arXiv subjects

Laura Classen

Publications and source records attributed to Laura Classen.

At least 37 records · Page 2Linked to original sources

arXiv2022

Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials

A simple yet paradigmatic model for the interplay of strong electronic correlations and geometric frustration is the triangular lattice Hubbard model. Recently it was proposed that moiré structures of transition metal dichalcogenides can be used to simulate extended versions that include non-local density-density interactions. We study competing instabilities of interacting electrons in such an extended Hubbard model on the triangular lattice near a filling where the density of states has a Van Hove singularity. We employ a truncated-unity functional renormalization group approach to investigate two cases: a paradigmatic minimally extended Hubbard model and a specific model with parameters that are applicable to hetero-bilayers of transition metal dichalcogenides. We unravel rich phase diagrams, including tendencies to spin-density-wave order and unconventional pairing, which can give rise to topological superconductivity. We classify the symmetry of the superconducting instabilities according to their irreducible representations and show that higher lattice harmonics are dominant when the nearest-neighbor interaction is sizable indicating pair formation between second-nearest neighbors. The phenomenological consequences can be enhanced spin and thermal quantum Hall responses in a topological superconductor.

cond-mat.str-el↗

arXiv2021

Interaction-induced velocity renormalization in magic angle twisted trilayer graphene

Twistronics heterostructures provide a novel route to control the electronic single particle velocity and thereby to engineer strong effective interactions. Here we show that the reverse may also hold, i.e. that these interactions strongly renormalize the band structure. We demonstrate this mechanism for mirror-symmetric magic angle twisted trilayer graphene at charge neutrality and in the vicinity of a phase transition which can be described by an Ising Gross-Neveu critical point corresponding, e.g., to the onset of valley Hall or Hall order. While the non-interacting model displays massless Dirac excitations with strongly different velocities, we show that interaction corrections make them equal in the infrared. However, the RG flow of the velocities and of the coupling to the critical bosonic mode is strongly non-monotonic and dominated by the vicinity of a repulsive fixed point. We predict experimental consequences of this theory for tunneling and transport experiments and discuss the expected behavior at other quantum critical points, including those corresponding to intervalley coherent ordering.

cond-mat.mes-hall↗

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

SU(4) symmetry in twisted bilayer graphene - an itinerant perspective

We study symmetry-broken phases in twisted bilayer graphene at small filling above charge neutrality and at Van Hove filling. We argue that the Landau functionals for the particle-hole order parameters at these fillings both have an approximate SU(4) symmetry, but differ in the sign of quartic terms. We determine the order parameter manifold of the ground state and analyze its excitations. For small fillings, we find a strong 1st-order transition to an SU(3)$\otimes$U(1) manifold of orders that break spin-valley symmetry and induce a 3-1 splitting of fermionic excitations. For Van Hove filling, we find a weak 1st-order transition to an SO(4)$\otimes$U(1) manifold of orders that preserves the two-fold band degeneracy. We discuss the effect of particle-hole orders on superconductivity and compare with strong-coupling approaches.

cond-mat.str-el↗

arXiv2021

Superconductivity of incoherent electrons in Yukawa-SYK model

We study a model of $N$ fermions in a quantum dot, coupled to $M$ bosons by a disorder-induced complex Yukawa coupling (Yukawa-SYK model), in order to explore the interplay between non-Fermi liquid and superconductivity in a strongly coupled, (quantum-)critical environment. We analyze the phase diagram of the model for an arbitrary complex interaction and arbitrary ratio of $N/M$, with special focus on the two regimes of non-Fermi-liquid behavior: an SYK-like behavior with a power-law frequency dependence of the fermionic self-energy and an impurity-like behavior with frequency independent self-energy. We show that the crossover between the two. can be reached by varying either the strength of the fermion-boson coupling or the ratio $M/N$. We next argue that in both regimes the system is unstable to superconductivity if the strength of time-reversal-symmetry-breaking disorder is below a certain threshold. We show how the corresponding onset temperatures vary between the two regimes. We argue that the superconducting state is highly unconventional with an infinite set of minima of the condensation energy at $T=0$, corresponding to topologically different gap functions. We discuss in detail similarities and differences between this model and the model of dispersion-full fermions tuned to a metallic quantum-critical point, with an effective singular dynamical interaction $V(Ω) \propto 1/|Ω|^γ$ (the $γ-$model).

cond-mat.str-el↗

arXiv2020

Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene

We analyze density-wave and Pomeranchuk orders in twisted bilayer graphene. This compliments our earlier analysis of the pairing instabilities. We assume that near half-filling of either conduction or valence band, the Fermi level is close to Van Hove points, where the density of states diverges, and study potential instabilities in the particle-hole channel within a patch model with two valley degrees of freedom. The hexagonal symmetry of twisted bilayer graphene allows for either six or twelve Van Hove points. We consider both cases and find the same two leading candidates for particle-hole order. One is an SU(2)-breaking spin state with ferromagnetism within a valley. A subleading inter-valley hopping induces antiferromagnetism between the valleys. The same state has also been obtained in strong coupling approaches, indicating that this order is robust. The other is a mixed state with $120^\circ$ complex spin order and orthogonal complex charge order. In addition, we find a weaker, but still attractive interaction in nematic channels, and discuss the type of a nematic order.

cond-mat.str-el↗

arXiv2020

Nematic superconductivity in twisted bilayer graphene

Twisted bilayer graphene displays insulating and superconducting phases caused by exceptional flattening of its lowest energy bands. Superconductivity with highest $T_c$ appears at hole and electron dopings, near half-filling for valence or conduction bands. In the hole-doped case, the data show that three-fold lattice rotation symmetry is broken in the superconducting phase, i.e., a superconductor is also a nematic. We present the mechanism for nematic superconductivity. We take as an input the fact that at relevant dopings the Fermi energy lies in the vicinity of twist-induced Van Hove singularities in the density of states and argue that the low-energy physics can be properly described by patch models with six Van Hove points for electron doping and twelve Van Hove points for hole doping. We obtain pairing interactions for the patch models in terms of parameters of the microscopic model for the flat bands, which contains both local and twist-induced non-local interactions and show that the latter gives rise to attraction in different superconducting channels. For hole-doping, we find two attractive channels, $g$ and $i$-waves, with almost equal coupling constants. We show that in the co-existence state, where both order parameters are non-zero, the three-fold lattice rotation symmetry is broken, i.e., a superconductor is also a nematic. We find two possible nematic states, one is time-reversal symmetric, the other additionally breaks time-reversal symmetry. Our scenario for nematic superconductivity is based on generic symmetry considerations, and we expect it to be applicable also to other systems with two (or more) attractive channels with similar couplings.

cond-mat.supr-con↗

arXiv2020

Competing orders at higher-order Van Hove points

Van Hove points are special points in the energy dispersion, where the density of states exhibits analytic singularities. When a Van Hove point is close to the Fermi level, tendencies towards density wave orders, Pomeranchuk orders, and superconductivity can all be enhanced, often in more than one channel, leading to a competition between different orders and unconventional ground states. Here we consider the effects from higher-order Van Hove points, around which the dispersion is flatter than near a conventional Van Hove point, and the density of states has a power-law divergence. We argue that such points are present in intercalated graphene and other materials. We use an effective low-energy model for electrons near higher-order Van Hove points and analyze the competition between different ordering tendencies using an unbiased renormalization group approach. For purely repulsive interactions, we find that two key competitors are ferromagnetism and chiral superconductivity. For a small attractive exchange interaction, we find a new type of spin Pomeranchuk order, in which the spin order parameter winds around the Fermi surface. The supermetal state, predicted for a single higher-order Van Hove point, is an unstable fixed point in our case.

cond-mat.str-el↗

arXiv2019

Competing phases of interacting electrons on triangular lattices in moiré heterostructures

We study the quantum many-body instabilities of interacting electrons with SU(2)$\times$SU(2) symmetry in spin and orbital degrees of freedom on the triangular lattice near van-Hove filling. Our work is motivated by effective models for the flat bands in hexagonal moiré heterostructures like twisted bilayer boron nitride and trilayer graphene-boron nitride systems. We consider an extended Hubbard model including onsite Hubbard and Hund's couplings, as well as nearest-neighbor exchange interactions and analyze the different ordering tendencies with the help of an unbiased functional renormalization group approach. We find three classes of instabilities controlled by the filling and bare interactions. For a nested Fermi surface at van-Hove filling, Hund-like couplings induce a weak instability towards spin or orbital density wave phases. An SU(4) exchange interaction moves the system towards a Chern insulator, which is robust with respect to perturbations from Hund-like interactions or deviations from perfect nesting. Further, in an extended range of fillings and interactions, we find topological $d\pm id$ and (spin-singlet)-(orbital-singlet) $f$-wave superconductivity.

cond-mat.str-el↗

arXiv2019

Ladder-like optical conductivity in the spin-fermion model

In the nested limit of the spin-fermion model for the cuprates, one-dimensional physics in the form of half-filled two-leg ladders emerges. We show that the renormalization group flow of the corresponding ladder is towards the d-Mott phase, a gapped spin-liquid with short-ranged d-wave pairing correlations, and reveals an intermediate SO(5)$\times$SO(3) symmetry. We use the results of the renormalization group in combination with a memory-function approach to calculate the optical conductivity of the spin-fermion model in the high-frequency regime, where processes within the hot spot region dominate the transport. We argue that umklapp processes play a major role. For finite temperatures, we determine the resistivity in the zero-frequency (dc) limit. Our results show an approximate linear temperature dependence of the resistivity and a conductivity that follows a non-universal power law. A comparison to experimental data supports our assumption that the conductivity is dominated by the antinodal contribution above the pseudogap.

cond-mat.str-el↗

arXiv2018

Orbital order in FeSe - the case for vertex renormalization

We study the structure of the d-wave orbital order in FeSe in light of recent STM and ARPES data, which detect the shapes of hole and electron pockets in the nematic phase. The geometry of the pockets indicates that the sign of the orbital order $Γ= \langle d^{\dagger}_{xz} d_{xz}- d^{\dagger}_{yz} d_{yz}\rangle$ is different between hole and electron pockets $(Γ_h$ and $Γ_e$). We argue that this sign change cannot be reproduced if one solves for the orbital order within mean-field approximation, as the mean-field analysis yields either no orbital order, or order with the same sign of $Γ_e$ and $Γ_h$. We argue that another solution with the opposite signs of $Γ_e$ and $Γ_h$ emerges if we include the renormalizations of the vertices in $d-$wave orbital channel. We show that the ratio $|Γ_e/Γ_h|$ is of order one, independent on the strength of the interaction. We also compute the temperature variation of the energy of $d_{xz}$ and $d_{yz}$ orbitals at the center of electron pockets and compare the results with ARPES data.

cond-mat.str-el↗

arXiv2018

3D non-Fermi liquid behavior from 1D quantum critical local moments

We study the temperature dependence of the electrical resistivity in a system composed of critical spin chains interacting with three dimensional conduction electrons and driven to criticality via an external magnetic field. The relevant experimental system is Yb$_2$Pt$_2$Pb, a metal where itinerant electrons coexist with localized moments of Yb-ions which can be described in terms of effective S = 1/2 spins with dominantly one-dimensional exchange interaction. The spin subsystem becomes critical in a relatively weak magnetic field, where it behaves like a Luttinger liquid. We theoretically examine a Kondo lattice with different effective space dimensionalities of the two interacting subsystems. We characterize the corresponding non-Fermi liquid behavior due to the spin criticality by calculating the electronic relaxation rate and the dc resistivity and establish its quasi linear temperature dependence.

cond-mat.str-el↗

arXiv2018

Fermion-induced quantum criticality with two length scales in Dirac systems

The quantum phase transition to a $\mathbb{Z}_3$-ordered Kekulé valence bond solid in two-dimensional Dirac semimetals is governed by a fermion-induced quantum critical point, which renders the putatively discontinuous transition continuous. We study the resulting universal critical behavior in terms of a functional RG approach, which gives access to the scaling behavior on the symmetry-broken side of the phase transition, for general dimension and number of Dirac fermions. In particular, we investigate the emergence of the fermion-induced quantum critical point for space-time dimensions $2<d<4$. We determine the integrated RG flow from the Dirac semi-metal to the symmetry-broken regime and analyze the underlying fixed point structure. We show that the fermion-induced criticality leads to a scaling form with two divergent length scales, due to the breaking of the discrete $\mathbb{Z}_3$ symmetry. This provides another source of scaling corrections, besides the one stemming from being in the proximity to the first order transition.

cond-mat.str-el↗

arXiv2017

Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents

We establish a scenario where fluctuations of new degrees of freedom at a quantum phase transition change the nature of a transition beyond the standard Landau-Ginzburg paradigm. To this end we study the quantum phase transition of gapless Dirac fermions coupled to a $\mathbb{Z}_3$ symmetric order parameter within a Gross-Neveu-Yukawa model in 2+1 dimensions, appropriate for the Kekulé transition in honeycomb lattice materials. For this model the standard Landau-Ginzburg approach suggests a first order transition due to the symmetry-allowed cubic terms in the action. At zero temperature, however, quantum fluctuations of the massless Dirac fermions have to be included. We show that they reduce the putative first-order character of the transition and can even render it continuous, depending on the number of Dirac fermions $N_f$. A non-perturbative functional renormalization group approach is employed to investigate the phase transition for a wide range of fermion numbers. For the first time we obtain the critical $N_f$, where the nature of the transition changes. Furthermore, it is shown that for large $N_f$ the change from the first to second order of the transition as a function of dimension occurs exactly in the physical 2+1 dimensions. We compute the critical exponents and predict sizable corrections to scaling for $N_f =2$.

cond-mat.str-el↗

arXiv2016

Interplay between magnetism, superconductivity, and orbital order in a 5-pocket model for iron-based superconductors - a parquet renormalization group study

We report the results of the parquet renormalization group (RG) analysis of the phase diagram of the most general 5-pocket model for Fe-based superconductors. We use as an input the orbital structure of excitations near the five pockets made out of $d_{xz}$, $d_{yz}$, and $d_{xy}$ orbitals and argue that there are 40 different interactions between low-energy fermions in the orbital basis. All interactions flow under RG, as one progressively integrates out fermions with higher energies. We find that the low-energy behavior is amazingly simple, despite the large number of interactions. Namely, at low-energies the full 5-pocket model effectively reduces either to a 3-pocket model made of one $d_{xy}$ hole pocket and two electron pockets, or a 4-pocket model made of two $d_{xz}/d_{yz}$ hole pockets and two electron pockets. The leading instability in the effective 4-pocket model is a spontaneous orbital (nematic) order, followed by $s^{+-}$ superconductivity. In the effective 3-pocket model orbital fluctuations are weaker, and the system develops either $s^{+-}$ superconductivity or stripe SDW. In the latter case, nematicity is induced by composite spin fluctuations.

cond-mat.supr-con↗

arXiv2016

Competing instabilities, orbital ordering and splitting of band degeneracies from a parquet renormalization group analysis of a 4-pocket model for iron-based superconductors: application to FeSe

We report the results of a parquet renormalization group (RG) study of competing instabilities in the full 2D four pocket, three orbital low-energy model for iron-based superconductors. We derive and analyze the RG flow of the couplings, which describe all symmetry-allowed interactions between low-energy fermions. Despite that the number of the couplings is large, we argue that there are only two stable fixed trajectories of the RG flow and one weakly unstable fixed trajectory with a single unstable direction. Each fixed trajectory has a finite basin of attraction in the space of initial system parameters. On the stable trajectories, either interactions involving only $d_{xz}$ and $d_{yz}$ or only $d_{xy}$ orbital components on the electron pockets dominate, while on the weakly unstable trajectory interactions involving $d_{xz}$ ($d_{yz}$) and $d_{xy}$ orbital states on the electron pockets remain comparable. The behavior along the two stable fixed trajectories has been analyzed earlier [A.V. Chubukov, M. Khodas, and R.M. Fernandes, arXiv:1602.05503]. Here we focus on the system behavior along the weakly unstable trajectory and apply the results to FeSe. We find, based on the analysis of susceptibilities along this trajectory, that the leading instability upon lowering the temperature is towards a {\it three-component} d-wave orbital nematic order. Two components are the differences between fermionic densities on $d_{xz}$ and $d_{yz}$ orbitals on hole pockets and on electron pockets, and the third one is the difference between the densities of $d_{xy}$ orbitals on the two electron pockets. We argue that this order is consistent with the splitting of band degeneracies, observed in recent photoemission data on FeSe by A. Fedorov et al [arXiv:1606.03022].

cond-mat.str-el↗

arXiv2015

Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization

We study the competition of spin- and charge-density waves and their quantum multicritical behavior for the semimetal-insulator transitions of low-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawa theory with two order parameters as a model for graphene and a growing number of other two-dimensional Dirac materials allows us to describe the physics near the multicritical point at which the semimetallic and the spin- and charge-density-wave phases meet. With the help of a functional renormalization group approach, we are able to reveal a complex structure of fixed points, the stability properties of which decisively depend on the number of Dirac fermions $N_f$. We give estimates for the critical exponents and observe crucial quantitative corrections as compared to the previous first-order $ε$ expansion. For small $N_f$, the universal behavior near the multicritical point is determined by the chiral Heisenberg universality class supplemented by a decoupled, purely bosonic, Ising sector. At large $N_f$, a novel fixed point with nontrivial couplings between all sectors becomes stable. At intermediate $N_f$, including the graphene case ($N_f = 2$) no stable and physically admissible fixed point exists. Graphene's phase diagram in the vicinity of the intersection between the semimetal, antiferromagnetic and staggered density phases should consequently be governed by a triple point exhibiting first-order transitions.

cond-mat.str-el↗

arXiv2015

Mott multicriticality of Dirac electrons in graphene

We study the multicritical behavior for the semimetal-insulator transitions on graphene's honeycomb lattice using the Gross-Neveu-Yukawa effective theory with two order parameters: the SO(3) (Heisenberg) order parameter describes the antiferromagnetic transition, and the $\mathbb{Z}_2$ (Ising) order parameter describes the transition to a staggered density state. Their coupling induces multicritical behavior which determines the structure of the phase diagram close to the multicritical point. Depending on the number of fermion flavors $N_f$ and working in the perturbative regime in vicinity of three (spatial) dimensions, we observe first order or continuous phase transitions at the multicritical point. For the graphene case of $N_f=2$ and within our low order approximation, the phase diagram displays a tetracritical structure.

cond-mat.str-el↗