We study aspects of Berry phase in gapped many-body quantum systems by means of effective field theory. Once the parameters are promoted to spacetime-dependent background fields, such adiabatic phases are described by Wess-Zumino-Witten (WZW) and similar terms. In the presence of symmetries, there are also quantized invariants capturing generalized Thouless pumps. Consideration of these terms provides constraints on the phase diagram of many-body systems, implying the existence of gapless points in the phase diagram which are stable for topological reasons. We describe such diabolical points, realized by free fermions and gauge theories in various dimensions, which act as sources of "higher Berry curvature" and are protected by the quantization of the corresponding WZW terms or Thouless pump terms. These are analogous to Weyl nodes in a semimetal band structure. We argue that in the presence of a boundary, there are boundary diabolical points---parameter values where the boundary gap closes---which occupy arcs ending at the bulk diabolical points. Thus the boundary has an "anomaly in the space of couplings" in the sense of Córdova et al. Consideration of the topological effective action for the parameters also provides some new checks on conjectured infrared dualities and deconfined quantum criticality in 2+1d.
Topological Phenomena Protected by Diabolical Textures
Harish-Chandra Research Institute (HRI)（哈里什-钱德拉研究所（HRI））；University of Texas at Dallas（德克萨斯大学达拉斯分校）；National Institute of Technology (NIT), Rourkela（鲁尔克拉国家理工学院（NIT））；Homi Bhabha National Institute (HBNI)（霍米·巴巴国家研究所（HBNI））
Chiral anomaly and the novel quantum phenomena it induces have been widely studied for Dirac and Weyl fermions. In most typical cases, the Lorentz covariance is assumed and thus the linear dispersion relations are maintained. However, in realistic materials, such as Dirac and Weyl semimetals, the non-linear dispersion relations appear naturally. We develop a kinetic framework to study the chiral anomaly for Weyl fermions with non-linear dispersions by using the methods of Wigner function and semi-classical equations of motion. In this framework, the chiral anomaly is sourced by Berry monopoles…
We consider the Anomalous Hall (AH) state induced by interactions in a three-orbital per unit-cell model. To be specific we consider a model appropriate for the Copper-Oxide lattice to highlight the necessary conditions for time-reversal breaking states which are AH states and which are not. We compare the singularities of the wave-functions of the three-orbital model, which are related to the nonzero Berry curvature, and their variation with a change of gauge to those in the two-orbital model introduced in a seminal paper by Haldane. Explicit derivation using wave-functions rather than the mo…
A notion of the Berry phase is a powerful means to unravel the non-trivial role of topology in various novel phenomena observed in chiral magnetic materials and structures. A celebrated example is the intrinsic anomalous Hall effect (AHE) driven by the non-vanishing Berry phase in the momentum space. As the AHE is highly dependent on details of the band structure near the Fermi edge, the Berry phase and AHE can be altered in thin films whose chemical potential is tunable by dimensionality and disorder. Here, we demonstrate that in ultrathin SrRuO$_3$ films the Berry phase can be effectively ma…
Berry phase plays an important role in many non-trivial phenomena over a broad range of many-body systems. In this thesis we focus on the Berry phase due to the change of the particles' momenta, and study its effects in free and interacting fermionic systems. We start with reviewing the semi-classical kinetic theory with Berry phase for a non-interacting ensemble of fermions -- a Berry Fermi gas -- which might be far-from-equilibrium. We particularly review the famous Berry phase contribution to the anomalous Hall current. We then provide a concrete and general path integral derivation for the…
A crossover between the Bose Einstein condensation (BEC) and BCS superconducting state is described topologically in the chiral symmetric fermion system with attractive interaction. Using a local Z_2 Berry phase, we found a quantum phase transition between the BEC and BCS phases without accompanying the bulk gap closing.
Understanding and control of spin degrees of freedom on the surfaces of topological materials are key to future applications as well as for realizing novel physics such as the axion electrodynamics associated with time-reversal (TR) symmetry breaking on the surface. We experimentally demonstrate magnetically induced spin reorientation phenomena simultaneous with a Dirac-metal to gapped-insulator transition on the surfaces of manganese-doped Bi2Se3 thin films. The resulting electronic groundstate exhibits unique hedgehog-like spin textures at low energies, which directly demonstrate the mechani…
The wavefuntion of conduction electrons moving in the background of a non-coplanar spin structure can gain a quantal phase - Berry phase - as if the electrons were moving in a strong fictitious magnetic field. Such an emergent magnetic field effect is approximately proportional to the solid angle subtended by the spin moments on three neighbouring spin sites, termed the scalar spin chirality. The entire spin chirality of the crystal, unless macroscopically canceled, causes the geometrical Hall effect of real-space Berry-phase origin, whereas the intrinsic anomalous Hall effect (AHE) in a conve…
Quantum Geometry Phenomena in Condensed Matter Systems
Fundamental Quantum Science Program (FQSP), TRIP Headquarters, RIKEN（基础量子科学项目（FQSP），TRIP总部，理化学研究所）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所涌现物质科学中心）；Department of Physics and Astronomy and California NanoSystems Institute, University of California, Los Angeles（物理与天文学系及加州纳米系统研究所，加利福尼亚大学洛杉矶分校）；Department of Chemistry and Chemical Biology, Harvard University（化学与化学生物学系，哈佛大学）
When electrons are confined in two-dimensional (2D) materials, quantum mechanically enhanced transport phenomena, as exemplified by the quantum Hall effects (QHE), can be observed. Graphene, an isolated single atomic layer of graphite, is an ideal realization of such a 2D system. Here, we report an experimental investigation of magneto transport in a high mobility single layer of graphene. Adjusting the chemical potential using the electric field effect, we observe an unusual half integer QHE for both electron and hole carriers in graphene. Vanishing effective carrier masses is observed at Dir…
Controlling the interplay between localized spins and itinerant electrons at the oxide interfaces can lead to exotic magnetic states. Here we devise SrTiO3/LaTiO3/SrTiO3 heterostructures with varied thickness of the LaTiO3 layer (n monolayers) to investigate the magnetic interactions in the two-dimensional electron gas system. The heterostructures exhibit significant Kondo effect when the LaTiO3 layer is rather thin (n = 2, 10), manifesting the strong interaction between the itinerant electrons and the localized magnetic moments at the interfaces, while the Kondo effect is greatly inhibited wh…
Weyl semimetal, a three-dimensional electronic system with relativistic linear energy dispersion around gapless points carrying nontrivial Berry charge, is predicted to exhibit a wealth of unique response and transport properties.A crucial question is whether those properties are robust against disorder and whether Anderson localization occurs.In this work, the effects of nonperturbative topological (vortex loop) excitations and Berry phase in disordered time-reversal invariant 3d Weyl semimetal are studied.It is shown that the chiral symmetry is restored in the nonlinear sigma model describin…
Several emergent phenomena and phases in solids arise from configurations of the electronic Berry phase in momentum space that are similar to gauge field configurations in real space such as magnetic monopoles. We show that the momentum-space analogue of the "axion electrodynamics" term $\mathbf{E}\cdot\mathbf{B}$ plays a fundamental role in a unified theory of Berry-phase contributions to optical gyrotropy in time-reversal invariant materials and the chiral magnetic effect. The Berry-phase mechanism predicts that the rotatory power along the optic axes of a crystal must sum to zero, a constra…
Geometric phases in condensed matter play a central role in topological transport phenomena such as the quantum, spin and anomalous Hall effect (AHE). In contrast to the quantum Hall effect - which is characterized by a topological invariant and robust against perturbations - the AHE depends on the Berry curvature of occupied bands at the Fermi level and is therefore highly sensitive to subtle changes in the band structure. A unique platform for its manipulation is provided by transition metal oxide heterostructures, where engineering of emergent electrodynamics becomes possible at atomically …
Topologically non-trivial electronic structures can give rise to a range of unusual physical phenomena, and the interplay of band topology with other effects such as electronic correlations and magnetism requires further exploration. The rare earth monopnictides $X$(Sb,Bi) ($X$ = lanthanide) are a large family of semimetals where these different effects may be tuned by the substitution of rare-earth elements. Here we observe anomalous behavior in the quantum oscillations of one member of this family, antiferromagnetic SmSb. The analysis of Shubnikov-de Haas (SdH) oscillations provides evidence…
Topological nontrivial berry phase in altermagnet CrSb
China Jiliang University（中国计量大学）；Beijing National Laboratory for Condensed Matter Physics and Institute of physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家研究中心）；University of Chinese Academy of Sciences（中国科学院大学）；Beijing Polytechnic College（北京工业职业技术学院）；School of Physics, Zhejiang University（浙江大学物理学院）；School of Physics, Hangzhou Normal University（杭州师范大学物理学院）；Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, Chinese Academy of Sciences（中国科学院合肥物质科学研究院强磁场科学中心）
