Transcript The orbital characters of bands in BaFe1.85Co0.15As2

Quantum Chaotic Dynamics of Electron in Solid State Environment
Weihang Zhou1, Zhanghai Chen1,2,*, Bo Zhang2, C. H. Yu2, Wei Lu2, and S. C. Shen2,1,*
1
Surface Physics Laboratory, Department of Physics, Fudan University, Shanghai 200433, P. R. China
2
National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, P. R. China
Abstract
We report the first experimental study on the quantum chaotic dynamics of hydrogen analogues in solid state environment. We realized the hydrogen analogue in
anisotropic crystal field by introducing an isolated phosphorus donor in Si and study its quantum chaotic dynamics by means of photo-thermal ionization spectroscopy
technique. The interference of electron wave packets which leads to quasi-Landau resonances were observed. By analyzing the magnetic field dependence of the statistical
energy level distributions, we observed smooth transitions between the Poisson limit and the Wigner limit for the impurity energy level distributions, demonstrating the
magnetic field control of the quantum chaotic dynamics of hydrogen analogues in an anisotropic crystal field. Effects of the crystal field anisotropy on the quantum chaotic
dynamics have been studied and good agreements between theoretical calculations and the experimental data were found.
Realization of Anisotropic Diamagnetic Kepler Problem in a Solid State Environment
Experimental Technique
Motivation
Highly excited Rydberg atoms in strong magnetic fields are
particularly suitable for studying the quantum manifestation of
underlying chaotic dynamics due to their physical simplicity
and experimental feasibility.
Hydrogen-like shallow impurities in semi-conductors resemble the
energy level structures of the hydrogen atom but with a much
smaller energy scale. Conditions for the arising of quantum chaos
can be greatly lowered. Moreover, series of material parameters
can be manipulated in a semi-conductor. Thus, highly-excited
impurity atoms in semi-conductors provide promising testing
ground for the study of quantum chaos.
Sample: Ultra-pure single crystalline Si with 1011 cm-3
of residual P impurities
conduction band
phonon
excited states
photon
ground state
k
PTI spectrum of P impurities in Si under magnetic fields
at 17 k. (A) B || k || <111>; (B) B || k || <100>. The vertical
dashed lines denote the field-free ionization threshold.
The corresponding closed-orbits were found by
numerical integration of the equations of motion:
Fourier-transformed spectra of P impurities in Si under magnetic fields
ranging from 1.0 T to 4.0 T at 17 k with a step of 0.2 T. (A) B || k || <111>;
(B) B || k || <100>; (C) Linear fit for the observed resonance series, B || k ||
<111>; (D) Linear fit for the observed resonance series, B || k || <100>.
Two Hamiltonians were constructed in the case
of B || k || <100> and thus two sets ( Series II and
Series III ) of orbits are presented ( Series II is
calculated with parameter m* = 0.19 me and
Series III with m* = 0.42 me )
Typical Fourier spectra taken at B = 4.0 T and the related
closed-classical orbits leading to the observed resonances.
(A) B || k || <111>; (B) B || k || <100>.
Magnetic Field Control of the Quantum Chaotic Dynamics of Hydrogen Analogues in Anisotropic Crystal Field
Motivation
The control and anti-control of chaos have been the subject of
growing interdisciplinary interest in the past decades. The possibility
of controlling chaos is not only interesting from the point of view of
fundamental physics, but also of immense practical importance.
On the other hand, the presence of chaos in quantum mechanics
(sometimes referred to as quantum chaos) has been demonstrated and
can be found in quantum systems. A large amount of work has been
stimulated since its introduction in 1970s. However, understanding the
underlying physics of such quantum chaotic systems and finding ways
of controlling them remain a major scientific challenge in this field.
Typical PTI spectra of phosphorus impurities in Si taken under
magnetic fields of 2.4T at 17k. (a) B || <111>. (b) B || <100>. The
red dash-dot-dot line denotes the field-free ionization threshold.
Calculated chaoticity parameter q under magnetic
fields ranging from 0.2 to 3.4T with a step of 0.2T. (a)
B || <111>; (b) B || <100>.
Nearest-neighbor spacing distribution
For integrable systems:
P( s ) 
For chaotic systems:
Spectral rigidity:
Left panel: the integrated nearest-neighbor-spacing
distribution taken at magnetic fields 0.4 and 3.0T for B ||
<111>, respectively. Right panel: the corresponding
spectral rigidity and predictions from RMT.
Left panel: the integrated nearest-neighbor-spacing distribution taken at
magnetic fields 1.8 and 3.4T for B || <100>, respectively. Right panel:
the corresponding spectral rigidity and predictions from RMT.

2
s 2
s exp{
1
 3 ( L,  )  min
L A, B
For integrable systems:
For chaotic systems:
P(s)  exp{s}
4
}
(Poisson)
(Wigner)
 L
2
[
N
(

)

A


B
]
d


3 ( L, )  L / 15
 3 ( L,  ) 
1

2
(ln L  0.0687 )
Conclusion
We realized experimentally, for the first time, the anisotropic diamagnetic Kepler problem in a solid state environment by introducing an isolated phosphorus donor in Si and under
external magnetic field. The interference of electron wave packets which leads to quasi-Landau resonances were observed. We identified their corresponding closed classical orbits by
applying the closed-orbit theory to solid state environment. On the other hand, we analyzed the magnetic field dependence of the statistical energy level distributions for the impurity
electrons and presented a smooth transition between regularity and chaos for both field orientations, demonstrating the magnetic field control of the quantum chaotic dynmaics. Effects
of the crystal field anisotropy on the observed quasi-Landau resonances and the chaos control mechanism have been studied and excellent agreements have been found.