arXiv subjects

Dante M. Kennes

Publications and source records attributed to Dante M. Kennes.

At least 109 records · Page 6Linked to original sources

arXiv2022

TU$^2$FRG -- a scalable approach for truncated unity functional renormalization group in generic fermionic models

Describing the emergence of phases of condensed matter is one of the central challenges in physics. For this purpose many numerical and analytical methods have been developed, each with their own strengths and limitations. The functional renormalization group is one of these methods bridging between efficiency and accuracy. In this paper we derive a new truncated unity (TU) approach unifying real- and momentum space TU, called TU$^2$FRG. This formalism significantly improves the scaling compared to conventional momentum (TU)FRG when applied to large unit-cell models and models where the translational symmetry is broken.

cond-mat.str-el↗

arXiv2022

Cavity Quantum Materials

The emergent field of cavity quantum materials bridges collective many-body phenomena in solid-state platforms with strong light-matter coupling in cavity quantum electrodynamics (cavity QED). This brief review provides an overview of the state of the art of cavity platforms and highlights recent theoretical proposals and first experimental demonstrations of cavity control of collective phenomena in quantum materials. This encompasses light-matter coupling between electrons and cavity modes, cavity superconductivity, cavity phononics and ferroelectricity, correlated systems in a cavity, light-magnon coupling, cavity topology and the quantum Hall effect, as well as superradiance. An outlook of potential future developments is given.

quant-ph↗

arXiv2022

Moiré Engineering of Spin-Orbit Coupling in Twisted Platinum Diselenide

We study the electronic structure and correlated phases of twisted bilayers of platinum diselenide using large-scale ab initio simulations combined with the functional renormalization group. PtSe$_2$ is a group-X transition metal dichalcogenide, which hosts emergent flat bands at small twist angles in the twisted bilayer. Remarkably, we find that moiré engineering can be used to tune the strength of Rashba spin-orbit interactions, altering the electronic behavior in a novel manner. We reveal that an effective triangular lattice with a twist-controlled ratio between kinetic and spin-orbit coupling scales can be realized. Even dominant spin-orbit coupling can be accessed in this way and we discuss consequences for the interaction driven phase diagram, which features pronounced exotic superconducting and entangled spin-charge density waves.

cond-mat.str-el↗

arXiv2022

Unconventional Superconductivity in Magic-Angle Twisted Trilayer Graphene

Magic-angle twisted trilayer graphene (MATTG) recently emerged as a highly tunable platform for studying correlated phases of matter, such as correlated insulators and superconductivity. Superconductivity occurs in a range of doping levels that is bounded by van Hove singularities which stimulates the debate of the origin and nature of superconductivity in this material. In this work, we discuss the role of spin-fluctuations arising from atomic-scale correlations in MATTG for the superconducting state. We show that in a phase diagram as function of doping ($ν$) and temperature, nematic superconducting regions are surrounded by ferromagnetic states and that a superconducting dome with $T_c \approx 2\,\mathrm{K}$ appears between the integer fillings $ν=-2$ and $ν= -3$. Applying a perpendicular electric field enhances superconductivity on the electron-doped side which we relate to changes in the spin-fluctuation spectrum. We show that the nematic unconventional superconductivity leads to pronounced signatures in the local density of states detectable by scanning tunneling spectroscopy measurements.

cond-mat.supr-con↗

arXiv2021

Ultra-Strong Spin-Orbit Coupling and Topological Moiré Engineering in Twisted ZrS2 Bilayers

We predict that twisted bilayers of 1T-ZrS$_2$ realize a novel and tunable platform to engineer two-dimensional topological quantum phases dominated by strong spin-orbit interactions. At small twist angles, ZrS$_2$ heterostructures give rise to an emergent and twist-controlled moiré Kagomé lattice, combining geometric frustration and strong spin-orbit coupling to give rise to a moiré quantum spin Hall insulator with highly controllable and nearly-dispersionless bands. We devise a generic pseudo-spin theory for group-IV transition metal dichalcogenides that relies on the two-component character of the valence band maximum of the 1T structure at $Γ$, and study the emergence of a robust quantum anomalous Hall phase as well as possible fractional Chern insulating states from strong Coulomb repulsion at fractional fillings of the topological moiré Kagomé bands. Our results establish group-IV transition metal dichalcogenide bilayers as a novel moiré platform to realize strongly-correlated topological phases in a twist-tunable setting.

cond-mat.str-el↗

arXiv2021

TMDs as a platform for spin liquid physics: A strong coupling study of twisted bilayer WSe$_2$

The advent of twisted moiré heterostructures as a playground for strongly correlated electron physics has led to a plethora of experimental and theoretical efforts seeking to unravel the nature of the emergent superconducting and insulating states. Amongst these layered compositions of two dimensional materials, transition metal dichalcogenides (TMDs) are by now appreciated as highly-tunable platforms to simulate reinforced electronic interactions in the presence of low-energy bands with almost negligible bandwidth. Here, we focus on the twisted homobilayer WSe$_2$ and the insulating phase at half-filling of the flat bands reported therein. More specifically, we explore the possibility of realizing quantum spin liquid (QSL) physics on the basis of a strong coupling description, including up to second nearest neighbor Heisenberg couplings $J_1$ and $J_2$, as well as Dzyaloshinskii-Moriya (DM) interactions. Mapping out the global phase diagram as a function of an out-of-plane displacement field, we indeed find evidence for putative QSL states, albeit only close to SU$(2)$ symmetric points. In the presence of finite DM couplings and XXZ anisotropy, long-range order is predominantly present, with a mix of both commensurate and incommensurate magnetic phases.

cond-mat.str-el↗

arXiv2021

Engineering Three Dimensional Moiré Flat Bands

We demonstrate that the concept of moiré flat bands can be generalized to achieve electronic band engineering in all three spatial dimensions. For many two dimensional van der Waals materials, twisting two adjacent layers with respect to each other leads to flat electronic bands in the two corresponding spatial directions -- a notion sometimes referred to as twistronics as it enables a wealth of physical phenomena. Within this two dimensional plane, large moiré patterns of nanometer size form. The basic concept we propose here is to stack multiple twisted layers on top of each other in a predefined pattern. If the pattern is chosen such that with respect to the stacking direction of layers, the large spatial moiré features are spatially shifted from one twisted layer to the next, the system exhibits twist angle controlled flat bands in all of the three spatial directions. With this, our proposal extends the use of twistronic to three dimensions. We exemplify the general concept by considering graphitic systems, boron nitride and WSe$_2$ as candidate materials, but the approach is applicable to any two-dimensional van der Waals material. For hexagonal boron nitride we develope an ab initio fitted tight binding model that captures the corresponding three dimensional low-energy electronic structure. We outline that interesting three dimensional correlated phases of matter can be induced and controlled following this route, including quantum magnets and unconventional superconducting states.

cond-mat.mtrl-sci↗

arXiv2021

Transport in Stark Many Body Localized Systems

Using numerically exact methods we study transport in an interacting spin chain which for sufficiently strong spatially constant electric field is expected to experience Stark many-body localization. We show that starting from a generic initial state, a spin-excitation remains localized only up to a finite delocalization time, which depends exponentially on the size of the system and the strength of the electric field. This suggests that bona fide Stark many-body localization occurs only in the thermodynamic limit. We also demonstrate that the transient localization in a finite system and for electric fields stronger than the interaction strength can be well approximated by a Magnus expansion up-to times which grow with the electric field strength.

cond-mat.dis-nn↗

arXiv2021

$\mathcal{N}=4$ chiral superconductivity in moiré transition metal dichalcogenides

Experimental demonstrations of tunable correlation effects in magic-angle twisted bilayer graphene have put two-dimensional moiré quantum materials at the forefront of condensed-matter research. Other twisted few-layer graphitic structures, boron-nitride, and homo- or hetero-stacks of transition metal dichalcogenides (TMDs) have further enriched the opportunities for analysis and utilization of correlations in these systems. Recently, within the latter material class, strong spin-orbit coupling or excitonic physics were experimentally explored. The observation of a Mott insulating state and other fascinating collective phenomena such as generalized Wigner crystals, stripe phases and quantum anomalous Hall insulators confirmed the relevance of many-body interactions, and demonstrated the importance of their extended range. Since the interaction, its range, and the filling can be tuned experimentally by twist angle, substrate engineering and gating, we here explore Fermi surface instabilities and resulting phases of matter of hetero-bilayer TMDs. Using an unbiased renormalization group approach, we establish in particular that hetero-bilayer TMDs are unique platforms to realize topological superconductivity with winding number $|\mathcal{N}|=4$. We show that this state reflects in pronounced experimental signatures, such as distinct quantum Hall features.

cond-mat.str-el↗

arXiv2021

Flat bands, electron interactions and magnetic order in magic-angle mono-trilayer graphene

Starting with twisted bilayer graphene, graphene-based moiré materials have recently been established as a new platform for studying strong electron correlations. In this paper, we study twisted graphene monolayers on trilayer graphene and demonstrate that this system can host flat bands when the twist angle is close to the magic-angle of 1.16$^\circ$. When monolayer graphene is twisted on ABA trilayer graphene, the flat bands are not isolated, but are intersected by a Dirac cone with a large Fermi velocity. In contrast, graphene twisted on ABC trilayer graphene (denoted AtABC) exhibits a gap between flat and remote bands. Since ABC trilayer graphene and twisted bilayer graphene are known to host broken-symmetry phases, we further investigate the ostensibly similar magic angle AtABC system. We study the effect of electron-electron interactions in AtABC using both Hartree theory and an atomic Hubbard theory to calculate the magnetic phase diagram as a function of doping, twist angle, and perpendicular electric field. Our analysis reveals a rich variety of magnetic orderings, including ferromagnetism and ferrimagnetism, and demonstrates that a perpendicular electric field makes AtABC more susceptible to magnetic ordering.

cond-mat.mes-hall↗

arXiv2021

Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems

We study fractional boundary charges (FBCs) for two classes of strongly interacting systems. First, we study strongly interacting nanowires subjected to a periodic potential with a period that is a rational fraction of the Fermi wavelength. For sufficiently strong interactions, the periodic potential leads to the opening of a charge density wave gap at the Fermi level. The FBC then depends linearly on the phase offset of the potential with a quantized slope determined by the period. Furthermore, different possible values for the FBC at a fixed phase offset label different degenerate ground states of the system that cannot be connected adiabatically. Next, we turn to the fractional quantum Hall effect (FQHE) at odd filling factors $ν=1/(2l+1)$, where $l$ is an integer. For a Corbino disk threaded by an external flux, we find that the FBC depends linearly on the flux with a quantized slope that is determined by the filling factor. Again, the FBC has $2l+1$ different branches that cannot be connected adiabatically, reflecting the $(2l+1)$-fold degeneracy of the ground state. These results allow for several promising and strikingly simple ways to probe strongly interacting phases via boundary charge measurements.

cond-mat.mes-hall↗

arXiv2021

Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints

The boundary charge that accumulates at the edge of a one-dimensional single-channel insulator is known to possess the universal property, that its change under a lattice shift towards the edge by one site is given by the sum of the average bulk electronic density and a topologically invariant contribution, restricted to the values $0$ and $-1$ [Phys. Rev. B 101, 165304 (2020)]. This quantized contribution is associated with particle-hole duality, ensures charge conservation and fixes the mod(1) ambiguity appearing in the Modern Theory of Polarization. In the present work we generalize the above-mentioned single-channel results to the multichannel case by employing the technique of boundary Green's functions. We show that the topological invariant associated with the change in boundary charge under a lattice shift in multichannel models can be expressed as a winding number of a certain combination of components of bulk Green's functions as function of the complex frequency, as it encircles the section of the energy axis that corresponds to the occupied part of the spectrum. We observe that this winding number is restricted to values ranging from $-N_c$ to $0$, where $N_c$ is the number of channels (orbitals) per site. Furthermore, we consider translationally invariant one-dimensional multichannel models with an impurity and introduce topological indices which correspond to the quantized charge that accumulates around said impurity. These invariants are again given in terms of winding numbers of combinations of components of bulk Green's functions. Through this construction we provide a rigorous mathematical proof of the so called nearsightedness principle formulated by W. Kohn [Phys. Rev. Lett. 76, 3168 (1996)] for noninteracting multichannel lattice models.

cond-mat.mes-hall↗

arXiv2021

Universal properties of boundary and interface charges in continuum models of one-dimensional insulators

We study single-channel continuum models of one-dimensional insulators induced by periodic potential modulations which are either terminated by a hard wall (the boundary model) or feature a single region of dislocations and/or impurity potentials breaking translational invariance (the interface model). We investigate the universal properties of excess charges accumulated near the boundary and the interface, respectively. We find a rigorous analytic proof for the earlier observed linear dependence of the boundary charge on the phase of the periodic potential modulation as well as extend these results to the interface model. The linear dependence on the phase shows a universal value for the slope, and is intersected by discontinuous jumps by plus or minus one electron charge at the phase points where localized states enter or leave a band of extended states. Both contributions add up such that the periodicity of the excess charge in the phase over a $2π$-cycle is maintained. While in the boundary model this property is usually associated with the bulk-boundary correspondence, in the interface model a correspondence of scattering state and localized state contributions to the total interface charge is unveiled on the basis of the so-called nearsightedness principle.

cond-mat.mes-hall↗

arXiv2021

Nematicity Arising from a Chiral Superconducting Ground State in Magic-Angle Twisted Bilayer Graphene under In-Plane Magnetic Fields

Recent measurements of the resistivity in magic-angle twisted bilayer graphene near the superconducting transition temperature show two-fold anisotropy, or nematicity, when changing the direction of an in-plane magnetic field [Cao \textit{et al.}, Science \textbf{372}, 264 (2021)]. This was interpreted as strong evidence for exotic nematic superconductivity instead of the widely proposed chiral superconductivity. Counter-intuitively, we demonstrate that in two-dimensional chiral superconductors the in-plane magnetic field can hybridize the two chiral superconducting order parameters to induce a phase that shows nematicity in the transport response. Its paraconductivity is modulated as $\cos(2θ_{\bf B})$, with $θ_{\bf B}$ being the direction of the in-plane magnetic field, consistent with experiment in twisted bilayer graphene. We therefore suggest that the nematic response reported by Cao \textit{et al.} does not rule out a chiral superconducting ground state.

cond-mat.supr-con↗

arXiv2021

Magnetic ordering tendencies in hexagonal boron nitride-bilayer graphene moiré structures

When hexagonal boron nitride (hBN) and graphene are aligned at zero or small twist angle, a moiré structure is formed due to the small lattice constant mismatch between the two structures. In this work, we analyze magnetic ordering tendencies, driven by onsite Coulomb interactions, of encapsulated bilayer graphene (BG) forming a moiré structure with one (hBN-BG) or both hBN layers (hBN-BG-hBN), using the random phase approximation. The calculations are performed in a fully atomistic Hubbard model that takes into account all $π$-electrons of the carbon atoms in one moiré unit cell. We analyze the charge neutral case and find that the dominant magnetic ordering instability is uniformly antiferromagnetic. Furthermore, at low temperatures, the critical Hubbard interaction $U_c$ required to induce magnetic order is slightly larger in those systems where the moiré structure has caused a band gap opening in the non-interacting picture, although the difference is less than 6%. Mean-field calculations are employed to estimate how such an interaction-induced magnetic order may change the observable single-particle gap sizes.

cond-mat.str-el↗

arXiv2021

Universality of Abelian and non-Abelian Wannier functions in one dimension

Within a Dirac model in $1+1$ dimensions, a prototypical model to describe low-energy physics for a wide class of lattice models, we propose a field-theoretical version for the representation of Wannier functions, the Zak-Berry connection, and the geometric tensor. In two natural Abelian gauges we present universal scaling of the Dirac Wannier functions in terms of four fundamental scaling functions that depend only on the phase $γ$ of the gap parameter and the charge correlation length $ξ$ in an insulator. The two gauges allow for a universal low-energy formulation of the surface charge and surface fluctuation theorem, relating the boundary charge and its fluctuations to bulk properties. Our analysis describes the universal aspects of Wannier functions for the wide class of one-dimensional generalized Aubry-André-Harper lattice models. In the low-energy regime of small gaps we demonstrate universal scaling of all lattice Wannier functions and their moments in the corresponding Abelian gauges. We also discuss non-Abelian lattice gauges and find that lattice Wannier functions of maximal localization show universal scaling and are uniquely related to the Dirac Wannier function of the lower band. Our results present evidence that universal aspects of Wannier functions and of the boundary charge are uniquely related and can be elegantly described within universal low-energy theories.

cond-mat.mes-hall↗

arXiv2021

Electronic instabilities in Penrose quasi-crystals: competition, coexistence and collaboration of order

Quasicrystals lack translational symmetry, but can still exhibit long-ranged order, promoting them to candidates for unconventional physics beyond the paradigm of crystals. Here, we apply a real-space functional renormalization group approach to the prototypical quasicrystalline Penrose tiling Hubbard model treating} competing electronic instabilities in an unbiased, beyond-mean-field fashion. {\color{red} Our work reveals a delicate interplay between charge and spin degrees of freedom in quasicrystals}. Depending on the range of interactions and hopping amplitudes, we unveil a rich phase diagram including antiferromagnetic orderings, charge density waves and subleading, superconducting pairing tendencies. For certain parameter regimes we find a competition of phases, which is also common in crystals, but additionally encounter phases coexisting in a spatially separated fashion and ordering tendencies which mutually collaborate to enhance their strength. We therefore establish that quasicrystalline structures open up a route towards this rich ordering behavior uncommon to crystals and that an unbiased, beyond-mean-field approach is essential to describe this physics of quasicrystals correctly.

cond-mat.str-el↗

arXiv2021

Importance of long-ranged electron-electron interactions for the magnetic phase diagram of twisted bilayer graphene

Electron-electron interactions are intrinsically long ranged, but many models of strongly interacting electrons only take short-ranged interactions into account. Here, we present results of atomistic calculations including both long-ranged and short-ranged electron-electron interactions for the magnetic phase diagram of twisted bilayer graphene and demonstrate that qualitatively different results are obtained when long-ranged interactions are neglected. In particular, we use Hartree theory augmented with Hubbard interactions and calculate the interacting spin susceptibility at a range of doping levels and twist angles near the magic angle to identify the dominant magnetic instabilities. At the magic angle, mostly anti-ferromagnetic order is found, while ferromagnetism dominates at other twist angles. Moreover, long-ranged interactions significantly increase the twist angle window in which strong correlation phenomena can be expected. These findings are in good agreement with available experimental data.

cond-mat.str-el↗