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.
A fundamental issue concerning iron-based superconductivity is the roles of electronic nematicity and magnetism in realising high transition temperature ($T_{\rm c}$). To address this issue, FeSe is a key material, as it exhibits a unique pressure phase diagram involving nonmagnetic nematic and pressure-induced antiferromagnetic ordered phases. However, as these two phases in FeSe overlap with each other, the effects of two orders on superconductivity remain perplexing. Here we construct the three-dimensional electronic phase diagram, temperature ($T$) against pressure ($P$) and isovalent S-su…
Nematicity and magnetism are two key features in Fe-based superconductors, and their interplay is one of the most important unsolved problems. In FeSe, the magnetic order is absent below the structural transition temperature $T_{str}=90$K, in stark contrast that the magnetism emerges slightly below $T_{str}$ in other families. To understand such amazing material dependence, we investigate the spin-fluctuation-mediated orbital order ($n_{xz}\neq n_{yz}$) by focusing on the orbital-spin interplay driven by the strong-coupling effect, called the vertex correction. This orbital-spin interplay is v…
To understand the rich electronic phase diagram in FeSe under pressure that vividly demonstrates the strong interplay between the nematicity, magnetism and superconductivity, we analyze the electronic states by including the higher-order many-body effects called the vertex correction (VC). We predict the pressure-induced emergence of xy-orbital hole-pocket based on the first-principles analysis. Due to this pressure-induced Lifshitz transition, the spin fluctuations on the xy orbital are enhanced, whereas those on xz,yz orbitals are gradually reduced. For this reason, nonmagnetic orbital order…
We report a $^{75}$As nuclear magnetic resonance study in LaFeAsO single crystals, which undergoes nematic and antiferromagnetic transitions at $T_\text{nem}\sim 156$ K and $T_N \sim 138$ K, respectively. Below $T_\text{nem}$, the $^{75}$As spectrum splits sharply into two for an external magnetic field parallel to the orthorhombic $a$ or $b$ axis in the FeAs planes. Our analysis of the data demonstrates that the NMR line splitting arises from an electronically driven rotational symmetry breaking. The $^{75}$As spin-lattice relaxation rate as a function of temperature shows that spin fluctuati…
Iron-based superconductors are well-known for their intriguing phase diagrams, which manifest a complex interplay of electronic, magnetic and structural degrees of freedom. Among the phase transitions observed are superconducting, magnetic, and several types of structural transitions, including a tetragonal-to-orthorhombic and a collapsed-tetragonal transition. In particular, the widely-observed tetragonal-to-orthorhombic transition is believed to be a result of an electronic order that is coupled to the crystalline lattice and is, thus, referred to as nematic transition. Nematicity is therefo…
CeRhIn$_5$ provides a textbook example of quantum criticality in a heavy fermion system: Pressure suppresses local-moment antiferromagnetic (AFM) order and induces superconductivity in a dome around the associated quantum critical point (QCP) near $p_{c} \approx 23\,$kbar. Strong magnetic fields also suppress the AFM order at a field-induced QCP at $B_{\rm c}\approx 50\,$T. In its vicinity, a nematic phase at $B^*\approx 28\,$T characterized by a large in-plane resistivity anisotropy emerges. Here, we directly investigate the interrelation between these phenomena via magnetoresistivity measure…
In the magic angle twisted bilayer graphene (MATBG), one of the most remarkable observations is the $C_3$-symmetry-breaking nematic state. We identify that the nematicity in MATBG is the $E$-symmetry ferro bond order, which is the modulation of correlated hopping integrals owing to the $E$-symmetry particle-hole pairing condensation. The nematicity in MATBG originates from prominent quantum interference among $SU(4)$ valley+spin composite fluctuations. This novel "valley + spin fluctuation interference mechanism" is revealed by the density wave equation analysis for realistic multiorbital Hubb…
The importance of antiferromagnetic fluctuations are widely acknowledged in most unconventional superconductors. In addition, cuprates and iron pnictides often exhibit unidirectional (nematic) electronic correlations, including stripe and orbital orders, whose fluctuations may also play a key role for electron pairing. However, these nematic correlations are intertwined with antiferromagnetic or charge orders, preventing us to identify the essential role of nematic fluctuations. This calls for new materials having only nematicity without competing or coexisting orders. Here we report systemati…
Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) on FeSe and iron pnictide families of iron-based superconductors, we have studied the orbital nematic order and its interplay with antiferromagnetism within the two-orbital Hubbard model. We used random phase approximation (RPA) to calculate the dependence of the orbital and magnetic susceptibilities on the strength of interactions and electron density (doping). To account for strong electron correlations not captured by RPA, we further employed non-perturbative variational cluster approximation (VCA) capable of capturin…
Phononic enhancement and detection of hidden spin-nematicity and dynamics in quantum magnets
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
The nematic order (nematicity) is considered one of the essential ingredients to understand the mechanism of Fe-based superconductivity. In most Fe-based superconductors (pnictides), nematic order is reasonably close to the antiferromagnetic order. In FeSe, in contrast, a nematic order emerges below the structure phase transition at T_s = 90 K with no magnetic order. The case of FeSe is of paramount importance to a universal picture of Fe-based superconductors. The polarized ultrafast spectroscopy provides a tool to probe simultaneously the electronic structure and the magnetic interactions th…
Electronic nematicity in correlated metals often occurs alongside another instability such as magnetism. As a result, the question remains whether nematicity alone can drive unconventional superconductivity or anomalous (quantum critical) transport in such systems. In FeSe, nematicity emerges in isolation, providing a unique opportunity to address this question. Studies to date, however, have proved inconclusive; while signatures of nematic criticality are observed upon sulfur substitution, they appear to be quenched under the application of pressure due to the emergent magnetism. Here, we stu…
Although the existence of nematic order in iron-based superconductors is now a well-established experimental fact, its origin remains controversial. Nematic order breaks the discrete lattice rotational symmetry by making the $x$ and $y$ directions in the Fe plane non-equivalent. This can happen because of (i) a tetragonal to orthorhombic structural transition, (ii) a spontaneous breaking of an orbital symmetry, or (iii) a spontaneous development of an Ising-type spin-nematic order - a magnetic state that breaks rotational symmetry but preserves time-reversal symmetry. The Landau theory of phas…
The electronic nematic responses in Fe-based superconductors have been observed ubiquitously in various experimental probes. One novel nematic character is the d-wave {\it bond} orbital-relevant nematic charge order which was firstly proposed by symmetry analysis and then conformed by angle-resolved photoemission spectroscopy. In this paper, we present a mechanism that the driving force of the orbital-relevant nematic charge order is the reduction of the large Hubbard energy in the particle-hole charge channel by virtual hopping processes. This is one scenario from strong-coupling consideratio…
Recent experiments have explored two-dimensional electron gases (2DEGs) at oxide (111) surfaces and interfaces, finding evidence for hexagonal symmetry breaking in SrTiO$_3$ at low temperature. We discuss many-body instabilities of such (111) 2DEGs, incorporating multiorbital interactions in the $t_{2g}$ manifold which can induce diverse magnetic and orbital orders. Such broken symmetries may partly account for the observed nematicity, cooperating or competing with phonon mechanisms. We present an effective field theory for the interplay of magnetism and nematic charge order, and discuss impli…
Magnetism induced by external pressure ($p$) was studied in a FeSe crystal sample by means of muon-spin rotation. The magnetic transition changes from second-order to first-order for pressures exceeding the critical value $p_{\rm c}\simeq2.4-2.5$ GPa. The magnetic ordering temperature ($T_{\rm N}$) and the value of the magnetic moment per Fe site ($m_{\rm Fe}$) increase continuously with increasing pressure, reaching $T_{\rm N}\simeq50$~K and $m_{\rm Fe}\simeq0.25$ $μ_{\rm B}$ at $p\simeq2.6$ GPa, respectively. No pronounced features at both $T_{\rm N}(p)$ and $m_{\rm Fe}(p)$ are detected at $…
The interplay between strong correlations and non-trivial topology in twisted moiré systems can give rise to a rich landscape of ordered states that intertwine the spin, valley, and charge degrees of freedom. In this paper, we investigate the properties of a system that displays long-range valley-polarized nematic order. Besides breaking the threefold rotational symmetry of the triangular moiré superlattice, this type of order also breaks twofold rotational and time-reversal symmetries, which leads to interesting properties. First, we develop a phenomenological model to describe the onset of t…
Twisted graphene bilayers provide a versatile platform to engineer metamaterials with novel emergent properties by exploiting the resulting geometric moiré superlattice. Such superlattices are known to host bulk valley currents at tiny angles ($α\approx 0.3 ^\circ$) and flat bands at magic angles ($α\approx 1^\circ$). We show that tuning the twist angle to $α^*\approx 0.8^\circ$ generates flat bands away from charge neutrality with a triangular superlattice periodicity. When doped with $\pm 6$ electrons per moiré cell, these bands are half-filled and electronic interactions produce a symmetry-…
Two-dimensional moire superlattices have recently emerged as a fertile ground for creating novel electronic phases of matter with unprecedented control. Despite intensive efforts, theoretical investigation of correlated moire systems has been challenged by the large number of atoms in a superlattice unit cell and the inherent difficulty of treating electron correlation. The physics of correlated moire systems is governed by low-energy electrons in a coarse-grained long-wavelength potential, unlike the singular Coulomb potential of atomically-spaced ions in natural solids. Motivated by the sepa…
We predict that neutral graphene bilayers are pseudospin magnets in which the charge density-contribution from each valley and spin spontaneously shifts to one of the two layers. The band structure of this system is characterized by a momentum-space vortex which is responsible for unusual competition between band and kinetic energies leading to symmetry breaking in the vortex core. We discuss the possibility of realizing a pseudospin version of ferromagnetic metal spintronics in graphene bilayers based on hysteresis associated with this broken symmetry.
Spin-driven nematicity, or the breaking of the point-group symmetry of the lattice without long-range magnetic order, is clearly quite important in iron-based superconductors. From a symmetry point of view, nematic order can be described as a coherent locking of spin fluctuations in two interpenetrating Néel sublattices with ensuing nearest-neighbor bond order and an absence of static magnetism. Here, we argue that the low-temperature state of the recently discovered superconductor BaTi$_2$Sb$_2$O is a strong candidate for a more exotic form of spin-driven nematic order, in which fluctuations …
Charge carriers in magic angle graphene come in eight flavors described by a combination of their spin, valley, and sublattice polarizations. When the inversion and time reversal symmetries are broken by the substrate or by strong interactions, the degeneracy of the flavors can be lifted and their corresponding bands can be filled sequentially. Due to their non-trivial band topology and Berry curvature, each of the bands is classified by a topological Chern number, leading to the quantum anomalous Hall and Chern insulator states at integer fillings $ν$ of the bands. It has been recently predic…
We provide a complete theoretical interpretation of the metallic broken spin/valley symmetry states recently discovered in ABC trilayer graphene (ABC) perturbed by a large transverse displacement field. Our conclusions combine insights from ABC trilayer graphene electronic structure models and mean field theory, and are guided by precise magneto-oscillation Fermi-surface-area measurements. We conclude that the physics of ABC trilayer graphene is shaped by the principle of momentum-space condensation, which favors Fermi surface reconstructions enabled by broken spin/valley flavor symmetries whe…
2D materials based superlattices have emerged as a promising platform to modulate band structure and its symmetries. In particular, moiré periodicity in twisted graphene systems produces flat Chern bands. The recent observation of anomalous Hall effect (AHE) and orbital magnetism in twisted bilayer graphene has been associated with spontaneous symmetry breaking of such Chern bands. However, the valley Hall state as a precursor of AHE state, when time-reversal symmetry is still protected, has not been observed. Our work probes this precursor state using the valley Hall effect. We show that brok…
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, a…
Flat band moiré superlattices have recently emerged as unique platforms for investigating the interplay between strong electronic correlations, nontrivial band topology, and multiple isospin 'flavor' symmetries. Twisted monolayer-bilayer graphene (tMBG) is an especially rich system owing to its low crystal symmetry and the tunability of its bandwidth and topology with an external electric field. Here, we find that orbital magnetism is abundant within the correlated phase diagram of tMBG, giving rise to the anomalous Hall effect (AHE) in correlated metallic states nearby most odd integer fillin…
Detecting magnetic order at the nanoscale is of central interest for the study of quantum magnetism in general, and the emerging field of moiré magnets in particular. Here, we analyze the exciton band structure that arises from a periodic modulation of the valley Zeeman effect. Despite long-range electron-hole exchange interactions, we find a sizable splitting in the energy of the bright circularly-polarized exciton Umklapp resonances, which serves as a direct optical probe of magnetic order. We first analyze quantum moiré magnets realized by periodic ordering of electron spins in Mott-Wigner …
We report the observation of spin-polarized superconductivity in Bernal bilayer graphene when doped to a saddle-point van Hove singularity generated by large applied perpendicular electric field. We observe a cascade of electrostatic gate-tuned transitions between electronic phases distinguished by their polarization within the isospin space defined by the combination of the spin and momentum-space valley degrees of freedom. While all of these phases are metallic at zero magnetic field, we observe a transition to a superconducting state at finite $B_\parallel\approx 150$mT applied parallel to …
Recent applications of Quantum Monte Carlo (QMC) technique to Fe-based superconductors opened a way to directly verify the applicability of the itinerant scenario for these systems. Fe-based superconductors undergo various instabilities upon lowering temperature (magnetism, superconductivity, nematicity/orbital order), and one can check whether the hierarchy of instabilities obtained within the itinerant approach is the same as in unbiased QMC simulations. In a recent paper [arXiv:1512:08523] the authors considered the simplest two-band model with interaction tailored to favor orbital order. T…
Ferromagnetism is most common in transition metal compounds but may also arise in low-density two-dimensional electron systems, with signatures observed in silicon, III-V semiconductor systems, and graphene moiré heterostructures. Here we show that gate-tuned van Hove singularities in rhombohedral trilayer graphene drive the spontaneous ferromagnetic polarization of the electron system into one or more spin- and valley flavors. Using capacitance measurements on graphite-gated van der Waals heterostructures, we find a cascade of density- and electronic displacement field tuned phase transitions…
Magic-angle twisted bilayer graphene (tBLG) has been studied extensively owing to its wealth of symmetry-broken phases, correlated Chern insulators, orbital magnetism, and superconductivity. In particular, the anomalous Hall effect (AHE) has been observed at odd integer filling factors ($ν=1$ and $3$) in a small number of tBLG devices, indicating the emergence of a zero-field orbital magnetic state with spontaneously broken time-reversal symmetry. However, the AHE is typically not anticipated at half filling ($ν=2$) owing to competing intervalley coherent states, as well as spin-polarized and …
Graphene-based moiré systems have attracted considerable interest in recent years as they display a remarkable variety of correlated phenomena. Besides insulating and superconducting phases in the vicinity of integer fillings of the moiré unit cell, there is growing evidence for electronic nematic order both in twisted bilayer graphene and twisted double-bilayer graphene (tDBG), as signaled by the spontaneous breaking of the threefold rotational symmetry of the moiré superlattices. Here, we combine symmetry-based analysis with a microscopic continuum model to investigate the structure of the n…
