphene, appearing in the N$=$2 Landau level. Similar to high-mobility GaAs/AlGaAs heterostructures, the effect is due to a competition between incompressible fractional quantum Hall states, and electron solid phases. The tunability of graphene allows us to measure the $B$-$T$ phase diagram of the electron-solid phase. The hierarchy of reentrant states suggest spin and valley degrees of freedom play a role in determining the ground state energy. We find that the melting temperature scales with magnetic field, and construct a phase diagram of the electron liquid-solid transition.

cond-mat.mes-hall↗

arXiv2017

Topological states at the (001) surface of SrTiO3

Defect-free SrTiO3 (STO) is a band insulator but Angle Resolved Photoemission Spectroscopy (ARPES) experiments have demonstrated the existence of a nanometer thin two-dimensional electron liquid (2DEG) at the (001) oriented surface of this compound. The bulk is a trivial insulator, but our theoretical study reveals that the parity of electronic wavefunctions in this 2DEG is inverted in the vicinity of special points in reciprocal space where the low-energy dispersion consists of four gapped Dirac cones with a tilted and anisotropic shape. This gives rise to linearly dispersing topological edge states at the one-dimensional boundary. We propose to probe these modes by measuring the Josephson radiation from gapless bound Andreev states in STO based junctions, as it is predicted that they display distinctive signatures of topology.

cond-mat.mtrl-sci↗

arXiv2017

Magnetic description of the Fermi arc in type-I and type-II Weyl semimetals

We consider finite-sized interfaces of a Weyl semi-metal and show that the corresponding confinement potential is similar to the application of a magnetic field. Among the numerous states, which can be labeled by indices n like in Landau levels, the n = 0 surface state describes the Weyl semimetal Fermi arc at a given chemical potential. Moreover, the analogy with a magnetic field shows that an external in-plane magnetic field can be used to distort the Fermi arc and would explain some features of magneto-transport in Weyl semimetals. We derive the Fermi arc for type-I and type-II Weyl semimetals where we deal with the tilt anisotropy by the use of Lorentz boosts. In the case of type-II Weyl semimetals, this leads to many additional topologically trivial surface states at low energy. Finally, we extend the Aharonov-Casher argument and demonstrate the stability of the Fermi arc over fluctuations of the surface potential.

cond-mat.mes-hall↗

arXiv2017

Spin-valley skyrmions in graphene at filling factor $ν=-1$

We model quantum Hall skyrmions in graphene monolayer at quarter filling by a theory of CP3 fields and study the energy minimizing skyrmions in presence of valley pseudospin anisotropy and Zeeman coupling. We present a diagram of all types of skyrmions in a wide range of the anisotropy parameters. For each type of skyrmion, we visualize it on three Bloch spheres, and present the profiles of its texture on the graphene honeycomb lattice, thus providing references for the STM/STS imaging of spin-pseudospin textures in graphene monolayer in quantum Hall regime. Besides the spin and pseudospin skyrmions for the corresponding degrees of freedom of an electron in the N=0 Landau level, we discuss two unusual types -- the "entanglement skyrmion" whose texture lies in the space of the entanglement of spin and pseudospin, as well as the "deflated pseudospin skyrmion" with partial entanglement. For all skyrmion types, we study the dependence of the energy and the size of a skyrmion on the anisotropy parameters and perpendicular magnetic field. We also propose three ways to modify the anisotropy energy, namely the sample tilting, the substrate anisotropy and the valley pseudospin analogue of Zeeman coupling.

cond-mat.str-el↗

arXiv2016

Magnetic-field-induced relativistic properties in type-I and type-II Weyl semimetals

We investigate Weyl semimetals with tilted conical bands in a magnetic field. Even when the cones are overtilted (type-II Weyl semimetal), Landau-level quantization can be possible as long as the magnetic field is oriented close to the tilt direction. Most saliently, the tilt can be described within the relativistic framework of Lorentz transformations that give rise to a rich spectrum, displaying new transitions beyond the usual dipolar ones in the optical conductivity. We identify particular features in the latter that allow one to distinguish between semimetals of different types.

cond-mat.mes-hall↗

arXiv2016

SU(4) Skyrmions in the $ν=\pm 1$ Quantum Hall State of Graphene

We explore different skyrmion types in the lowest Landau level of graphene at a filling factor $ν=\pm 1$. In addition to the formation of spin and valley pseudospin skyrmions, we show that another type of spin-valley entangled skyrmions can be stabilized in graphene due to an approximate SU(4) spin-valley symmetry that is affected by sublattice symmetry-breaking terms. These skyrmions have a clear signature in spin-resolved density measurements on the lattice scale, and we discuss the expected patterns for the different skyrmion types.

cond-mat.mes-hall↗

arXiv2015

Magneto-optics of quasi-relativistic electrons in tilted Dirac cones in graphene and $α$-(BEDT-TTF)$_2$I$_3$

Massless Dirac fermions occur as low-energy modes in several quasi-two-dimensional condensed matter systems such as graphene, the surface of bulk topological insulators, and in layered organic semiconductors. When the rotational symmetry in such systems is reduced either by an in-plane electric field or an intrinsic tilt of the Dirac cones, the allowed dipolar optical transitions evolve from a few selected transitions into a wide fan of interband transitions. We show that the Lorentz covariance of the low-energy carriers allows for a concise analysis of the emerging magneto-optical properties. We predict that infrared absorption spectra yield quantitative information on the tilted Dirac cone structure in organic compounds such as $α$-(BEDT-TTF)$_2$I$_3$.

cond-mat.mes-hall↗

arXiv2014

Dirac Fermions in condensed matter and beyond

This review aims at a theoretical discussion of Dirac points in two-dimensional systems. Whereas Dirac points and Dirac fermions are prominent low-energy electrons in graphene (two-dimensional graphite), research on Dirac fermions in low-energy physics has spread beyond condensed-matter systems. In these alternative systems, a large versatility in the manipulation of the relevant band parameters can be achieved. This allows for a systematic study of the motion and different possible fusions of Dirac points, which are beyond the physical limits of graphene. We introduce the basic properties of Dirac fermions and the motion of Dirac points here and aim at a topological classification of these motions. The theoretical concepts are illustrated in particular model systems.

cond-mat.mes-hall↗