arXiv subjects

B. Andrei Bernevig

Publications and source records attributed to B. Andrei Bernevig.

At least 73 records · Page 4Linked to original sources

arXiv2024

Emergent Symmetry and Valley Chern Insulator in Twisted Double-Bilayer Graphene

Theoretical calculations show that twisted double bilayer graphene (TDBG) under a transverse electric field develops a valley Chern number 2 at charge neutrality. Using thermodynamic and thermal activation measurements we report the experimental observation of a universal closing of the charge neutrality gap in the Hofstadter spectrum of TDBG at 1/2 magnetic flux per unit cell, in agreement with theoretical predictions for a valley Chern number 2 gap. Our theoretical analysis of the experimental data shows that the interaction energy, while larger than the flat-band bandwidth in TDBG near 1°does not alter the emergent valley symmetry or the single-particle band topology.

cond-mat.mes-hall↗

arXiv2024

A New Moiré Platform Based on M-Point Twisting

We introduce a new class of moiré systems and materials based on monolayers with triangular lattices and low-energy states at the M points of the Brillouin zone. These M-point moiré materials are fundamentally distinct from those derived from $Γ$- or K-point monolayers, featuring three time-reversal-preserving valleys related by three-fold rotational symmetry. We propose twisted bilayers of experimentally exfoliable 1T-SnSe$_2$ and 1T-ZrS$_2$ as realizations of this new class. Using extensive ab initio simulations, we develop quantitative continuum models and analytically show that the corresponding M-point moiré Hamiltonians exhibit emergent momentum-space non-symmorphic symmetries and a kagome plane-wave lattice in momentum space. This represents the first experimentally viable realization of a projective representation of crystalline space groups in a non-magnetic system. With interactions, these materials represent six-flavor Hubbard simulators with Mott physics, as can be seen by their flat Wilson loops. Furthermore, the presence of a non-symmorphic momentum-space in-plane mirror symmetry makes some of the M-point moiré Hamiltonians quasi-one-dimensional in each valley, suggesting the possibility of realizing Luttinger liquid physics. We predict the twist angles at which a series of (conduction) flat bands appear, provide a faithful continuum Hamiltonian, analyze its topology and charge density and briefly discuss several aspects of the physics of this new platform.

cond-mat.str-el↗

arXiv2024

Competing phases in kagome magnet FeGe from functional renormalization

The discovery of a charge density wave in FeGe extends the discussion of the nature of charge order in kagome metals to a magnetic compound. Motivated by this observation, we combine density functional theory (DFT) and functional-renormalization-group calculations to study interaction-induced Fermi-surface instabilities of the magnetic state of FeGe. We argue that the leading intra-band contribution to electronic correlations are approximately 2D and come from Van Hove points at the projected $M$~points. By varying parameters around DFT values, we determine a phase diagram for the quasi-2D scenario as function of on-site and nearest-neighbor interactions. We discuss universal aspects in the electronic mechanisms for the resulting phases, as well as the role of SU(2) symmetry breaking. We find FeGe to be in a regime of strong competition between $p$-wave charge density wave, $f$-wave pairing, and $d$-wave spin Pomeranchuk instabilities. This interplay can be influenced in favor of superconducting pairing for slightly increased nearest-neighbor interaction, suggesting a potential to induce superconductivity in FeGe.

cond-mat.str-el↗

arXiv2024

Universal Moiré-Model-Building Method without Fitting: Application to Twisted MoTe$_2$ and WSe$_2$

We develop a comprehensive method to construct analytical continuum models for moiré systems directly from first-principle calculations without any parameter fitting. The core idea of this method is to interpret the terms in the continuum model as a basis, allowing us to determine model parameters as coefficients of this basis through Gram-Schmidt orthogonalization. We apply our method to twisted MoTe$_2$ and WSe$_2$ with twist angles ranging from 2.13$^\circ$ to 3.89$^\circ$, producing continuum models that exhibit excellent agreement with both energy bands and wavefunctions obtained from first-principles calculations. We further propose a strategy to integrate out the higher-energy degrees of freedom to reduce the number of the parameters in the model without sacrificing the accuracy for low-energy bands. Our findings reveal that decreasing twist angles typically need an increasing number of harmonics in the moiré potentials to accurately replicate first-principles results. We provide parameter values for all derived continuum models, facilitating further robust many-body calculations. Our approach is general and applicable to any commensurate moiré materials accessible by first-principles calculations.

cond-mat.mes-hall↗

arXiv2024

"Quantum Geometric Nesting" and Solvable Model Flat-Band Systems

We introduce the concept of "quantum geometric nesting'' (QGN) to characterize the idealized ordering tendencies of certain flat-band systems implicit in the geometric structure of the flat-band subspace. Perfect QGN implies the existence of an infinite class of local interactions that can be explicitly constructed and give rise to solvable ground states with various forms of possible fermion bi-linear order, including flavor ferromagnetism, density waves, and superconductivity. For the ideal Hamiltonians constructed in this way, we show that certain aspects of the low-energy spectrum can also be exactly computed including, in the superconducting case, the phase stiffness. Examples of perfect QGN include flat bands with certain symmetries (e.g. chiral or time-reversal), and non-symmetry-related cases exemplified with an engineered model for pair-density-wave. Extending this approach, we obtain exact superconducting ground states with nontrivial pairing symmetry.

cond-mat.str-el↗

arXiv2024

Semi-Dirac Fermions in a Topological Metal

Topological semimetals with massless Dirac and Weyl fermions represent the forefront of quantum materials research. In two dimensions (2D), a peculiar class of fermions that are massless in one direction and massive in the perpendicular direction was predicted sixteen years ago. These highly exotic quasiparticles - the semi-Dirac fermions - ignited intense theoretical and experimental interest but remain undetected. Using magneto-optical spectroscopy, we demonstrate the defining feature of semi-Dirac fermions - $B^{2/3}$ scaling of Landau levels - in a prototypical nodal-line metal ZrSiS. In topological metals, including ZrSiS, nodal-lines extend the band degeneracies from isolated points to lines, loops or even chains in the momentum space. With $\textit{ab initio}$ calculations and theoretical modeling, we pinpoint the observed semi-Dirac spectrum to the crossing points of nodal-lines in ZrSiS. Crossing nodal-lines exhibit a continuum absorption spectrum but with singularities that scale as $B^{2/3}$ at the crossing. Our work sheds light on the hidden quasiparticles emerging from the intricate topology of crossing nodal-lines and highlights the potential to explore quantum geometry with linear optical responses.

cond-mat.mtrl-sci↗

arXiv2024

Topological Heavy Fermion Principle For Flat (Narrow) Bands With Concentrated Quantum Geometry

We propose a general principle for the low-energy theory of narrow bands with concentrated Berry curvature and Fubini-Study metric in the form of a map to Anderson-"+" models composed of heavy fermions hybridizing and interacting with semi-metallic modes. This map resolves the obstruction preventing topological bands from being realized in a local Hamiltonian acting on the low-energy degrees of freedom. The concentrated quantum geometry is reproduced through band inversion with a dispersive semi-metal, leaving a nearly flat, trivial band which becomes the heavy fermion. This representation is natural when the narrow band is not energetically isolated on the scale of the interaction and an enlarged Hilbert space is inescapable, but also provides analytical insight into the projected-interaction limit. First exemplified in twisted bilayer graphene (TBG), we extend it to (1) the twisted checkerboard, which we find has a chiral symmetric stable anomaly that forbids a lattice realization at all energies, and (2) the Lieb lattice with gapless flat bands, where we show the heavy fermions can be obtained by minimizing a Euclidean instanton action to saturate its BPS bound. The heavy fermion approach is widely applicable and physically transparent: heavy electrons carry the strong correlations and dispersive electrons carry the topology. This simple picture unifies the dichotomous phenomena observed in TBG and points to connections between moiré and stoichiometric materials.

cond-mat.str-el↗

arXiv2024

Catalogue of Phonon Instabilities in Symmetry Group 191 Kagome MT$_6$Z$_6$ Materials

Kagome materials manifest rich physical properties due to the emergence of abundant electronic phases. Here, we carry out a high-throughput first-principles study of the kagome 1:6:6 family MT$_6$Z$_6$ materials in space group 191, focusing on their phonon instability and electronic flat bands. Different MT$_6$Z$_6$ kagome candidates reveal a remarkable variety of kagome flat bands ranging from unfilled, partially filled, to fully filled. Notably, the Mn/Fe-166 compounds exhibit partially filled flat bands with a pronounced sharp peak in the density of states near the Fermi level, leading to magnetic orders that polarize the bands and stabilize the otherwise unstable phonon. When the flat bands are located away from the Fermi level, we find a large number of phonon instabilities, which can be classified into three types, based on the phonon dispersion and vibrational modes. Type-I instabilities involve the in-plane distortion of kagome nets, while type-II and type-III present out-of-plane distortion of trigonal M and Z atoms. We take MgNi$_6$Ge$_6$ and HfNi$_6$In$_6$ as examples to illustrate the possible CDW structures derived from the emergent type-I and type-II instabilities. The type-I instability in MgNi$_6$Ge$_6$ suggests a nematic phase transition, governed by the local twisting of kagome nets. The type-II instability in HfNi$_6$In$_6$ may result in a hexagonal-to-orthorhombic transition, offering insight into the formation of MT$_6$Z$_6$ in other space groups. Additionally, the predicted ScNb$_6$Sn$_6$ is analyzed as an example of the type-III instability. Our predictions suggest a vast kagome family with rich properties induced by the flat bands, possible CDW transitions, and their interplay with magnetism.

cond-mat.mtrl-sci↗

arXiv2024

Nodal Nematic Superconductivity in Multiple-Flat-Band Land

In this work, we propose a mechanism of inducing stable nodal superconductivity for multiple-flat-band systems. This mechanism is based on the degenerate flat band nature, so that not only intra-eigen-band pairing, but also inter-eigen-band pairing has a significant influence on the superconductivity properties. Based on the Bogoliubov de Gennes formalism of the heavy fermion model for the twisted bilayer graphene as an example, we show that although the nodal nematic d-wave pairing has higher energy around the nodal points compared to the chiral d-wave pairing in the momentum space, the inter-eigen-band pairing can lower the energy in other momenta away from the nodes, so that the nematic d-wave pairing is energetically favored for its overall condensation energy. This type of mechanism is particular to multiple-flat-band systems with no Fermi surfaces.

cond-mat.supr-con↗

arXiv2024

New magnetic topological materials from high-throughput search

We conducted a high-throughput search for topological magnetic materials on 522 new, experimentally reported commensurate magnetic structures from MAGNDATA, doubling the number of available materials on the Topological Magnetic Materials database. This brings up to date the previous studies which had become incomplete due to the discovery of new materials. For each material, we performed first-principle electronic calculations and diagnosed the topology as a function of the Hubbard U parameter. Our high-throughput calculation led us to the prediction of 250 experimentally relevant topologically non-trivial materials, which represent 47.89% of the newly analyzed materials. We present five remarkable examples of these materials, each showcasing a different topological phase: Mn${}_2$AlB${}_2$ (BCSID 1.508), which exhibits a nodal line semimetal to topological insulator transition as a function of SOC, CaMnSi (BCSID 0.599), a narrow gap axion insulator, UAsS (BCSID 0.594) a 5f-orbital Weyl semimetal, CsMnF${}_4$ (BCSID 0.327), a material presenting a new type of quasi-symmetry protected closed nodal surface and FeCr${}_2$S${}_4$ (BCSID 0.613), a symmetry-enforced semimetal with double Weyls and spin-polarised surface states.

cond-mat.mtrl-sci↗

arXiv2024

Dynamical correlations and order in magic-angle twisted bilayer graphene

In magic angle twisted bilayer graphene, transport, thermodynamic and spectroscopic experiments pinpoint at a competition between distinct low-energy states with and without electronic order. We use Dynamical Mean Field Theory (DMFT) on the topological heavy Fermion (THF) model of twisted bilayer graphene to investigate the emergence of electronic correlations and long-range order in the absence of strain. We contrast moment formation, Kondo screening and ordering on a temperature basis and explain the nature of emergent correlated states based on three central phenomena: (i) the formation of local spin and valley isospin moments around 100K, (ii) the ordering of the local isospin moments around 10K preempting Kondo screening, and (iii) a cascadic redistribution of charge between localized and delocalized electronic states upon doping. At integer fillings, we find that low energy spectral weight is depleted in the symmetric phase, while we find insulating states with gaps enhanced by exchange coupling in the zero-strain ordered phases. Doping away from integer filling results in distinct metallic states: a "bad metal" above the ordering temperature, where scattering off the disordered local moments suppresses electronic coherence, and a "good metal" in the ordered states with coherence of quasiparticles facilitated by isospin order. This finding reveals coherence from order as the microscopic mechanism behind the Pomeranchuk effect observed experimentally. Upon doping, there is a periodic charge reshuffling between localized and delocalized electronic orbitals leading to cascades of doping-induced Lifshitz transitions, local spectral weight redistributions and periodic variations of the electronic compressibility. Our findings provide a unified understanding of the most puzzling aspects of scanning tunneling spectroscopy, transport, and compressibility experiments.

cond-mat.str-el↗

arXiv2024

Frustrated charge density wave and quasi-long-range bond-orientational order in the magnetic kagome FeGe

The intrinsic frustrated nature of a kagome lattice is amenable to the realization of exotic phases of matter, such as quantum spin liquids or spin ices, and more recently the multiple-$\mathrm{\textbf{q}}$ charge density waves (CDW) in the kagome metals. Despite intense efforts to understand the mechanism driving the electronic modulations, its origin is still unknown and hindered by competing interactions and intertwined orders. Here, we identify a dimerization-driven 2D hexagonal charge-diffuse precursor in the antiferromagnetic kagome metal FeGe and demonstrate that the fraction of dimerized/undimerized states is the relevant order parameter of the multiple-$\mathrm{\textbf{q}}$ CDW of a continuous phase transition. The pretransitional charge fluctuations with propagation vector $\mathrm{\textbf{q}=\textbf{q}_M}$ at T$_{\mathrm{CDW}}$$<$T$<$T$^*$(125 K) are anisotropic, hence holding a quasi-long-range bond-orientational order. The broken translational symmetry emerges from the anisotropic diffuse precursor, akin to the Ising scenario of antiferromagnetic triangular lattices. The temperature and momentum dependence of the critical scattering show parallels to the stacked hexatic $\mathrm{B}$-phases reported in liquid crystals and transient states of CDWs and highlight the key role of the topological defect-mediated melting of the CDW in FeGe.

cond-mat.str-el↗

arXiv2024

Strongly interacting Hofstadter states in magic-angle twisted bilayer graphene

Magic-angle twisted bilayer graphene (MATBG) hosts a multitude of strongly correlated states at partial fillings of its flat bands. In a magnetic field, these flat bands further evolve into a unique Hofstadter spectrum renormalized by strong Coulomb interactions. Here, we study the interacting Hofstadter states spontaneously formed within the topological magnetic subbands of an ultraclean MATBG device, notably including symmetry-broken Chern insulator (SBCI) states and fractional quantum Hall (FQH) states. The observed SBCI states form a cascade with their Chern numbers mimicking the main sequence correlated Chern insulators. The FQH states in MATBG form in Jain sequence; however, they disappear at high magnetic field, distinct from conventional FQH states which strengthen with increasing magnetic field. We reveal a unique magnetic field-driven phase transition from composite fermion phases to a dissipative Fermi liquid. Our theoretical analysis of the magnetic subbands hosting FQH states predicts non uniform quantum geometric properties far from the lowest Landau level. This points towards a more natural interpretation of these FQH states as in-field fractional Chern insulators of the magnetic subbands.

cond-mat.mes-hall↗

arXiv2024

Majorana corner modes in unconventional monolayers of the 1T-PtSe2 family

In this work, we propose that Majorana zero modes can be realized at the corners of the two-dimensional unconventional insulator. We demonstrate that 1T-PtSe2 is a symmetry indicator-free (SI-free) unconventional insulator, originating from orbital hybridization between Pt $d$ and Se $p_{x,y}$ states. The kind of SI-free unconventionality has no symmetry eigenvalue indication. Instead, it is diagnosed directly by the Wannier charge centers by using the one-dimensional Wilson loop method. The obstructed edge states exhibit strong anisotropy and large Rashba splitting. By introducing superconducting proximity and an external magnetic field, the Majorana corner modes can be obtained in the 1T-PtSe2 monolayer. In the end, we construct a two-Bernevig-Hughes-Zhang model with anisotropy to capture the Majorana physics.

cond-mat.mtrl-sci↗

arXiv2024

Moiré Fractional Chern Insulators IV: Fluctuation-Driven Collapse of FCIs in Multi-Band Exact Diagonalization Calculations on Rhombohedral Graphene

The fractional Chern insulators (FCIs) observed in pentalayer rhombohedral graphene/hexagonal boron nitride superlattices have a unique origin contrary to theoretical expectations: their non-interacting band structure is gapless, unlike standard FCIs and the Landau level. Hartree-Fock (HF) calculations at filling $ν=1$ yield a gapped ground state with Chern number 1 through band mixing, identifying a possible parent state. However, many-body calculations restricted to the occupied HF band predispose the system towards FCIs and are essentially uncontrolled. In this work, we use unbiased multi-band exact diagonalization (ED) to allow fluctuations into the gapless bands for two normal-ordering schemes. In the "charge neutrality" scheme, the weak moiré potential leads to theoretical proposals based on Wigner crystal-like states. However, we find that FCIs seen in 1-band ED calculations are destroyed by band mixing, becoming gapless as fluctuations are included. In the "average" scheme, the Coulomb interaction with the periodic valence charge background sets up a stronger moiré potential. On small systems, FCIs at $ν=1/3$ are destroyed in multi-band calculations, while those at $ν=2/3$ are initially strengthened. However we do not converge to a stable FCI at $ν=2/3$ even on the largest accessible systems. These findings question prior results obtained within projection to a single HF band. They suggest that current models do not support FCIs with correlation length small enough to be converged in accessible, unbiased ED calculations, or do not support FCIs at all.

cond-mat.str-el↗

arXiv2024

When Could Abelian Fractional Topological Insulators Exist in Twisted MoTe$_2$ (and Other Systems)

Using comprehensive exact diagonalization calculations on $θ\approx 3.7 ^{\circ}$ twisted bilayer MoTe$_2$ ($t$MoTe$_2$), as well as idealized Landau level models also relevant for lower $θ$, we extract general principles for engineering fractional topological insulators (FTIs) in realistic situations. First, in a Landau level setup at $ν=1/3+1/3$, we investigate what features of the interaction destroy an FTI. For both pseudopotential interactions and realistic screened Coulomb interactions, we find that sufficient suppression of the short-range repulsion is needed for stabilizing an FTI. We then study $θ\approx 3.7 ^{\circ}$ $t$MoTe$_2$ with realistic band-mixing and anisotropic non-local dielectric screening. Our finite-size calculations only find an FTI phase at $ν=-4/3$ in the presence of a significant additional short-range attraction $g$ that acts to counter the Coulomb repulsion at short distances. We discuss how further finite-size drifts, dielectric engineering, Landau level character, and band-mixing effects may reduce the required value of $g$ closer towards the experimentally relevant conditions of $t$MoTe$_2$. Projective calculations into the $n=1$ Landau level, which resembles the second valence band of $θ\simeq 2.1^\circ$ $t$MoTe$_2$, do not yield FTIs for any $g$, suggesting that FTIs at low-angle $t$MoTe$_2$ for $ν=-8/3$ and $-10/3$ may be unlikely. While our study highlights the challenges, at least for the fillings considered, to obtaining an FTI with transport plateaus, even in large-angle $t$MoTe$_2$ where fractional Chern insulators are experimentally established, we also provide potential sample-engineering routes to improve the stability of FTI phases.

cond-mat.str-el↗

arXiv2024

Topological heavy fermions in magnetic field

The recently introduced topological heavy fermion model (THFM) provides a means for interpreting the low-energy electronic degrees of freedom of the magic angle twisted bilayer graphene as hybridization amidst highly dispersing topological conduction and weakly dispersing localized heavy fermions. In order to understand the Landau quantization of the ensuing electronic spectrum, a generalization of THFM to include the magnetic field B is desired, but currently missing. Here we provide a systematic derivation of the THFM in B and solve the resulting model to obtain the interacting Hofstadter spectra for single particle charged excitations. While naive minimal substitution within THFM fails to correctly account for the total number of magnetic subbands within the narrow band i.e. its total Chern number, our method -- based on projecting the light and heavy fermions onto the irreducible representations of the magnetic translation group -- reproduces the correct total Chern number. Analytical results presented here offer an intuitive understanding of the nature of the (strongly interacting) Hofstadter bands.

cond-mat.str-el↗

arXiv2024

Nontrivial Quantum Geometry and the Strength of Electron-Phonon Coupling

The coupling of electrons to phonons (electron-phonon coupling) is crucial for the existence of various phases of matter, in particular superconductivity and density waves. Here, we devise a theory that incorporates the quantum geometry of the electron bands into the electron-phonon coupling, demonstrating the crucial contributions of the Fubini-Study metric or its orbital selective version to the dimensionless electron-phonon coupling constant. We apply the theory to two materials, graphene and MgB$_2$ where the geometric contributions account for approximately 50\% and 90\% of the total electron-phonon coupling constant, respectively. The quantum geometric contributions in the two systems are further bounded from below by topological contributions. Our results suggest that the nontrivial electron band geometry/topology might favor superconductivity with relatively high critical temperature.

cond-mat.supr-con↗