We study the electromagnetic response of a chiral ${\rm d_{xy}+id_{x^2-y^2}}$ charge density wave state. Due to parity (${\cal P}$) and time reversal (${\cal T}$) violation, Chern-Simons terms emerge in the effective action of the U(1) gauge field. As a consequence electric and magnetic fields are coupled providing the possibility of observing the Spontaneous Quantum Hall Effect i.e. generation of Hall voltage via the sole application of an electric field. We show how the Chern-Simons terms are induced and discuss the topological origin of the quantization of Hall conductance.
Using exact diagonalization of bilayer quantum Hall systems at total filling factor $ν_T=1$ in the torus geometry, we show that there is a new long-range interlayer phase coherence due to spontaneous pseudospin spiral order at interlayer distances larger than the critical value at which the pseudospin ferromagnetic order is destroyed. We emphasize the distinction between the interlayer phase coherence and the pseudospin ferromagnetic order.
This tutorial paper reviews some of the physics of quantum Hall bilayers with a focus on the case where there is low or zero tunnelling between the two layers. We describe the interlayer coherent states at filling factors nu=1 and nu=2 as exciton condensates and discuss some of the theory associated with these states.
Using exact diagonalization in the disc geometry we predict a novel even-odd effect in the Coulomb blockade spectra of vertically coupled double quantum dots under an external magnetic field. The even-odd effect in the tunneling conductance is a direct manifestation of spontaneous interlayer phase coherence, and is similar to the even-odd resonance in the Cooper pair box problem in mesoscopic superconducting grains. Coherent fluctuations in the number of Cooper pairs in superconductors is analogous to the fluctuations in the relative number difference between the two layers in quantum Hall dro…
We elucidate the nature of neutral collective excitations of fractional quantum Hall liquids in the long-wavelength limit. We demonstrate that they are chiral gravitons carrying angular momentum - 2, which are quanta of quantum motion of an internal metric, and show up as resonance peaks in the systems response to what is the fractional Hall analog of gravitational waves. Relation with existing and possible future experimental work that can detect these fractional quantum Hall gravitons and reveal their chirality are discussed.
Gapless electronic systems containing topologically nontrivial Fermi points are sources of various topological insulators. Whereas most of these special band-crossing points are built in the electronic structure of the non-interacting lattice models, we show that a quadratic Fermi point characterized by a non-zero winding number emerges with a collinear triple-Q spin-density-wave state that arises from a perfectly nested but topologically trivial Fermi surface. We obtain a universal low-energy Hamiltonian for the quadratic Fermi point and show that such collinear orderings are unstable against…
We use the microscopic Hartree-Fock approximation to investigate various quantum phase transitions associated with possible spontaneous symmetry breaking induced by a tilted magnetic field in the integral quantum Hall regime of wide parabolic wells and zero width double well (bilayer) systems. We propose a general class of variational wavefunctions that describe several types of parity, spin, and translational symmetry breaking, including spin and charge density wave phases. Zero temperature quantum phase diagrams for these systems are calculated in the parameter regime of experimental interes…
It is widely believed that integer quantum Hall systems do not have fractional excitations. Here we show the converse to be true for a class of systems where integer quantum Hall effect emerges spontaneously due to the interplay of itinerant electrons and noncoplanar magnetic ordering. We show that magnetic $Z_2$ vortices in such systems, whose topological stability is guaranteed by the structure of the order parameter, indeed carry fractional charge.
We uncover topological features of neutral particle-hole pair excitations of correlated quantum anomalous Hall (QAH) insulators whose approximately flat conduction and valence bands have equal and opposite non-zero Chern number. Using an exactly solvable model we show that the underlying band topology affects both the center-of-mass and relative motion of particle-hole bound states. This leads to the formation of topological exciton bands whose features are robust to nonuniformity of both the dispersion and the Berry curvature. We apply these ideas to recently-reported broken-symmetry spontane…
Both topological crystalline insulators surfaces and graphene host multi-valley massless Dirac fermions which are not pinned to a high-symmetry point of the Brillouin zone. Strain couples to the low-energy electrons as a time-reversal invariant gauge field, leading to the formation of pseudo-Landau levels (PLL). Here we study periodic pseudo-magnetic fields originating from strain superlattices. We study the low-energy Dirac PLL spectrum induced by the strain superlattice and analyze the effect of various polarized states. Through self-consistent Hartree-Fock calculations we establish that, du…
We study the Kondo Lattice and Hubbard models on a triangular lattice for band filling factor 3/4. We show that a simple non-coplanar chiral spin ordering (scalar spin chirality) is naturally realized in both models due to perfect nesting of the Fermi surface. The resulting triple-Q magnetic ordering is a natural counterpart of the collinear Neel ordering of the half-filled square lattice Hubbard model. We show that the obtained chiral phase exhibits a spontaneous quantum Hall-effect with sigma_{xy}= e^2/h.
Chirally stacked N-layer graphene systems with N >= 2 exhibit a variety of distinct broken symmetry states in which charge density contributions from different spins and valleys are spontaneously transferred between layers. We explain how these states are distinguished by their charge, spin, and valley Hall conductivities, by their orbital magnetizations, and by their edge state properties. We argue that valley Hall states have [N/2] edge channels per spin-valley.
Much has been learned about the topological transport in real materials. We investigate the interplay between magnetism and topology in the magneto-transport of PrRhC$_2$. The four-fold degeneracy reduces to two-fold followed by non-degenerate Weyl nodes when the orientation of the magnetic quantization axis is changed from easy axis to body-diagonal through face-diagonal. This engenders chirality imbalance between positive and negative chirality Weyl nodes around the Fermi energy. We observe a significant enhancement in the chiral anomaly mediated response such as planar Hall conductivity and…
Non-interacting topological states of matter can be realized in band insulators with intrinsic spin-orbital couplings as a result of the nontrivial band topology. In recent years, the possibility of realizing novel interaction-driven topological phase has attracted a lot of research activities, which may significantly extend the classes of topological states of matter. Here, we report a new finding of an interaction-driven spontaneous quantum Hall effect (QHE) (Chern insulator) emerging in an extended fermion-Hubbard model on kagome lattice. By means of the state-of-the-art density-matrix reno…
A ferromagnet with spin anisotropies on the 2D Kagome lattice is theoretically studied. This is a typical example of the flat-band ferromagnet. The Berry phase induced by the tilting of the spins opens the band gap and quantized Hall conductance σ_{xy}=\pm e^2/h is realized without external magnetic field. This is the most realistic chiral spin state based on the ferromagnetism. We also discuss the implication of our results to anomalous Hall effect observed in the metallic pyrochlore ferromagnets R_2Mo_2O_7(R=Nd, Sm, Gd).
We study the behavior of the quarter-filled Kondo lattice model on a triangular lattice by combining a zero-temperature variational approach and finite-temperature Monte-Carlo simulations. For intermediate coupling between itinerant electrons and classical moments ${\bf S}_j$, we find a thermodynamic phase transition into an exotic spin ordering with uniform scalar spin chirality and $< {\bf S}_j >=0$. The state exhibits spontaneous quantum Hall effect. We also study how its properties are affected by application of an external magnetic field.
As novel topological phases in correlated electron systems, we have found two examples of non-ferromagnetic states that exhibit a large anomalous Hall effect. One is the chiral spin liquid compound Pr$_{2}$Ir$_{2}$O$_{7}$, which exhibits a spontaneous Hall effect in a spin liquid state due to spin ice correlation. The other is the chiral antiferromagnets Mn$_{3}$Sn and Mn$_{3}$Ge that exhibit a large anomalous Hall effect at room temperature. The latter shows a sign change of the anomalous Hall effect by a small change in the magnetic field by a few 100 G, which should be useful for various ap…
A formation of tetrahedral spin clusters is discovered by Monte Carlo simulation for a spin-ice type double-exchange model on a pyrochlore lattice. The spin-cluster phase is magnetically disordered, but breaks spatial inversion symmetry spontaneously by developing noncoplanar four-spin molecules periodically on the pyrochlore lattice. We find that the system exhibits a nonzero spin Hall conductivity in the spin-cluster phase. The result suggests that an intersite-multipole order induces the unconventional spin Hall state without the spin-orbit interaction.
In the quantum anomalous Hall effect, chiral edge modes are expected to conduct spin polarized current without dissipation and thus hold great promise for future electronics and spintronics with low energy consumption. However, spin polarization of chiral edge modes has never been established in experiments. In this work, we theoretically study spin polarization of chiral edge modes in the quantum anomalous Hall effect, based on both the effective model and more realistic tight-binding model constructed from the first principles calculations. We find that spin polarization can be manipulated b…
The effective field theory of the fractional quantum Hall edge is reformulated from microscopic dynamics. Noncommutative Chern-Simons theory is a microscopic description for the quantum Hall fluid. We use it for reference. Considering relabeling symmetry of the electrons and incompressibility of the fluid, we obtain a constraint and derive a chiral Tomonaga-Luttinger liquid theory containing interaction terms. We calculate one-loop corrections to the phonon and electron propagators and get a new tunneling exponent. It agrees with experiments.
We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry. We show that this chiral Hall effect resembles the familiar topological Hall effect in e…
Bilayer graphene and its thicker cousins with Rhombohedral stacking have attracted considerable attention because of their susceptibility to a variety of broken chiral symmetry states. Due to large density-of-states and quantized Berry phases near their gapless band touching points, each spin-valley flavor spontaneously transfers charge between layers to yield opening of energy gaps in quasiparticle spectra and spreading of momentum-space Berry curvatures. In this article we review the development of theories that predicted such chiral symmetry breaking and classified the possible topological …
For topologically nontrivial and very narrow bands, Coulomb repulsion between electrons has been predicted to give rise to a spontaneous fractional quantum-Hall (FQH) state in absence of magnetic fields. Here we show that strongly correlated electrons in a t_2g-orbital system on a triangular lattice self-organize into a spin-chiral magnetic ordering pattern that induces precisely the required topologically nontrivial and flat bands. This behavior is very robust and does not rely on fine tuning. In order to go beyond mean field and to study the impact of longer-range interactions, we map the lo…
Due to an uprise in the variety of candidate compounds, kagome metals have recently gained significant attention. Among other features, kagome metals host Dirac cones as a key band structure feature away from half filling, and potentially yield an exceptionally large fine structure, beyond values found in other 2D Dirac materials such as graphene. We investigate the possibility of chiral symmetry breaking in kagome metals. Based on a heuristic lattice model, we determine the critical coupling strength and the ordering pattern by means of a Schwinger-Dyson mean-field analysis. As the leading in…
We report on a topological Hall effect possibly induced by scalar spin chirality in a quasi-two- dimensional helimagnet Fe$_{1+x}$Sb. In the low-temperature region where the spins on interstitial- Fe (concentration $x=0.3$) intervening the $120^\circ$ spin-ordered triangular planes tend to freeze, a non-trivial component of Hall resistivity with opposite sign of the conventional anomalous Hall term is observed under magnetic field applied perpendicular to the triangular-lattice plane. The observed unconventional Hall effect is ascribed to the scalar spin chirality arising from the heptamer spi…
The effect of thermal fluctuation on the spin-chirality-induced anomalous Hall effect in itinerant magnets is theoretically studied. Considering a triangular-lattice model as an example, we find that a multiple-spin scattering induced by the fluctuating spins increases the Hall conductivity at a finite temperature. The temperature dependence of anomalous Hall conductivity is evaluated by a combination of an unbiased Monte Carlo simulation and a perturbation theory. Our results show that the Hall conductivity can increase up to $10^3$ times the ground state value; we discuss that this is a cons…
Frustration can introduce more-than-two minima in a spin dispersion relation even in a fully polarized magnet under high magnetic field. We generally discuss, on the fully polarized phase, the possibility of the chiral symmetry breaking where the number of magnons pumped by finite temperature deviates to one side of minima. We study this phase by constructing the Ginzburg-Landau energy which is controlled by the external magnetic field and interactions between magnons near the dispersion minima. This chirality breaking phase accompanies, not a magnetization perpendicular to the external field,…
We compute the Hall viscosity and conductivity of non-relativistic two-dimensional chiral superconductors, where fermions pair due to a short-range attractive potential, e.g. $p+\mathrm{i}p$ pairing, and interact via a long-range repulsive Coulomb force. For a logarithmic Coulomb potential, the Hall viscosity tensor contains a contribution that is singular at low momentum, which encodes corrections to pressure induced by an external shear strain. Due to this contribution, the Hall viscosity cannot be extracted from the Hall conductivity in spite of Galilean symmetry. For mixed-dimensional chir…
We revealed the electrical transport through surface ferromagnetic states of a nonmagnetic metal PdCoO2. Electronic reconstruction at the Pd-terminated surface of PdCoO2 induces Stoner-like ferromagnetic states, which could lead to spin-related phenomena among the highly conducting electrons in PdCoO2. Fabricating a series of nanometer-thick PdCoO2 thin films, we detected a surface-magnetization-driven anomalous Hall effect via systematic thickness- and termination-dependent measurements. Besides, we discuss that finite magnetic moments in electron doped CoO2 triangular lattices may have given…
We show that a finite Hall effect in zero applied magnetic field occurs for partially filled bands in certain time-reversal violating states with zero net flux per unit-cell. These states are the Magneto-chiral states with parameters in the effective one-particle Hamiltonian such that they do not satisfy the Haldane-type constraints for topological electronic states. The results extend an earlier discussion of the Kerr effect observed in the cuprates but may be applicable to other experimental situations.
Anomaly cancelation has been shown to occur in time-reversal symmetry-broken Weyl metals, which explains the existence of a Fermi arc. We extend this result in the case of inversion symmetry-broken Weyl metals. Constructing a minimal model that takes a double pair of Weyl points, we demonstrate the anomaly cancelation explicitly. This demonstration explains why a chiral pair of Fermi arcs appear in inversion symmetry-broken Weyl metals. In particular, we find that this pair of Fermi arcs gives rise to either "quantized" spin Hall or valley Hall effects, which corresponds to the "quantized" ver…
Rare earth pyrochlore Iridates (RE2Ir2O7) consist of two interpenetrating cation sublattices, the RE with highly-frustrated magnetic moments, and the Iridium with extended conduction orbitals significantly mixed by spin-orbit interactions. The coexistence and coupling of these two sublattices create a landscape for discovery and manipulation of quantum phenomena such as the topological Hall effect, massless conduction bands, and quantum criticality. Thin films allow extended control of the material system via symmetry-lowering effects such as strain. While bulk Pr2Ir2O7 shows a spontaneous hys…
We identify an intrinsic Hall effect in multiband chiral superconductors in the absence of a magnetic field (i.e., an anomalous Hall effect). This effect arises from interband transitions involving time-reversal symmetry-breaking chiral Cooper pairs. We discuss the implications of this effect for the putative chiral p-wave superconductor, Sr2RuO4, and show that it can contribute significantly to Kerr rotation experiments. Since the magnitude of the effect depends on the structure of the order parameter across the bands, this result may be used to distinguish between different models proposed f…
We report on a mean-field study of spontaneous breaking of chiral symmetry for Dirac fermions with contact interactions in the presence of chiral imbalance, which is modelled by nonzero chiral chemical potential. We point out that chiral imbalance lowers the vacuum energy of Dirac fermions, which leads to the increase of the renormalized chiral chemical potential upon chiral symmetry breaking. The critical coupling strength for the transition to the broken phase is slightly lowered as the chiral chemical potential is increased, and the transition itself becomes milder. Furthermore, we study th…
Chirally stacked N-layer graphene with N>=2 is susceptible to a variety of distinct broken symmetry states in which each spin-valley flavor spontaneously transfers charge between layers. In mean-field theory the neutral bilayer ground state is a layer antiferromagnet (LAF) state that has opposite spin-polarizations in opposite layers. In this Letter we analyze how the LAF and other competing states are influenced by Zeeman fields that couple to spin and by interlayer electric fields that couple to layer pseudospin, and comment on the possibility of using response and edge state signatures to i…
Vacua of two dimensional incompressible system, such as Fractional Quantum Hall system, are characterized by rational conformal field theory. We develop a method to express the wavefunctions of those systems in terms of chiral vertices. We formulate quantum mechanics on those expressions, which reveals the underlying simple structure of the conformal field theory discription of FQH systems. Also we argue the recent conjecture of Nayak and Wilczek on the spinor statistics of 2n quasihole state in paired quantum hall system.
Recent experiments on ultracold atoms in optical lattices have synthesized a variety of tunable bands with degenerate double-well structures in momentum space. Such degeneracies in the single particle spectrum strongly enhance quantum fluctuations, and may lead to exotic many-body ground states. Here we consider weakly interacting spinor Bose gases in such bands, and discover a universal quantum "order by disorder" phenomenon which selects a novel chiral spin superfluid with remarkable properties such as spontaneous anomalous spin Hall effect and momentum space antiferromagnetism. For bosons i…
We identify an intrinsic mechanism of the anomalous Hall effect for non-symmorphic chiral superconductors. This mechanism relies on both a nontrivial multi-band chiral superconducting order parameter, which is a mixture of pairings of even and odd angular momentum channels, and a complex normal state inter-sublattice hopping, both of which are consequences of the nonsymmorphic group symmetry of the underlying lattice. We apply this mechanism to the putative chiral superconducting phase of the heavy-fermion superconductor $\mathrm{UPt_3}$ and calculate the anomalous ac Hall conductivity in a si…
Chiral topological insulator (AIII-class) with Landau levels is constructed based on the Nambu 3-algebraic geometry. We clarify the geometric origin of the chiral symmetry of the AIII-class topological insulator in the context of non-commutative geometry of 4D quantum Hall effect. The many-body groundstate wavefunction is explicitly derived as a $(l,l,l-1)$ Laughlin-Halperin type wavefunction with unique $K$-matrix structure. Fundamental excitation is identified with anyonic string-like object with fractional charge ${1}/({1+2(l-1)^2})$. The Hall effect of the chiral topological insulators tur…
