DOCSLIB.ORG

Metallic Ferromagnetism in the Kondo Lattice

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Metallic Ferromagnetism in the Kondo Lattice Metallic ferromagnetism in the Kondo lattice Seiji J. Yamamotoa and Qimiao Sib,1 aNational High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310-3706; and bDepartment of Physics and Astronomy, Rice University, Houston, TX 77005 Communicated by M. Brian Maple, University of California, San Diego, La Jolla, CA, June 30, 2010 (received for review April 15, 2010) Metallic magnetism is both ancient and modern, occurring in such may then lead to an itinerant ferromagnet (23). With the general familiar settings as the lodestone in compass needles and the hard limitations of the Stoner approach in mind, here we carry out an drive in computers. Surprisingly, a rigorous theoretical basis for me- asymptotically exact analysis of the ferromagnetic state. We are tallic ferromagnetism is still largely missing. The Stoner approach able to do so by using a reference point that differs from either perturbatively treats Coulomb interactions when the latter need to the Stoner or Nagaoka approach (24), and accessing a ferromag- be large, whereas the Nagaoka approach incorporates thermody- netic phase whose excitations are of considerable interest in the namically negligible holes into a half-filled band. Here, we show context of heavy fermion ferromagnets. We should stress that a that the ferromagnetic order of the Kondo lattice is amenable to ferromagnetic order may also arise in different regimes of related an asymptotically exact analysis over a range of interaction para- models, such as in one dimension (25) or in the presence of meters. In this ferromagnetic phase, the conduction electrons and mixed-valency (26). 1 S local moments are strongly coupled but the Fermi surface does not Our model contains a lattice of spin-2 local moments ( i for enclose the latter (i.e., it is “small”). Moreover, non-Fermi-liquid be- each site i) with a ferromagnetic exchange interaction (I < 0), ~ havior appears over a range of frequencies and temperatures. Our a band of conduction electrons (c ~σ, where K is the wavevector σ K ϵ results provide the basis to understand some long-standing puzzles and the spin index) with a dispersion K~ and a characteristic in the ferromagnetic heavy fermion metals, and raise the prospect bandwidth W, and an on-site antiferromagnetic Kondo exchange 0 for a new class of ferromagnetic quantum phase transitions. interaction (JK > ) between the local moments and the spin of the conduction electrons. The corresponding Hamiltonian is Fermi surface ∣ itinerant magnetism ∣ non-Fermi liquid τa † a a a a † σσ0 H ¼ ϵ c c þ I S S þ J S c σ c σ0 : [1] contemporary theme in quantum condensed matter physics ∑ K~ K~σ K~σ ∑ i j ∑ K i i 2 i Aconcerns competing ground states and the accompanying no- K~ hiji i vel excitations (1). With a plethora of different phases, magnetic The symbol τ represents the Pauli matrices, with indices a ∈ heavy fermion materials should reign supreme as the prototype σ ∈ ↑ ↓ for competing order. So far, most of the theoretical scrutiny has fx;y;zg and f ; g. Here I represents the sum of direct ex- focused on antiferromagnetic heavy fermions (2, 3). Nonetheless, change interaction between the local moments and the effective exchange interaction generated by the conduction electron states the list of heavy fermion metals that are known to exhibit ferro- 1 magnetic order continues to grow. An early example subjected to that are not included in Eq. Incorporating this explicit ex- change interaction term allows the study of the global phase dia- extensive studies is CeRu2Ge2 (ref. 4 and references therein). Other ferromagnetic heavy fermion metals include CePt (5), gram of the Kondo lattice systems, and tuning a control para- 0 15 meter in any specific heavy fermion material represents taking CeSix (6), CeAgSb2 (7), and URu2−xRexSi2 at x> . (8, 9). More recently discovered materials include CeRuPO (10) and a cut within this phase diagram. The Hamiltonian above is to be contrasted with models for double-exchange ferromagnets UIr2Zn20 (11). Finally, systems such as UGe2 (12) and URhGe (13) are particularly interesting because they exhibit a supercon- in the context of, for example, manganites, where it is the “Kondo” coupling that is ferromagnetic due to Hund’s rule. ducting dome as their metallic ferromagnetism is tuned toward its ≪ ≪ The parameter region we will focus on is JK jIj W. Here border. Some fascinating and general questions have emerged 0 (14, 15, 16), yet they have hardly been addressed theoretically. we can use the limit JK ¼ as the reference point, which contains One central issue concerns the nature of the Fermi surface: Is the local moments, representing the f-electrons with strong repul- it “large,” encompassing both the local moments and conduction sions, and conduction electrons. As illustrated in Fig. 1, the local 0 electrons as in paramagnetic heavy fermion metals (17, 18), or is moments order in a ferromagnetic ground state because I < , it “small,” incorporating only conduction electrons? Measure- whereas the conduction electrons form a Fermi sea with a Fermi ments of the de Haas–van Alphen (dHvA) effect have suggested surface. A finite but small JK will couple these two components, and its effect is analyzed in terms of a fermion þ boson renorma- that the Fermi surface is small in CeRu2Ge2 (14–16), and have – provided evidence for Fermi surface reconstruction as a function lization group (RG) procedure (27 29). We will use an effective field theory approach, which we outline below and describe in of pressure in UGe2 (19, 20). At the same time, it is traditional to SI Text consider the heavy fermion ferromagnets as having a large Fermi detail in . Though our analysis will focus on this weak surface when their relationship with unconventional supercon- JK regime, the results will be germane to a more extended para- ductivity is discussed (12, 13, 21); an alternative form of the Fermi meter regime through continuity. surface in the ordered state could give rise to a new type of The Heisenberg part of the Hamiltonian, describing the local superconductivity near its phase boundary. All these point to moments alone, is mapped to a continuum field theory (30) in the σ the importance of theoretically understanding the ferromagnetic form of a Quantum Nonlinear Sigma Model (QNL M). In this phases of heavy fermion metals, and this will be the focus of the framework, the local moments are represented by an O(3) field, present work. We consider the Kondo lattice model in which a periodic array Author contributions: S.J.Y. and Q.S. designed research, performed research, and wrote of local moments interact with each other and with a conduction- the paper. electron band. Kondo lattice systems are normally studied in the The authors declare no conflict of interest. paramagnetic state, where Kondo screening leads to heavy quasi- 1To whom correspondence should be addressed. E-mail: [email protected]. particles in the single-electron excitation spectrum (17). The This article contains supporting information online at www.pnas.org/lookup/suppl/ Stoner (22) mean field treatment of these heavy quasiparticles doi:10.1073/pnas.1009498107/-/DCSupplemental. 15704–15707 ∣ PNAS ∣ September 7, 2010 ∣ vol. 107 ∣ no. 36 www.pnas.org/cgi/doi/10.1073/pnas.1009498107 Downloaded by guest on October 3, 2021 simplification is that the translational symmetry is preserved in the ferromagnetic phase. At the same time, two complications arise. Ferromagnetic order breaks time-reversal symmetry, which is manifested in the Zeeman splitting of the spin up and down bands. In addition, the effective field theory for a local-moment quantum ferromagnet involves a Berry phase term (30) such that Lorentz invariance is broken, even in the continuum limit; the dynamic exponent, connecting ω and q in Eq. 2,isz ¼ 2 instead of 1. The effective field theory, comprising Eqs. 2–5, is subjected to a two-stage RG analysis as detailed in SI Text. Results For energies and momenta above their respective cutoffs, Fig. 1. An illustration of the Kondo lattice. Local moments from f-orbitals ω ∼ ∕ 2 Δ2 ∼ ∕ Δ are in green, and are depicted here to be spin down. Spin-up conduction elec- c ðI W Þ and qc ðKF WÞ , the magnons are coupled trons are in red, which have a higher probability density than the spin-down to the continuum part of the transverse spin excitations of the conduction electrons in blue. The Hamiltonian for the model is given in Eq. 1 conduction electrons, see Fig. 2. Here, the Kondo coupling is re- where σ is the spin index and a refers to the three spin directions. Note that levant in the RG sense below three dimensions. This implies the Einstein summation convention is used on indices. For simplicity, we as- strong coupling between the conduction electrons and the local K2 sume ϵ ~ . The characteristic kinetic energy, W, is defined as W ≡ 1∕ρ0, σ K ¼ 2me moments, and both the QNL M as well as the action for the con- ρ ≡ ∑ δ E − ϵ where 0 K~ ð F K~Þ is the single-particle density of states at the Fermi duction electrons will be modified. Explicitly, the correction to energy (EF ). Both EF and the chemical potential, μ, scale like W. We use the the quadratic part of the QNLσMis ~ Shankar notation with K ¼jKj measured from the center of the Brillouin ω zone. Π ω ≈ 2 ρ 1 γ [6] ðq;~ Þ JK 0 þ i vFq m~, which is constrained nonlinearly with a continuum partition function. Combining the local moments with the conduction elec- where γ is a dimensionless constant prefactor. At the same time, trons, we reach the total partition function: Z ¼ ∫ Dm~D½ψ¯;ψ the conduction electrons acquire the following self-energy δ ~2 ~τ − 1 −S S S S0 S ðm ðx; Þ Þe , where ¼ m þ c þ K .
Load more

Recommended publications
  • Fermi Surface of Copper Electrons That Do Not Interact
    StringString theorytheory andand thethe mysteriousmysterious quantumquantum mattermatter ofof condensedcondensed mattermatter physics.physics. Jan Zaanen 1 String theory: what is it really good for? - Hadron (nuclear) physics: quark-gluon plasma in RIHC. - Quantum matter: quantum criticality in heavy fermion systems, high Tc superconductors, … Started in 2001, got on steam in 2007. Son Hartnoll Herzog Kovtun McGreevy Liu Schalm 2 Quantum critical matter Quark gluon plasma Iron High Tc Heavy fermions superconductors superconductors (?) Quantum critical Quantum critical 3 High-Tc Has Changed Landscape of Condensed Matter Physics High-resolution ARPES Magneto-optics Transport-Nernst effect Spin-polarized Neutron STM High Tc Superconductivity Inelastic X-Ray Scattering Angle-resolved MR/Heat Capacity ? Photoemission spectrum Hairy Black holes … 6 Holography and quantum matter But first: crash course in holography “Planckian dissipation”: quantum critical matter at high temperature, perfect fluids and the linear resistivity (Son, Policastro, …, Sachdev). Reissner Nordstrom black hole: “critical Fermi-liquids”, like high Tc’s normal state (Hong Liu, John McGreevy). Dirac hair/electron star: Fermi-liquids emerging from a non Fermi liquid (critical) ultraviolet, like overdoped high Tc (Schalm, Cubrovic, Hartnoll). Scalar hair: holographic superconductivity, a new mechanism for superconductivity at a high temperature (Hartnoll, Herzog,Horowitz) . 7 General relativity “=“ quantum field theory Gravity Quantum fields Maldacena 1997 = 8 Anti de Sitter-conformal
    [Show full text]
  • Chapter 13 Ideal Fermi
    Chapter 13 Ideal Fermi gas The properties of an ideal Fermi gas are strongly determined by the Pauli principle. We shall consider the limit: k T µ,βµ 1, B � � which defines the degenerate Fermi gas. In this limit, the quantum mechanical nature of the system becomes especially important, and the system has little to do with the classical ideal gas. Since this chapter is devoted to fermions, we shall omit in the following the subscript ( ) that we used for the fermionic statistical quantities in the previous chapter. − 13.1 Equation of state Consider a gas ofN non-interacting fermions, e.g., electrons, whose one-particle wave- functionsϕ r(�r) are plane-waves. In this case, a complete set of quantum numbersr is given, for instance, by the three cartesian components of the wave vector �k and thez spin projectionm s of an electron: r (k , k , k , m ). ≡ x y z s Spin-independent Hamiltonians. We will consider only spin independent Hamiltonian operator of the type ˆ 3 H= �k ck† ck + d r V(r)c r†cr , �k � where thefirst and the second terms are respectively the kinetic and th potential energy. The summation over the statesr (whenever it has to be performed) can then be reduced to the summation over states with different wavevectork(p=¯hk): ... (2s + 1) ..., ⇒ r � �k where the summation over the spin quantum numberm s = s, s+1, . , s has been taken into account by the prefactor (2s + 1). − − 159 160 CHAPTER 13. IDEAL FERMI GAS Wavefunctions in a box. We as- sume that the electrons are in a vol- ume defined by a cube with sidesL x, Ly,L z and volumeV=L xLyLz.
    [Show full text]
  • Science Journals
    SCIENCE ADVANCES | RESEARCH ARTICLE PHYSICS Copyright © 2019 The Authors, some Orbital-selective Kondo lattice and enigmatic f electrons rights reserved; exclusive licensee emerging from inside the antiferromagnetic phase American Association for the Advancement of a heavy fermion of Science. No claim to original U.S. Government 1 1 1 2,3 4 Works. Distributed Ioannis Giannakis , Justin Leshen , Mariam Kavai , Sheng Ran *, Chang-Jong Kang , under a Creative 2,3 2,5 2 2 6,7 6 Shanta R. Saha , Y. Zhao ,Z.Xu*, J. W. Lynn , Lin Miao , L. Andrew Wray , Commons Attribution 4,8 2,3 1† Gabriel Kotliar , Nicholas P. Butch , Pegor Aynajian NonCommercial License 4.0 (CC BY-NC). Novel electronic phenomena frequently form in heavy-fermions because of the mutual localized and itinerant na- ture of f-electrons. On the magnetically ordered side of the heavy-fermion phase diagram, f-moments are expected to be localized and decoupled from the Fermi surface. It remains ambiguous whether Kondo lattice can develop inside the magnetically ordered phase. Using spectroscopic imaging with scanning tunneling microscope, complemented by neutron scattering, x-ray absorption spectroscopy, and dynamical mean field theory, we probe Downloaded from the electronic states in antiferromagnetic USb2. We visualize a large gap in the antiferromagnetic phase within which Kondo hybridization develops below ~80 K. Our calculations indicate the antiferromagnetism and Kondo lattice to reside predominantly on different f-orbitals, promoting orbital selectivity as a new conception into how these phenomena coexist in heavy-fermions. Finally, at 45 K, we find a novel first order–like transition through abrupt emergence of nontrivial 5f-electronic states that may resemble the “hidden-order” phase of URu2Si2.
    [Show full text]
  • Extent of Fermi-Surface Reconstruction in the High-Temperature Superconductor Hgba2cuo4+Δ
    Extent of Fermi-surface reconstruction in the high-temperature superconductor HgBa2CuO4+δ Mun K. Chana,1, Ross D. McDonalda, Brad J. Ramshawd, Jon B. Bettsa, Arkady Shekhterb, Eric D. Bauerc, and Neil Harrisona aPulsed Field Facility, National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA; bNational High Magnetic Field Laboratory, Florida State University, Tallahassee, Forida 32310, USA; cLos Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA; dLaboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 148.3, USA This manuscript was compiled on June 17, 2020 High magnetic fields have revealed a surprisingly small Fermi- change at TH ≈ 20 K. These results attest to the high-quality surface in underdoped cuprates, possibly resulting from Fermi- of the present crystals and confirm prior results indicating surface reconstruction due to an order parameter that breaks trans- Fermi-surface reconstruction in Hg1201 at similar doping lev- lational symmetry of the crystal lattice. A crucial issue concerns els (6,9, 10). the doping extent of this state and its relationship to the principal We have also found a peak in the planar resistivity ρ(T ) pseudogap and superconducting phases. We employ pulsed mag- at high fields, Figs.1C&D. ρ(T ) upturns at a temperature netic field measurements on the cuprate HgBa2CuO4+δ to identify coincident with the steep downturn in Rxy(T ), as shown in signatures of Fermi surface reconstruction from a sign change of the Fig.1D and SI Appendix Fig. S7. The common character- Hall effect and a peak in the temperature-dependent planar resistiv- istic temperatures suggest the features in ρ(T ) are related ity.
    [Show full text]
  • Chapter 6 Free Electron Fermi Gas
    理学院 物理系 沈嵘 Chapter 6 Free Electron Fermi Gas 6.1 Electron Gas Model and its Ground State 6.2 Thermal Properties of Electron Gas 6.3 Free Electrons in Electric Fields 6.4 Hall Effect 6.5 Thermal Conductivity of Metals 6.6 Failures of the free electron gas model 1 6.1 Electron Gas Model and its Ground State 6.1 Electron Gas Model and its Ground State I. Basic Assumptions of Electron Gas Model Metal: valence electrons → conduction electrons (moving freely) ü The simplest metals are the alkali metals—lithium, sodium, 2 potassium, cesium, and rubidium. 6.1 Electron Gas Model and its Ground State density of electrons: Zr n = N m A A where Z is # of conduction electrons per atom, A is relative atomic mass, rm is the density of mass in the metal. The spherical volume of each electron is, 1 3 1 V 4 3 æ 3 ö = = p rs rs = ç ÷ n N 3 è 4p nø Free electron gas model: Suppose, except the confining potential near surfaces of metals, conduction electrons are completely free. The conduction electrons thus behave just like gas atoms in an ideal gas --- free electron gas. 3 6.1 Electron Gas Model and its Ground State Basic Properties： ü Ignore interactions of electron-ion type (free electron approx.) ü And electron-eletron type (independent electron approx). Total energy are of kinetic type, ignore potential energy contribution. ü The classical theory had several conspicuous successes 4 6.1 Electron Gas Model and its Ground State Long Mean Free Path: ü From many types of experiments it is clear that a conduction electron in a metal can move freely in a straight path over many atomic distances.
    [Show full text]
  • Bulk Fermi Surface Coexistence with Dirac Surface State in Bi2se3: a Comparison of Photoemission and Shubnikov–De Haas Measurements
    PHYSICAL REVIEW B 81, 205407 ͑2010͒ Bulk Fermi surface coexistence with Dirac surface state in Bi2Se3: A comparison of photoemission and Shubnikov–de Haas measurements James G. Analytis,1,2 Jiun-Haw Chu,1,2 Yulin Chen,1,2 Felipe Corredor,1,2 Ross D. McDonald,3 Z. X. Shen,1,2 and Ian R. Fisher1,2 1Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA 2Geballe Laboratory for Advanced Materials and Department of Applied Physics, Stanford University, Stanford, California 94305, USA 3Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA ͑Received 2 February 2010; published 5 May 2010͒ Shubnikov-de Haas ͑SdH͒ oscillations and angle-resolved photoemission spectroscopy ͑ARPES͒ are used to probe the Fermi surface of single crystals of Bi2Se3. We find that SdH and ARPES probes quantitatively agree on measurements of the effective mass and bulk band dispersion. In high carrier density samples, the two probes also agree in the exact position of the Fermi level EF, but for lower carrier density samples discrepan- cies emerge in the position of EF. In particular, SdH reveals a bulk three-dimensional Fermi surface for samples with carrier densities as low as 1017 cm−3. We suggest a simple mechanism to explain these differ- ences and discuss consequences for existing and future transport studies of topological insulators. DOI: 10.1103/PhysRevB.81.205407 PACS number͑s͒: 72.20.My, 03.65.Vf, 71.70.Di, 73.25.ϩi Recently, a new state of matter, known as a topological high level of consistency across all samples measured from insulator, has been predicted to exist in a number of materi- the same batch.
    [Show full text]
  • Heavy-Fermion Superconductivity in Cecoin5 at 2.3 K
    Heavy-fermion superconductivity in CeCoIn5 at 2.3 K C. Petrovic1, P.G. Pagliuso2, M.F. Hundley2, R. Movshovich2, J.L. Sarrao2, J.D. Thompson2, Z. Fisk1,2, and P. Monthoux3 1National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32306 USA 2Condensed Matter and Thermal Physics, Los Alamos National Laboratory, Los Alamos, NM 87545 USA 3Cavendish Laboratory, University of Cambridge, Cambridge CB3 OHE, UK Abstract We report the observation of heavy-fermion superconducitivity in CeCoIn5 at Tc=2.3 K. When compared to the pressure-induced Tc of its cubic relative CeIn3 (Tc~200 mK), the Tc of CeCoIn5 is remarkably high. We suggest that this difference may arise from magnetically mediated superconductivity in the layered crystal structure of CeCoIn5. Superconductivity is distinct in the correlation often evident between structure and properties: certain crystal structures or substructures favor superconductivity.1 In particular, what underlies this relationship in the high-Tc cuprates and heavy-Fermion materials, which border so closely on magnetically ordered phases, is of essential interest both fundamentally and in the search for new superconducting materials.2,3 For example, fully half of the known heavy-Fermion superconductors crystallize in the tetragonal ThCr2Si2 structure, which is also the structure type of the La2CuO4 family of high-Tc superconductors.4 In the cuprates, there is no consensus on the origin of superconductivity, but their quasi-2D structure and proximity to magnetic order have been shown to be particularly favorable for an unconventional form of superconductivity in which a pairwise attractive interaction among quasiparticles is mediated by magnetic correlations.5 Here, we report the discovery of a possible heavy-Fermion analogue of the cuprates, a new layered superconductor CeCoIn5, with the highest known ambient- pressure superconducting transition temperature Tc in the class of heavy-Fermion materials.
    [Show full text]
  • Universality in Fermi Liquids
    1 Universality in Fermi Liquids Petr Hoˇrava Center for Theoretical Physics, University of California, Berkeley and Lawrence Berkeley National Laboratory 1 Universality in Fermi Liquids, D-Branes and K-Theory Petr Hoˇrava Center for Theoretical Physics, University of California, Berkeley and Lawrence Berkeley National Laboratory 1 Universality in Fermi Liquids, D-Branes and K-Theory Petr Hoˇrava Center for Theoretical Physics, University of California, Berkeley and Lawrence Berkeley National Laboratory hep-th/0503006, Phys. Rev. Lett. (2005) 2 What is this about? This is a colloquium about condensed matter physics . 2 What is this about? This is a colloquium about condensed matter physics . or perhaps about string theory . 2 What is this about? This is a colloquium about condensed matter physics . or perhaps about string theory . or the mathematics of K-theory . 2 What is this about? This is a colloquium about condensed matter physics . or perhaps about string theory . or the mathematics of K-theory . In fact, it is a review of a field that does not quite exist yet! Stanis law Lem 3 More seriously . I will present: • Motivation (from string theory) • Hard-core results (in condensed matter) • Speculations (mostly about string theory again) 4 Outline • Preliminaries: Strings and D-branes D-branes: nonperturbative solitonic defects in string theory Goal in string theory: Understand the underlying degrees of freedom. 4 Outline • Preliminaries: Strings and D-branes D-branes: nonperturbative solitonic defects in string theory Goal in string theory: Understand the underlying degrees of freedom. • D-branes and K-theory Classification of D-branes desired: D-brane charges classified by a generalized cohomology theory, known as “K-theory” 5 • Preliminaries II: Fermi liquids in d dimensions Universality classes of nonrelativistic quantum systems described microscopically by ψ(x, t).
    [Show full text]
  • Fermi Surface Manipulation by External Magnetic Field Demonstrated for a Prototypical Ferromagnet
    PHYSICAL REVIEW X 6, 041048 (2016) Fermi Surface Manipulation by External Magnetic Field Demonstrated for a Prototypical Ferromagnet E. Młyńczak,1,2,* M. Eschbach,1 S. Borek,3 J. Minár,3,4 J. Braun,3 I. Aguilera,1 G. Bihlmayer,1 S. Döring,1 M. Gehlmann,1 P. Gospodarič,1 S. Suga,1,5 L. Plucinski,1 S. Blügel,1 H. Ebert,3 and C. M. Schneider1 1Peter Grünberg Institut PGI, Forschungszentrum Jülich and JARA- Fundamentals of Future Information Technologies, 52425 Jülich, Germany 2Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland 3Department Chemie, Ludwig-Maximilians-Universität München, Butenandtstrasse 5-13, 81377 München, Germany 4New Technologies-Research Centre, University of West Bohemia, Univerzitni 8, 306 14 Pilsen, Czech Republic 5Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, Japan (Received 1 May 2016; revised manuscript received 12 October 2016; published 9 December 2016) We consider the details of the near-surface electronic band structure of a prototypical ferromagnet, Fe(001). Using high-resolution angle-resolved photoemission spectroscopy, we demonstrate openings of the spin-orbit-induced electronic band gaps near the Fermi level. The band gaps, and thus the Fermi surface, can be manipulated by changing the remanent magnetization direction. The effect is of the order of ΔE ¼ 100 meV and Δk ¼ 0.1 Å−1. We show that the observed dispersions are dominated by the bulk band structure. First-principles calculations and one-step photoemission calculations suggest that the effect is related to changes in the electronic ground state and not caused by the photoemission process itself.
    [Show full text]
  • Arxiv:2103.03256V3 [Cond-Mat.Str-El] 5 Jul 2021 Tunneling Spectra[9, 10, 12, 13] with a Distinct Asym- Metry in Terms of Particle Addition and Removal
    Doped Mott Insulators Break Z2 Symmetry of a Fermi Liquid: Stability of Strongly Coupled Fixed Points 1, 2, 1, Edwin W. Huang, ∗ Gabriele La Nave, ∗ and Philip W. Phillips ∗ 1Department of Physics and Institute for Condensed Matter Theory, University of Illinois, 1110 W. Green Street, Urbana, IL 61801 2Department of Mathematics, University of Illinois, Urbana, Il. 61820 While the Mott transition from a Fermi liquid is correctly believed to obtain without the breaking of any continuous symmetry, we show that in fact a discrete Z2 symmetry of the Fermi surface is bro- ken. The extra Z2 symmetry of the Fermi liquid appears to be little known although it was pointed out by Anderson and Haldane[1] and we use it here to classify all possible Fermi liquids topologi- cally by invoking K-homology. It is this Z2 symmetry breaking that signals the onset of particle-hole asymmetry, a widely observed[2{10] phenomenon in strongly correlated systems. In addition from this principle, we are able to classify which interactions suffice to generate the Z2-symmetry-broken phase. As this is a symmetry breaking in momentum space, the local-in-momentum space inter- action of the Hatsugai-Kohmoto (HK)[11] model suffices as well as the Hubbard interaction as it contains the HK interaction. We then use the Bott topological invariant to establish the stability of a Luttinger surface. Our proof demonstrates that the strongly coupled fixed point only corresponds to those Luttinger surfaces with co-dimension p + 1 with p odd. We conclude that the Hubbard and HK models both lie in the same high temperature universality class and are controlled by this fixed point.
    [Show full text]
  • Solid State Physics NEARLY FREE ELECTRON MODEL
    Solid State Physics NEARLY FREE ELECTRON MODEL (Contd) Lecture 19 A.H. Harker Physics and Astronomy UCL 7.3 An exactly-soluble model We know from second-year quantum mechanics that square well po- tentials are quite easy to deal with. The Kronig-Penney model is based on this. For details of the calculation, see for example Kittel Introduction to Solid State Physics. 2 We can seen the gaps in the energy spectrum – regions of energy in which there are no allowed states. 3 The free electron approximation remains a good approximation well away from the edges of the Brillouin zone – only wave-vectors close to a multiple of π/a are mixed together and have their energies altered by the periodic potential. Translational symmetry is not essential for producing a band gap – amorphous solids also have band gaps. 4 7.4 Sketching energy bands 7.4.1 The empty lattice Imagine first that the periodic crystal potential is vanishingly small. Then we want to impose periodic structure without distorting the free electron dispersion curves.We now have E(k) = E(k + G), where G is a reciprocal lattice vector. We can use the extended zone scheme (left) or displace all the seg- ments of the dispersion curve back into the first Brillouin zone (right). 5 7.4.2 The nearly free electron Modify the free electron picture by opening up small gaps near the zone boundaries. 6 7.5 Consequences of the energy gap 7.5.1 Density of states The number of allowed k values in a Brillouin zone is equal to the number of unit cells in the crystal.
    [Show full text]
  • 1 Introduction
    Catalysis, Heavy Fermions, Solitons, Cold Fusion, Low Energy Nuclear Reactions (LENR) and all that M. W. Kalinowski IMDIK PAN Pracownia Bioinformatyki ul. Pawi´nskiego5, 02-106 Warsaw, Poland e-mails: markwkalbioexploratorium.pl, mkalinowskiimdik.pan.pl, phone: +48228499358 To the memory of my friend Stanis law Radzki, a chemist with wide horizons Abstract. We consider in the paper an idea of a soliton and heavy fermion catalysis for a cold fusion similar to a muon catalysis. This catalysis is achieved via quasi- chemical bonds for heavy fermions and solitons as well. We consider also a soliton catalysis (for KP-solutions), which is quite different. This kind of catalysis is similar to enzymatic catalysis. In the paper we construct a model for a cold fusion reactor based on Onsager{Prigogine irreversible thermodynamics. We give examples of several compounds with heavy fermions (heavy electrons) which are hydrogen storages. Samples of those compounds can be (in principle) cold fusion reactors if filled with a deuter. It is necessary to do several experiments (de- scribed in the paper) in order to find a proper compound which will be a base for a battery device. We consider also a case with cold plasma (e.g. in metals) filled with a deuter. Solitons in a plasma can catalyse a fusion in two regimes: as quasiparticles and in enzymatic-like regime. Key words: solitons, heavy fermions, cold fusion, catalysis, hydrogen storage, low energy nuclear reactions, chemically assisted nuclear reactions, quasi-chemical bonds, KdV equation, plasma physics, KP equations, Onsager{Prigogine principle, deuter, quasiparticles. 1 Introduction In the paper we consider three types of catalysis for a cold fusion: heavy fermion, 1-soliton and n-soliton.
    [Show full text]