We study the spontaneous non-magnetic time-reversal symmetry breaking in a two-dimensional Fermi liquid without breaking either the translation symmetry or the U(1) charge symmetry. Assuming that the low-energy physics is described by fermionic quasiparticle excitations, we identified an "emergent" local $U(1)^N$ symmetry in momentum space for an $N$-band model. For a large class of models, including all one-band and two-band models, we found that the time-reversal and chiral symmetry breaking can be described by the $U(1)^N$ gauge theory associated with this emergent local $U(1)^N$ symmetry. This conclusion enables the classification of the time-reversal symmetry-breaking states as types I and II, depending on the type of accompanying spatial symmetry breaking. The properties of each class are studied. In particular, we show that the states breaking both time-reversal and chiral symmetries are described by spontaneously generated Berry phases. We also show examples of the time-reversal symmetry-breaking phases in several different microscopically motivated models and calculate their associated Hall conductance within a mean-field approximation. The fermionic nematic phase with time-reversal symmetry breaking is also presented and the possible realizations in strongly correlated models such as the Emery model are discussed.
Phase transitions involving spontaneous time-reversal symmetry breaking are studied on the honeycomb lattice at finite hole-doping with next-nearest-neighbor repulsion. We derive an exact expression for the mean-field equation of state in closed form, valid at temperatures much less than the Fermi energy. Contrary to standard expectations, we find that thermally induced intraband particle-hole excitations can create and stabilize a uniform metallic phase with broken time-reversal symmetry as the temperature is "raised" in a region where the groundstate is a trivial metal.
We report experimental evidence of a remarkable spontaneous time reversal symmetry breaking in two dimensional electron systems formed by atomically confined doping of phosphorus (P) atoms inside bulk crystalline silicon (Si) and germanium (Ge). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si:P and Ge:P $δ-$layers, suggesting an effect driven by Coulomb interactions. In-plane magnetotransport measurements indicate the presence of intrinsic local spin fluctuations at low doping, pro…
We elucidate the close relationship between spontaneous time-reversal symmetry breaking and the physics of excitonic instabilities in strongly correlated multiband systems. The underlying mechanism responsible for the spontaneous breaking of time-reversal symmetry in a many-body system is closely related to the Cooper-like pairing instability of interband particle-hole pairs involving higher order symmetries. Studies of such pairing instabilites have, however, mainly focused on the mean-field aspects of the virtual exciton condensate, which ignores the presence of the underlying collective Fer…
When Landau levels (LLs) become degenerate near the Fermi energy in the quantum Hall regime, interaction effects can drastically modify the electronic ground state. We study the quantum Hall ferromagnet formed in a two-dimensional hole gas around the LL filling factor $ν=1$ in the vicinity of a LL crossing in the heave-hole valence band. Cavity spectroscopy in the strong-coupling regime allows us to optically extract the two-dimensional hole gas' spin polarization. By analyzing this polarization as a function of hole density and magnetic field, we observe a spin flip of the ferromagnet. Furthe…
The system of spinless fermions on a hexagonal lattice is studied . We have considered tight-binding model with the hopping integrals between the nearest-neighbor and next-nearest-neighbor lattice sites, that depend on the direction of the link. The links are divided on three types depending on the direction, the hopping integrals are defined by different phases along the links. The energy of the system depends on the phase differences, the solutions for the phases, that correspond to the minimums of the energy, lead to a topological insulator state with the nontrivial Chern numbers. We have a…
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.
We argue that that in their recent experiment in which they claim to have found evidence for a time-reversal symmetry broken state, Kaminski et al. overlooked small temperature dependent changes in the superstructure of Bi2212. These subtle changes may manifest themselves by changing the final state configurations of the photoemission process and thus invalidate their ultimate conclusions.
When matter undergoes a phase transition from one state to another, usually a change in symmetry is observed, as some of the symmetries exhibited are said to be spontaneously broken. The superconducting phase transition in the underdoped high-Tc superconductors is rather unusual, in that it is not a mean-field transition as other superconducting transitions are. Instead, it is observed that a pseudo-gap in the electronic excitation spectrum appears at temperatures T* higher than Tc, while phase coherence, and superconductivity, are established at Tc (Refs. 1, 2). One would then wish to underst…
We study the boundary Majorana modes for the single component p-wave weak topological superconductors or superfluids, which form zero energy flat bands protected by time-reversal symmetry in the orbital channel. However, due to the divergence of density of states, the band flatness of the edge Majorana modes is unstable under spontaneously generated spatial variations of Cooper pairing phases. Staggered current loops appear near the boundary and thus time-reversal symmetry is spontaneously broken in the orbital channel. This effect can appear in both condensed matter and ultra-cold atom system…
We consider the time-reversal odd dynamics of the bilayer graphene at low energies in the quantum Hall regime. A generating functional for the effective action that captures the electromagnetic response to all orders in momentum and frequency is presented and evaluated to the third order in the space-time gradient $\mathcal O(\partial^3)$. In addition, we calculate the Hall viscosity and derive an explicit relationship with the $q^2$ coefficient of the Hall conductivity. It is reminiscent of the Hoyos--Son relation in the Galilean invariant systems, which can be recovered in the limit of large…
Thin Co/Pd multilayers, with room temperature perpendicular anisotropy and an enhanced surface scattering, were studied for the possible use in the extraordinary Hall effect (EHE) - based magnetic memory devices. Polarity of the EHE signal was found to change from negative in thick samples to positive in thin ones. Reversal of EHE sign was also observed in thick samples with aging. The effect is argued to be related to the dominance of surface scattering having the EHE polarity opposite to that of the bulk.
We study adatom-covered single layers of CrSiTe$_3$ and CrGeTe$_3$ using first-principles calculations based on hybrid functionals. We find that the insulating ground state of a monolayer of La (Lu) deposited on single-layer CrSiTe$_3$ (CrGeTe$_3$) carries spontaneously generated current loops around the Cr sites, These "flux states" induce antiferromagnetically ordered orbital moments on the Cr sites and are also associated with nontrivial topological properties. The calculated Chern numbers for these systems are predicted to be $\pm 1$ even in the absence of spin-orbit coupling, with sizable…
We study the behavior of spinless fermions in superconducting state, in which the phases of the superconducting order parameter depend on the direction of the link. We find that the energy of the superconductor depends on the phase differences of the superconducting order parameter. The solutions for the phases corresponding to the energy minimuma, lead to a topological superconducting state with the nontrivial Chern numbers. We focus our quantitative analysis on the properties of topological states of superconductors with different crystalline symmetry and show that the phase transition in th…
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…
We provide an effective description of fractional topological insulators that include the fractional quantum spin Hall effect by considering the time-reversal symmetric pendant to the topological quantum field theories that encode the Abelian fractional quantum Hall liquids. We explain the hierarchical construction of such a theory and establish for it a bulk-edge correspondence by deriving the equivalent edge theory for chiral bosonic fields. Further, we compute the Fermi-Bose correlation functions of the edge theory and provide representative ground state wave functions for systems described…
Recent experiments have pointed to a chiral p-wave-like superconductivity in epitaxial Bi/Ni bilayers that are spontaneously time-reversal symmetry breaking (TRSB), making it a promising platform for exploring physics useful for topologically protected quantum computing. Quite intriguingly, evidence has emerged that in non-epitaxial Bi/Ni bilayers, superconductivity arises due to the formation of NiBi3, which has been reported to host coexisting ferromagnetic and superconducting orders at the surface. We perform high resolution surface magneto-optic Kerr effect (SMOKE) measurements using a Sag…
We present a calculation of the Hall coefficient in 2H-TaSe2 and 2H-Cu0.2NbS2 relied on the photoemission data and compare the results to transport observations. The approach, based on the solution of the semiclassical Boltzmann equation in the isotropic tau-approximation yields high-temperature Hall coefficient consistent with the one measured directly. Taking into account the opening of the pseudogap and redistribution of the spectral weight, recently observed in angle resolved photoemission spectra of 2H-TaSe2, allows us to reproduce the temperature dependence of the Hall coefficient includ…
The transport properties of La$_{1.89}$Ce$_{0.11}$CuO$_{4}$(LCCO) and La$_{1.89}$Ce$_{0.11}$(Cu$_{0.99}$Co$_{0.01}$)O$_{4}$ (LCCO:Co) superconducting thin films are investigated. When the external field $\bf H$ is applied along the crystallographic c-axis, a double sign reversal of the Hall voltage in the mixed state of LCCO:Co thin films is observed whereas a single sign reversal is detected in LCCO. A double sign reversal of the Hall signal in LCCO can be recovered if the magnetic field is tilted away from the plane of the film. We find that the transition from one to two of the Hall sign re…
Topological insulators (TIs) in three space dimensions can be characterized by a quantized magnetoelectric coefficient. However, this coupling does not have experimentally observable consequences in the presence of time-reversal symmetry, because the contributions of both bulk and surface states cancel each other. Instead, the characteristic response of a TI is a nonlinear magnetoelectric effect. Field theoretic aspects of the nonlinear magnetoelectric response and numerical calculations for experimentally relevant geometries are discussed. Distinct from this effect, the magnetoelectric coupli…
We consider a Weyl semimetal (WSM) with finite doping and tilt within a continuum model Hamiltonian with both broken time reversal and inversion symmetry. We calculate the absorptive part of the anomalous AC Hall conductivity as a function of photon energy ($Ω$) for both type I and type II Weyl semimetal. For a given Weyl node, changing the sign of its chirality or of its tilt changes the sign of its contribution to the absorptive Hall conductivity with no change in magnitude. For a noncentrosymmetric system we find that there are ranges of photon energies for which only the positive or only t…
States of matter that break time-reversal symmetry are invariably associated with magnetism or circulating currents. Recently, one of us proposed a phase, the directional scalar spin chiral order (DSSCO), as an exception: it breaks time-reversal symmetry via chiral ordering of spins along a particular direction, but is spin-rotation symmetric. In this work, we prove the existence of this state via state-of-the-art density matrix renormalization group (DMRG) analysis on a spin-1 chain with nearest-neighbor bilinear-biquadratic interactions and additional third-neighbor ferromagnetic Heisenberg …
In this work we report the opening of an energy gap at the filling factor $ν=3+1/3$, firmly establishing the ground state as a fractional quantum Hall state. This and other odd-denominator states unexpectedly break particle-hole symmetry. Specifically, we find that the relative magnitudes of the energy gaps of the $ν=3+1/3$ and $3+1/5$ states from the upper spin branch are reversed when compared to the $ν=2+1/3$ and $2+1/5$ counterpart states in the lower spin branch. Our findings raise the possibility that the former states have a non-conventional origin.
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.
It is observed experimentally that the sign of the Hall resistance can be flipped by a dc electric current in the twisted bilayer graphene (TBG) at 3/4 filling of the four-fold degenerate conduction flat bands. The experiment implies a switching of the valley polarization (VP) and topology in TBG. Here we present a theory on the current-induced switching of VP and topology. The presence of current in the bulk causes {the} redistribution of {electron occupation} in bands near the Fermi energy, which then deforms and shifts the band dispersion due to the Coulomb interaction. Above a critical cur…
In a recent comment [1], Armitage and Hu have suggested that our experiment observing dichroism in angle resolved photoemission (ARPES) [2] could not be conclusively interpreted as arising from time reversal symmetry breaking, arguing that our observations are likely due to structural effects. The concerns expressed by Armitage and Hu that our results could be due to a change in the mirror plane are as important as they are obvious. In fact the first part of their comment merely restates the results of Simon and Varma [3] about the relationship and contrast of effects due to time reversal symm…
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.
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 study the phase diagram of a model quantum spin Hall system as a function of band inversion and band-coupling strength, demonstrating that when band hybridization is weak, an interaction-induced nematic insulator state emerges over a wide range of band inversion. This property is a consequence of the long-range Coulomb interaction, which favors interband phase coherence that is weakly dependent on momentum and therefore frustrated by the single-particle Hamiltonian at the band inversion point. For weak band hybridization, interactions convert the continuous gap closing topological phase tra…
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…
The magnetic and ferroelectric properties of the multiferroic system Mn$_{1-x}$Co$_x$WO$_4$ (x=0.135, 0.15, and 0.17) are studied in magnetic fields $H_c$ oriented along the monoclinic $c$-axis. Mn$_{0.85}$Co$_{0.15}$WO$_4$, which is right at the phase boundary between two helical spin structures, exhibits a spontaneous sign change of the ferroelectric polarization when cooled in fields $H_c>$ 25 kOe. The origin of the ferroelectric polarization is studied and two magnetic exchange interactions contributing to the polarization are identified. In Mn$_{0.85}$Co$_{0.15}$WO$_4$ domains of the char…
Superconductivity and magnetism are antagonistic states of matter. The presence of spontaneous magnetic fields inside the superconducting state is, therefore, an intriguing phenomenon prompting extensive experimental and theoretical research. In this review, we discuss recent experimental discoveries of unconventional superconductors which spontaneously break time-reversal symmetry and theoretical efforts in understanding their properties. We discuss the main experimental probes and give an extensive account of theoretical approaches to understand the order parameter symmetries and the corresp…
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.
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…
The edge states in the quantum spin Hall effect are expected to be protected by time reversal symmetry. The experimental observation of the quantized conductance was reported in the InAs/GaSb quantum well {[}Du et al, arXiv:1306.1925{]}, up to a large magnetic field, which raises a question on the robustness of the edge states in the quantum spin Hall effect under time reversal symmetry breaking. Here we present a theoretical calculation on topological invariants for the Benevig-Hughes-Zhang model in an external magnetic field, and find that the quantum spin Hall effect retains robust up to a …
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…
The unique sensitivity of optical response to different types of symmetry breaking can be used to detect and identify spontaneously ordered many-body states in bilayer graphene. We predict a strong response at optical frequencies, sensitive to electronic phenomena at low energies, which arises because of nonzero inter-band matrix elements of the electric current operator. In particular, the polar Kerr rotation and reflection anisotropy provide fingerprints of the quantum anomalous Hall state and the nematic state, characterized by spontaneously broken time reversal symmetry and lattice rotatio…
Moir{é} superlattice realized in two-dimensional heterostructures offers an exciting platform to access strongly-correlated electronic states. In this work, we study transition metal dichalcogenides (TMD) Moir{é} superlattices with time-reversal-symmetry and nontrivial spin{/valley}-Chern numbers. Utilizing realistic material parameters and the method of exact diagonalization, we find that at a certain twisting angle and fractional filling, gapped fractional topological states, i.e., fractional Chern insulators, are naturally {stabilized} by simply introducing the Coulomb repulsion. In contras…
We present a class of time-reversal-symmetric fractional topological liquid states in two dimensions that support fractionalized excitations. These are incompressible liquids made of electrons, for which the charge Hall conductance vanishes and the spin Hall conductance needs not be quantized. We then analyze the stability of edge states in these two-dimensional topological fluids against localization by disorder. We find a Z_2 stability criterion for whether or not there exists a Kramers pair of edge modes that is robust against disorder. We also introduce an interacting electronic two-dimens…
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…
An interaction-driven nonzero quantum Hall conductivity is shown to occur in time-reversal symmetric massive Dirac materials, in the absence of any external agent. The effect is produced through the dynamical breakdown of time-reversal symmetry, which is generated by quantum fluctuations, when the full dynamical electromagnetic interaction among the electrons is taken into account. The manifestation of this emergent parity anomaly should be observed in materials such as silicene, stanene, germanene and transition metal dichalcogenides, at low enough temperatures.
Discoveries of ordered quantum states of matter are of great fundamental interest, and often lead to unique applications. The most well known example -- superconductivity -- is caused by the formation and condensation of pairs of electrons. A key property of superconductors is diamagnetism: magnetic fields are screened by dissipationless currents. Fundamentally, what distinguishes superconducting states from normal states is a spontaneously broken symmetry corresponding to long-range coherence of fermion pairs. Here we report a set of experimental observations in hole doped Ba$_{1-x}$K$_x$Fe$_…
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…
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…
