DOCSLIB.ORG

PH575 Spring 2014 Lecture #18 Free Electron Theory

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
PH575 Spring 2014 Lecture #18 Free Electron Theory PH575 Spring 2014 Lecture #18 Free electron theory: Sutton Ch. 7 pp 132 -> 144; Kittel Ch. 6. V 2m 3/2 2 2 " % 1/2 k D(E) = 2 $ 2 ' E E(k) = 2π # & 2m Assumption: electrons metal do not interact with each other, not with the potential due to the ions EXCEPT that the ion potential confines them to the region of space occupied by the material. We will see that this assumption leads to a spherical Fermi surface and explains the properties of simple metals. It does not predict gaps in the band structure, but it is remarkable that the theory works as well as it does, and it improves the classical Drude model that is still used with success. Paul Drude (1863-1906) Free electron bands & LCAO (tight binding) bands are qualitatively similar, with important exception of gaps. (Sutton, Fig. 7.6, Ge e.g.) So free electron model works well only for metals. FE bands (Na) LCAO band (Na) http://physics.njit.edu/~savrasov/Projects/Teaching/Phys%20485%20SPRING%202004/Lecture21Topics.htm Energy "Jellium" - free electrons a uniform positive BG 0 PE +PBC -V0 0 vacuum Metal, L vacuum L ˆ 1 ik⋅r H ψ k = Ek ψ k ψ k (r ) = e V 2 # d 2 d 2 d 2 & − Similar to % 2 + 2 + 2 ( ψ k = Ek ψ k 2m $dx dy dz ' Bloch form 2 2 2 2 − " d d d % 1 ik⋅r r e $ 2 + 2 + 2 'ψ k (r ) = Ekψ k (r ) ψ k ( ) = 2m #dx dy dz & V r = xxˆ + yyˆ + zzˆ; r = r = x2 + y2 + z2 k = k xˆ + k yˆ + k zˆ; k = k = k 2 + k 2 + k 2 x y z x y z E k = ?; k = ? k = ? k = ? ( ) x y z 2 2 2π 2π 2π k k = n ; k = n ; k = n E(k) = x x L y y L z z L 2m E0 kx ky 2 Free electron bands: square lattice 2 k + G E = 2m E kx (ky= 0) 2π 2π Real space Reciprocal G = a (0,0) G = a (±1,±1) 2π 2π 2π a1 = a(1,0) g1 = a (0,1) G = a (±1,0) G = a (0,2) a = a 0,1 g = 2π 1,0 2π 2π 2 ( ) 2 a ( ) G = a (0,1) G = a (±2,0) 2 Free electron bands: fcc lattice 2 k + G E = 2m From Hummel, Electronic Properties of Materials 2 Free electron bands: fcc lattice 2 k + G Example Copper E = 2m <- Calculated with pseudopotential methods. Note d-bands! <- Free electron bands From Tsymbal (UNL) There is a gap in the energy spectrum! This same result can be obtained by treating the periodic ion potential as a perturbation of the smooth potential (we won't do this, but it's discussed in Kittel, for example) http://www.chembio.uoguelph.ca/educmat/chm753/properties/electronic/nearly_free_model.html Free electrons (plane waves) don't interact with the lattice much until the wave vector becomes comparable with 1/a, then they are Bragg reflected and there is interference between oppositely directed plane waves (standing waves). Lower energy state piles up electron density on the atoms (stronger Coulomb attraction to cores), while the higher energy state piles up electron density between the atoms. Thus there is a gap in the energy spectrum! eikx − e−ikx sin(kx) eikx + e−ikx cos(kx) http://www.chembio.uoguelph.ca/educmat/chm753/properties/electronic/nearly_free_model.html Constant energy surfaces are spheres in k space Each state occupies 8π3/L3 in k-space When all N valence electrons have filled up k-states, reach the Fermi Energy EF and the sphere has radius Fermi wave vector kF 3 3 2 2 8π 1 4πkF kF N ≡ EF = V 2 3 2m Factor of 2 is from spin (2 electrons/state) 2 k 2 2π 2π 2π E(k) = kx = nx ; ky = ny ; kz = nz 2m L L L E0 kx ky Fermi parameters (see Kittel Ch.6, Table I): 1/3 " 2 % 8 -1 k 3 n kF = 0.92 × 10 cm : F = $ π ' # # e/vol& 2 k 2 F E = 3.2 eV: kinetic energy of Fermi level e EF = F 2m EF TF = 37,500 K: temp. above which e obey classical TF = statistics (can ignore quantum effects) kB k F v = 1.1 × 108 cm s-1 : 1% c vF = F m Sodium: n = 2.65 × 1022 e-/cm3 Reminder: 3-D Density of states for free electron: dS S counts the states. D(E) = ⇒ dS = D(E)dE dE 2 k 2 dE 2 k E = ; = dS = D (k) × annular vol of k-space 2m dk m 2V 2 = 3 × 4πk dk 2π ( ) E0 E0 + dE 2V 2 D (E)dE = 3 4πk dk (2π ) 8πk 2V dk k x D (E) = 3 (2π ) dE 3/2 V " 2m% 1/2 D (E) = 2 $ 2 ' E 2π # & ky Example: Find total energy at T = 0 (homework) Will use this later for electronic specific heat. EF E = E D E dE Tot ∫ ( ) 0 E E + dE 0 0 Total energy at T ≠ 0 ∞ E = E f E D E dE Tot ∫ ( ) ( ) kx 0 ∞ 1 = E D(E)dE ∫ (E−EF )/kBT 0 e +1 ky Fermi Function • Probability that a state of energy E is occupied at temperature T. • f(µ) = 0.5 • Varies sharply over width of ≈kBT about EF. Step function T = 0. 1 µ = 1eV f (E) = E − µ T = 0.015 eV = ?K e kBT + 1 T = 0.3 eV = ?K f E 0.5 1.0 0.4 0.8 kBT ⇥ k T 0.6 B 0.3 0.4 0.2 0.2 kBT 0.1 E eV 0.5 1.0 1.5 2.0 0.0 0.0 0.5 1.0 1.5 2.0 E ⇥ Electronic specific heat • Electrons are a repository of energy in metals and contribute to the specific heat. Dominant contribution at low T where phonons are frozen out. • If electrons are a "classical gas" (no QM), equipartition theorem => electronic energy is Eelec = (3/2)kBT. Electronic specific heat is Celec = dEelec/dT= (3/2)kB • Actual values in metals at low temperatures are less than 1% of this, and are NOT temperature independent. http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi2.html Electronic specific heat Nearly free electrons are a repository of energy in metals and contribute to the specific heat. At low temperatures, when phonons (lattice vibrations) are frozen out, this contribution dominates. ∞ E = E f E D E dE Tot ∫ ( ) ( ) df (E,T ) 0 dT ∞ 1 = E D(E)dE ∫ (E−µ)/kBT 0 e +1 many functions 2.0 1.5 3/2 1.0 V " 2m% 1/2 kBT 0.5 D(E) = 2 $ 2 ' E 2π # & E eV 0.5 1.0 1.5 2.0 0.5 1.0 ⇥ ∞ dETot df (E,T ) C = = E D E dE v ∫ ( ) dT 0 dT Area under black curve is electronic specific heat. Very slight asymmetry is crucial! Easy enough to calculate numerically, but let's look for analytical insight. What is dominant contribution? Weakest? many functions 2.0 1.5 EF = 1 eV 1.0 kBT = 0.1 eV 0.5 E eV 0.5 1.0 1.5 2.0 0.5 1.0 ⇥ ∞ dETot df (E,T ) C = = E D E dE v ∫ ( ) dT 0 dT D(E) varies slowly - remove from integral (but what value? Why can lower limit of integration be extended to -∞? df (E,T ) = ? dT E − µ Change variables: x = 2kBT ∞ x2 π 2 Helpful: dx = ∫ 2 -∞ cosh x 6 ∞ dETot df (E,T ) C = = E D E dE v ∫ ( ) dT 0 dT 2 π 2 Cv = D(EF )kBT 2 Interpretation: Depends linearly on temperature - NOT independent Size depends only on density of states at Fermi surface - small for semimetals; large for so-called “heavy fermions” Also interpreted as each electron near Fermi surface contributing roughly kB to heat capacity: Cv = D(EF )kBT × kB ∞ dETot df (E,T ) C = = E D E dE v ∫ ( ) dT 0 dT 2 π 2 Cv = D(EF )kBT 2 π 2 T Cv,FE = NkB 2 TF Much smaller than expected from classical theory: 3 C = Nk v,class 2 B electronic phonon C = γ T + AT 3 v,TOT γexpt ! γfe (mJ/mol/K2) (mJ/mol/K2) Cv,TOT Na 1.38 1.09 K 2.08 1.67 Temperature Cu 0.70 0.51 Cv,T O T Zn 0.64 0.75 T Slope A Ag 0.65 0.65 2 Intercept γ T EXTRA SLIDES ABOUT FREE ELECTRON BANDS Free electron bands: square lattice, reduced zone scheme E kx (ky=0) 2 2 k + G E = 2m Free electron bands & LCAO (tight binding) bands are qualitatively similar, with important exception of gaps. (Sutton, Fig. 7.6, Ge e.g.) So free electron model works well only for metals. FE bands (Na - bcc) LCAO band (Na) http://physics.njit.edu/~savrasov/Projects/Teaching/Phys%20485%20SPRING%202004/Lecture21Topics.htm Free electron bands & LCAO (tight binding) bands are qualitatively similar, with important exception of gaps. (Sutton, Fig. 7.6, Ge e.g.) So free electron model works well only for metals. FE bands (Na - bcc) LCAO band (Na) 2 Free electron bands: bcc lattice 2 k + G E = 2m http://www.tf.uni-kiel.de/matwis/amat/semi_en/kap_2/illustr/band_bcc_free.gif .
Load more

Recommended publications
  • Density of States Information from Low Temperature Specific Heat
    JOURNAL OF RESE ARC H of th e National Bureau of Standards - A. Physics and Chemistry Val. 74A, No.3, May-June 1970 Density of States I nformation from Low Temperature Specific Heat Measurements* Paul A. Beck and Helmut Claus University of Illinois, Urbana (October 10, 1969) The c a lcul ati on of one -electron d ensit y of s tate va lues from the coeffi cient y of the te rm of the low te mperature specifi c heat lin ear in te mperature is compli cated by many- body effects. In parti c ul ar, the electron-p honon inte raction may enhance the measured y as muc h as tw ofo ld. The e nha nce me nt fa ctor can be eva luat ed in the case of supe rconducting metals and a ll oys. In the presence of magneti c mo­ ments, add it ional complicati ons arise. A magneti c contribution to the measured y was ide ntifi e d in the case of dilute all oys and a lso of concentrated a lJ oys wh e re parasiti c antife rromagnetis m is s upe rim­ posed on a n over-a ll fe rromagneti c orde r. No me thod has as ye t bee n de vised to e valu ate this magne ti c part of y. T he separati on of the te mpera ture- li near term of the s pec ifi c heat may itself be co mpli cated by the a ppearance of a s pecific heat a no ma ly due to magneti c cluste rs in s upe rpa ramagneti c or we ak ly ferromagneti c a ll oys.
    [Show full text]
  • Mixed Valence Driven Heavy-Fermion Behavior and Superconductivity in Kni2se2
    Mixed Valence Driven Heavy-Fermion Behavior and Superconductivity in KNi2Se2 James R. Neilson,1,2† Anna Llobet,3 Andreas V. Stier,2 Liang Wu,2 Jiajia Wen,2 Jing Tao,4 Yimei Zhu,4 Zlatko B. Tesanovic,2 N. P. Armitage,2 and Tyrel M. McQueen1,2* 1 Department of Chemistry, Johns Hopkins University, Baltimore MD. 2 Institute for Quantum Matter, and Department of Physics and Astronomy, Johns Hopkins University, Baltimore MD. 3 Lujan Neutron Scattering Center, Los Alamos Neutron Science Center, Los Alamos National Laboratory, Los Alamos, NM. 4 Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY. †[email protected] *[email protected] Based on specific heat and magnetoresistance measurements, we report that a “heavy” electronic state exists below T ≈ 20 K in KNi2Se2, with an increased carrier mobility and enhanced effective electronic band mass, m* = 6mb to 18mb. This “heavy” state evolves into superconductivity at Tc = 0.80(1) K. These properties resemble that of a many-body heavy-fermion state, which derives from the hybridization between localized magnetic states and conduction electrons. Yet, no evidence for localized magnetism or magnetic order is found in KNi2Se2 from magnetization measurements or neutron diffraction. Instead, neutron pair-distribution-function analysis reveals the presence of local charge-density-wave distortions that disappear on cooling, an effect opposite to what is typically observed, suggesting that the low-temperature electronic state of KNi2Se2 arises from cooperative Coulomb interactions and proximity to, but avoidance of, charge order. Introduction Methods KNi Se was synthesized from the elements as a Many-body states, in which complex phenomena 2 2 polycrystalline, lustrous, purple-red powder, as previously arise from simple interactions, often exhibit rich phase described12; the same batch of sample was used for all diagrams and lack formal predictive theories.
    [Show full text]
  • Phonons – Thermal Properties
    Phonons – Thermal properties Till now everything was classical – no quantization, no uncertainty.... WHY DO WE NEED QUANTUM THEORY OF LATTICE VIBRATIONS? Classical – Dulong Petit law All energy values are allowed – classical equipartition theorem – energy per degree of freedom is 1/2kBT. Total energy independent of temperature! Detailed calculation gives C = 3NkB In reality C ~ aT +bT3 Figure 1: Heat capacity of gold Need quantum theory! Quantum theory of lattice vibrations: Hamiltonian for 1D linear chain Interaction energy is simple harmonic type ~ ½ kx2 Solve it for N coupled harmonic oscillators – 3N normal modes – each with a characteristic frequency where p is the polarization/branch. Energy of any given mode is is the zero-point energy th is called ‘excitation number’ of the particular mode of p branch with wavevector k PH-208 Phonons – Thermal properties Page 1 Phonons are quanta of ionic displacement field that describes classical sound wave. Analogy th with black body radiation - ni is the number of photons of the i mode of oscillations of the EM wave. Total energy of the system E = is the ‘Planck distribution’ of the occupation number. Planck distribution: Consider an ensemble of identical oscillators at temperature T in thermal equilibrium. Ratio of number of oscillators in (n+1)th state to the number of them in nth state is So, the average occupation number <n> is: Special case of Bose-Einstein distribution with =0, chemical potential is zero since we do not directly control the total number of phonons (unlike the number of helium atoms is a bath – BE distribution or electrons in a solid –FE distribution), it is determined by the temperature.
    [Show full text]
  • Thermodynamics of the Magnetic-Field-Induced "Normal
    Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2010 Thermodynamics of the Magnetic-Field- Induced "Normal" State in an Underdoped High T[subscript c] Superconductor Scott Chandler Riggs Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCES THERMODYNAMICS OF THE MAGNETIC-FIELD-INDUCED “NORMAL” STATE IN AN UNDERDOPED HIGH TC SUPERCONDUCTOR By SCOTT CHANDLER RIGGS A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy Degree Awarded: Summer Semester, 2010 The members of the committee approve the dissertation of Scott Chandler Riggs defended on March 27, 2010. Gregory Scott Boebinger Professor Directing Thesis David C. Larbalestier University Representative Jorge Piekarewicz Committee Member Nicholas Bonesteel Committee Member Luis Balicas Committee Member Approved: Mark Riley, Chair, Department of Physics Joseph Travis, Dean, College of Arts and Sciences The Graduate School has verified and approved the above-named committee members. ii ACKNOWLEDGMENTS I never thought this would be the most difficult section to write. From Tally, I’d have to start off by thanking Tim Murphy for letting me steal...er...borrow way too much from the instrumentation shop during the initial set-up of Greg’s lab. I still remember that night on the hybrid working with system ”D”. After that night it became clear that ”D” stands for Dumb. To Eric Palm, thank you for granting more power during our specific heat experiments. We still hold the record for most power consumed in a week! To Rob Smith, we should make a Portland experience every March.
    [Show full text]
  • Specific Heat
    8 Specific Heat more complicated, because not only standard repre- Electronic States of; Lattice Dynamics: Vibrational Modes; sentations but projective representations also occur. Periodicity and Lattices; Point Groups; Quantum Mechan- Finally, a basis for the full state space can be con- ics: Foundations; Quasicrystals; Scattering, Elastic structed as follows. The group of k is a subgroup of (General). the space group G. G can be decomposed according to PACS: 61.50.Ah; 02.30. À a G ¼ Gk þ g2Gk þ ? þ gsGk where the space group elements gi have homogeneous Further Reading parts Ri for which Rik ¼ ki. Then the basis is defined as C Cornwell JF (1997) Group Theory in Physics . San Diego: Aca- ij ¼ Tgi cj ½23 demic Press. Hahn Th. (ed.) (1992) Space-Group Symmetry. In: International The dimension of the representation is sd , where s is Tables for Crystallography. vol. A, Dordrecht: Kluwer. the number of points ki, and d the dimension of the Hahn T and Wondratschek H (1994) Symmetry of Crystals: In- point group representation D(Kk). The irreducible troduction to International Tables for Crystallography. vol. A . representation carried by the state space then is char- Sofia, Bulgaria: Heron Press. acterised by the so-called ‘‘star’’ of k (all vectors k ), Janssen T (1973) Crystallographic Groups. North-Holland: Am- i sterdam. and an irreducible representation of the point group Janssen T, Janner A, Looijenga-Vos A, and de Wolff PM (1999) Kk. This means that electronic states and phonons can Incommensurate and commensurate modulated structures. be characterized by k, v. Their transformation prop- In: Wilson AJC and Prince E, International Tables for erties under space group transformations follows from Crystallography, vol.
    [Show full text]
  • Phonon, Magnon and Electron Contributions to Low Temperature Specific Heat in Metallic State of La0·85Sr0·15Mno3 and Er0·8Y0·2Mno3 Manganites
    Bull. Mater. Sci., Vol. 36, No. 7, December 2013, pp. 1255–1260. c Indian Academy of Sciences. Phonon, magnon and electron contributions to low temperature specific heat in metallic state of La0·85Sr0·15MnO3 and Er0·8Y0·2MnO3 manganites DINESH VARSHNEY1,∗, IRFAN MANSURI1,2 and E KHAN1 1Materials Science Laboratory, School of Physics, Devi Ahilya University, Khandwa Road Campus, Indore 452 001, India 2Deparment of Physics, Indore Institute of Science and Technology, Pithampur Road, Rau, Indore 453 331, India MS received 19 June 2012; revised 21 August 2012 Abstract. The reported specific heat C (T) data of the perovskite manganites, La0·85Sr0·15MnO3 and Er0·8Y0·2MnO3, is theoretically investigated in the temperature domain 3 ≤ T ≤ 50 K. Calculations of C (T) have been made within the three-component scheme: one is the fermion and the others are boson (phonon and magnon) contributions. Lattice specific heat is well estimated from the Debye temperature for La0·85Sr0·15MnO3 and Er0·8Y0·2MnO3 manganites. Fermion component as the electronic specific heat coefficient is deduced using the band structure calculations. Later on, following double-exchange mechanism the role of magnon is assessed towards spe- cific heat and found that at much low temperature, specific heat shows almost T3/2 dependence on the temperature. The present investigation allows us to believe that electron correlations are essential to enhance the density of states over simple Fermi-liquid approximation in the metallic phase of both the manganite systems. The present numerical analysis of specific heat shows similar results as those revealed from experiments. Keywords. Oxide materials; crystal structure; specific heat; phonon.
    [Show full text]
  • Phys 446 Solid State Physics Lecture 7 (Ch. 4.1 – 4.3, 4.6.) Last Time
    Phys 446 Solid State Physics Electrons in metals: free electron model Lecture 7 • Simplest way to represent the electronic structure of metals (Ch. 4.1 – 4.3, 4.6.) • Although great simplification, works pretty well in many cases, describes many important properties of metals Last time: • In this model, the valence electrons of free atoms become conduction electrons in crystal and travel freely Finished with phonons, optical and thermal properties. • Neglect the interaction of conduction electrons with ions of the lattice and the interaction between the conduction electrons – a free electron gas Today: Start with electronic properties of metals. • Fundamental difference between the free electron gas and ordinary gas of molecules: Free electron model. 1) electrons are charged particles ⇒ to maintain the charge neutrality of Fermi energy. the whole crystal, we need to include positive ions. This is done within the jelly model : the positive charge of ions is smeared Density of states. out uniformly throughout the crystal - charge neutrality is maintained, no field on the electrons exerted Electronic heat capacity 2) Free electron gas must satisfy the Pauli exclusion principle, which Lecture 7 leads to important consequences. Free electron gas in one dimension What is Hamiltonian? Assume an electron of mass m is confined to a length L by infinite barriers Schrödinger equation for electron wave function ψn(x): En - the energy of electron orbital assume the potential lies at zero ⇒ H includes only the kinetic energy ⇒ Note: this is a one-electron equation – neglected electron-electron interactions General solution: Asin qnx+ Bcos qnx boundary conditions for the wave function: ⇒ B = 0; qn = πn/L ; n -integer Substitute, obtain the eigenvalues: Fermi energy First three energy levels and wave-functions of a free electron of mass m confined to a line of length L: We need to accommodate N valence electrons in these quantum states.
    [Show full text]
  • Heavy Fermion Physics
    Heavy Fermion Physics Hua Chen Course: Solid State II, Instructor: Elbio Dagotto, Semester: Spring 2008 Department of Physics and Astronomy, the University of Tennessee at Knoxville, 37996¤ This article is intended to be a very brief review on the most basic facts and concepts of heavy fermion physics. A general overview is given as an introduction. In the following part, the mechanism leading to the formation of heavy fermions is explained briefly, and its connection to Kondo e®ect is emphasized. Then we talk about heavy fermion theories in more detail, where the concepts like Kondo lattice, slave boson are introduced. Then there are two separate parts on Kondo insulators and heavy fermion superconductivity respectively. Keywords: heavy fermion, Kondo e®ect, Kondo insulator, superconductivity I. INTRODUCTION higher than usual, which is the origin of the name heavy fermion (Fig 1). Heavy fermion martials are those metallic compounds which have enormously large e®ective electron masses be- The ¯rst material of this kind in history is CeAl3 low certain temperatures. It is well known that, at tem- alloy, which was discovered by Andres, Graebner and peratures much below the Debye temperature and Fermi Ott [2] in 1975. Since then, bunch of other heavy fermion temperature, the heat capacity of metals can be written materials have been discovered and studied, which in- as the sum of electron and phonon contributions: clude CeCu2Si2, CeCu6, UBe13, UPt3, UCd11,U2Zn17, NpBe , etc. Among them, there are superconductors, 3 13 C = γT + AT (1) antiferromagnets and insulators. However, one common property of these compounds is that one of the con- and the electron term is linear in T and dominant at stituents of each is a rare-earth or actinide atom with low temperatures.
    [Show full text]
  • Specific Heat, Electrical Resistivity and Electronic Band Structure Properties
    www.nature.com/scientificreports OPEN Specific heat, Electrical resistivity and Electronic band structure properties of noncentrosymmetric Received: 22 August 2017 Accepted: 25 October 2017 Th7Fe3 superconductor Published: xx xx xxxx V. H. Tran & M. Sahakyan Noncentrosymmetric superconductor Th7Fe3 has been investigated by means of specific heat, electrical resisitivity measurements and electronic properties calculations. Sudden drop in the resistivity at 2.05 ± 0.15 K and specific heat jump at 1.98 ± 0.02 K are observed, rendering the superconducting transition. A model of two BCS-type gaps appears to describe the zero-magnetic-field specific heat better than those based on the isotropic BCS theory or anisotropic functions. A positive curvature of the upper critical fieldH c2(Tc) and nonlinear field dependence of the Sommerfeld coefficient at 0.4 K qualitatively support the two-gap scenario, which predicts Hc2(0) = 13 kOe. The theoretical densities of states and electronic band structures (EBS) around the Fermi energy show a mixture of Th 6d- and Fe 3d-electrons bands, being responsible for the superconductivity. Furthermore, the EBS and Fermi surfaces disclose significantly anisotropic splitting associated with asymmetric spin-orbit coupling (ASOC). The ASOC sets up also multiband structure, which presumably favours a multigap superconductivity. Electron Localization Function reveals the existence of both metallic and covalent bonds, the latter may have different strengths depending on the regions close to the Fe or Th atoms. The superconducting, electronic properties and implications of asymmetric spin-orbit coupling associated with noncentrosymmetric structure are discussed. Physical properties of noncentrosymmetric superconductors (NSC’s) are particularly interesting as long as the lack of inversion symmetry enhances asymmetric spin - orbit coupling (ASOC), which can remove some degener- acies related to the spin and then the parity conservation becomes violated according the Pauli principle1–4.
    [Show full text]
  • Heavy Fermion Material: Ce Versus Yb Case
    Heavy fermion material: Ce versus Yb case J Flouquet 1, H Harima 2 1/ INAC/SPSMS, CEA-Grenoble, 17 rue des Martyrs, 38054 Grenoble, France 2/ Department of Physics, Graduate School of Science, Kobe University, Kobe, Hyogo 657-8501, Japan Abstract: Heavy fermion compounds are complex systems but excellent materials to study quantum criticality with the switch of different ground states. Here a special attention is given on the interplay between magnetic and valence instabilities which can be crossed or approached by tuning the system by pressure or magnetic field. By contrast to conventional rare earth magnetism or classical s-wave superconductivity, strong couplings may occur with drastic changes in spin or charge dynamics. Measurements on Ce materials give already a sound basis with clear key factors. They have pointed out that close to a magnetic or a valence criticality unexpected phenomena such as unconventional superconductivity, non Fermi liquid behaviour and the possibility of re- entrance phenomena under magnetic field. Recent progresses in the growth of Yb heavy fermion compounds give the perspectives of clear interplays between valence and magnetic fluctuations and also the possibility to enter in new situations such as valence transitions inside a sole crystal field doublet ground state. 1/ Introduction motion, a phenomenon absent in the case of the 3He neutral atom. The interest in heavy fermion materials started three decades ago with the discovery that in a compound (CeAl 3) (1) (figure 1) the extrapolation of the Sommerfeld coefficient γ of the ratio S/T of the entropy (S) by the temperature (T) reaches a value γ near 1 J·mole -1K-2 i.e.
    [Show full text]
  • Searching for Heavy Fermion Materials in Ce Intermetallic Compounds Jinke Tang Iowa State University
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1989 Searching for heavy fermion materials in Ce intermetallic compounds Jinke Tang Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Condensed Matter Physics Commons Recommended Citation Tang, Jinke, "Searching for heavy fermion materials in Ce intermetallic compounds " (1989). Retrospective Theses and Dissertations. 9247. https://lib.dr.iastate.edu/rtd/9247 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS The most advanced technology has been used to photo­ graph and reproduce this manuscript from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are re­ produced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps.
    [Show full text]
  • Experimental Determination Op the Specific Heats of Sodium
    EXPERIMENTAL DETERMINATION OP THE SPECIFIC HEATS OF SODIUM, COBALT, MANGANESE, AND COBALT-IRON BELOW 1°K. DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By ROGER EDGAR GAUMER, B. S. The Ohio State University 1959 Approved by Adviser Department of Hiysics and Astronomy ACKNOWLEDGEMENTS I wish to acknowledge my debt to Dr. C. V. Heer for his continued support and guidance throughout the course of these investigations. Dr. R. A. Erickson should be acknowledged for a variety of invaluable suggestions concerning experimental procedures. To my fellow graduate student, Mr. David Murray, I extend sincere thanks for all manner of help. Finally, I wish to express gratitude to my wife, Suzanne Morrison Gaumer, for unfailing moral support during these lean years. This work was supported in part by funds granted to The Ohio State University by the Research Foundation and by a contract between the Air Force Office of Scientific Research and The Ohio State University Research Foundation. ii TABLE OF CONTENTS ACKNOWLEDGMENTS..................... * » . LIST OF TABLES .............................. LIST OF ILLUSTRATIONS ....................... INTRODUCTION ................................ Chapter I. THEORY OF THE SPECIFIC HEAT OF SOLIDS . Lattice Specific Heat Electronic Specific Heats in Metals II. EXPERIMENTAL TECHNIQUES ............... Cooling Above 1°K. Cooling Below 1°K. Apparatus Thermometry Vapor Pressure Thermometry Sampe Preparation III. EXPERIMENTAL RESULTS.................. General Methods Thermometer Calibration Copper Sodium Cobalt Manganese Cobalt-Iron Alloy IV. INTERPRETATION OF R E S U L T S ............. Section 1t Copper and Sodium Section 2* Cobalt, Cobalt-Iron Alloy, and Manganese LIST OF REFERENCES LIST OP TABLES Table Page 1* Uanganese Deviation Curve D a t a ...........
    [Show full text]