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Electronic Structure of Mott Insulators Studied by Inelastic X-ray Scattering
M. Z. Hasan,l* E. D. Isaacs,2 Z- X. Shen, L. L. Miller,3 K. Tsutsui,4 T. Tohyama,4 S. Maekawa4
1. Department of Applied Physics, Physics and Stanford Synchrotron Radiation Laboratory,
Stanford Linear Accelerator Center (SLAC), Stanford University, Stanford, CA 94305
2. Bell Laboratories, Lucent Technologies, Murray Hill, NJ 07974
3. Department of Physics & Ames Laboratory, Iowa State University, Ames, IA 50011
4. Institute of Materials Research, Tohoku University, Sendai 980-8577, Japan
* To whom correspondence should be addressed. E-mail : mzhasan@Stanford.edu
The electronic structure of Mott insulators
continues to be a major unsolved problem in physics
despite more than half-century of intense research
efforts. Well-developed momentum-resolved
spectroscopies such as photoemission or neutron
scattering cannot probe the full Mott gap. We report
observation of dispersive charge excitations across
the Mott gap in a high Tc parent cuprate Ca2CuO2Cl2
using high resolution resonant inelastic x-ray
scattering shedding light on the anisotropy of Mott-
gap. The results provide direct support for the
Hubbard model to describe charge excitations across
the Mott gap.
The discovery of high temperature superconductivity
and colossal magnetoresistance in doped transition metal
oxides has led to the extensive research interests in Mott
insulators. Such oxides are characterized by large onsite
Coulomb interaction and the consequent low-
temperature insulating state characterized by a charge-
excitation gap known as the Mott-gap. The gap is either
set by the Coulomb interaction U or the charge-transfer
energy A (energy to remove an electron from oxygen
orbital and put it on the copper site) depending on which
one is lower (1-4). Angle-resolved photoemission
(ARPES) which probes only the occupied electronic
states has been remarkably successful in characterizing
the electronic structure of cuprate based insulators (5-8).
Little is known about the momentum (k-) resolved
electronic structure of the unoccupied band which is a
major barrier for a coherent understanding of the nature
of the Mott gap and its related insulating state. In
addition, knowledge of the unoccupied upper Hubbard
band is essential to understand the physics of n-type
(electron doped) superconductors as the doped electrons
occupy the upper Hubbard band. Among the standard
probes of condensed matter systems (that allow
momentum-resolved studies), neutrons do not couple to
electron's charge density and (thermal) neutron energy is
too low to reach the Mott-edge. No k-resolved inverse
photoemission (Inv-ARPES) study is available because
of problems associated with sample charging as well as
the lack of required energy resolution. Inelastic electron
scattering which is known as the electron-energy-loss
spectroscopy (EELS) is possible and measures
electronic excitations from the occupied to the
unoccupied bands. Though very useful as a technique,
EELS requires extensive sample preparation and the
spectra need to be corrected for multiple scattering
effects in order to extract useful information (9).
Inelastic x-ray scattering is a natural and powerful
probe of electronic excitations in condensed matter
systems. It has the potential to fill an important gap of
knowledge by developing a good understanding of the
bulk electronic structure of correlated electron systems.
Inelastic scattering of x-ray photons covers a fairly
wide kinematic range in energy and momentum space
and the photons directly couple to the electronic charge
(and other electronic degrees of freedom like orbitals
and spins). However, as x-ray photons are highly
absorbed in high-Z materials, applications of the
technique have been mostly limited to low-Z systems
(10-13). Several recent studies, both experimental
results and theoretical/numerical investigations have
shown that by tuning the incident photon energy near
an x-ray absorption edge a Raman-like effect could be
measured with nonzero momentum transfer, despite the
high absorption cross-section, through the large
resonant enhancement which eventually dominates the
overall cross-section (14-19). An inelastically scattered
x-ray photon can probe the full charge-gap in a Mott
insulator through the creation of a hole in the occupied
band and promoting an electron across the gap to the
unoccupied band with a finite (tunable) momemtum
transferred into the system. A recent resonant inelastic
x-ray scattering (RIXS) study (17) has reported such
observation of a low-energy charge-transfer gap near
M.Z. Hasan et.aL, Science 288, 1811 (2000)
Work supported by US Department of Energy contract DE-AC02-76SF00515.
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Hasan, M. Z.; Isaacs, E. D.; Shen, Z. X.; Miller, L. L.; Tsutsui, K.; Tohyama, T. et al. Electronic Structure of Mott Insulators Studied by Inelastic X-Ray Scattering, article, November 6, 2012; United States. (digital.library.unt.edu/ark:/67531/metadc838324/m1/1/: accessed September 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.