scholarly journals Low temperature two STM tip tunneling measurements of a floating chemical potential Pb(111) surface

2019 ◽  
Vol 87 (3) ◽  
pp. 31001
Author(s):  
We-Hyo Soe ◽  
Corentin Durand ◽  
Christian Joachim
Keyword(s):  
Low Temperature ◽  
Chemical Potential ◽  
Physical Contact ◽  
Current Intensity ◽  
Scanning Tunnelling ◽  
Stm Tips ◽  
Tunnelling Current

On a Pb(111) superconducting surface, low temperature dI/dV tunnelling spectra are recorded between two scanning tunnelling microscopes (STM) metallic tips with the Pb(111) sample metallic support non-grounded. The tunnelling current intensity I passing between the 2 tips through the sample is controlled by changing one or both STM vacuum tunnelling junction resistances. The chemical potential of this floating Pb(111) surface depends on the normalized ratio between those two quantum resistances. When ungrounded, the Pb(111) sample chemical potential balances between those of the 2 STM tips while tuning their respective tip end atomic apex to Pb(111) surface distances with a picometer precision without any physical contact between the STM tips and the surface.

An Improved Method for the Preparation and TEM Examination of Sharp Pointed Tips used in APFIM and STM

1990 ◽  
Vol 48 (2) ◽  
pp. 102-103
Author(s):  
E.A. Fischione ◽  
P.E. Fischione ◽  
J.J. Haugh ◽  
M.G. Burke
Keyword(s):  
Atom Probe ◽  
Preparation Process ◽  
Improved Method ◽  
Ion Milling ◽  
Polishing Process ◽  
Probe Field ◽  
Scanning Tunnelling ◽  
Stm Tips ◽  
Tunnelling Microscopy ◽  
Ion Microscopy

A common requirement for both Atom Probe Field-Ion Microscopy (APFIM) and Scanning Tunnelling Microscopy (STM) is a sharp pointed tip for use as either the specimen (APFIM) or the probe (STM). Traditionally, tips have been prepared by either chemical or electropolishing techniques. Recently, ion-milling has been successfully employed in the production of APFIM tips [1]. Conventional electropolishing techniques are applicable to a wide variety of metals, but generally require careful manual adjustments during the polishing process and may also be time-consuming. In order to reduce the time and effort involved in the preparation process, a compact, self-contained polishing unit has been developed. This system is based upon the conventional two-stage electropolishing technique in which the specimen/tip blank is first locally thinned or “necked”, and subsequently electropolished until separation occurs.[2,3] The result of this process is the production of two APFIM or STM tips. A mechanized polishing unit that provides these functions while automatically maintaining alignment has been designed and developed.

scholarly journals Notes on massless scalar field partition functions, modular invariance and Eisenstein series

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Francesco Alessio ◽  
Glenn Barnich ◽  
Martin Bonte
Keyword(s):  
Scalar Field ◽  
Partition Function ◽  
Low Temperature ◽  
Eisenstein Series ◽  
Chemical Potential ◽  
Proper Time ◽  
Series Representation ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Spacetime Manifold

Abstract The partition function of a massless scalar field on a Euclidean spacetime manifold ℝd−1 × 𝕋2 and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is computed. It is modular covariant and admits a simple expression in terms of a real analytic SL(2, ℤ) Eisenstein series with s = (d + 1)/2. Different techniques for computing the partition function illustrate complementary aspects of the Eisenstein series: the functional approach gives its series representation, the operator approach yields its Fourier series, while the proper time/heat kernel/world-line approach shows that it is the Mellin transform of a Riemann theta function. High/low temperature duality is generalized to the case of a non-vanishing chemical potential. By clarifying the dependence of the partition function on the geometry of the torus, we discuss how modular covariance is a consequence of full SL(2, ℤ) invariance. When the spacetime manifold is ℝp × 𝕋q+1, the partition function is given in terms of a SL(q + 1, ℤ) Eisenstein series again with s = (d + 1)/2. In this case, we obtain the high/low temperature duality through a suitably adapted dual parametrization of the lattice defining the torus. On 𝕋d+1, the computation is more subtle. An additional divergence leads to an harmonic anomaly.

scholarly journals Spectrum of QCD at Finite Isospin Density

2018 ◽  
Vol 175 ◽  
pp. 07042 ◽  
Author(s):  
Philipp Scior ◽  
Lorenz von Smekal ◽  
Dominik Smith
Keyword(s):  
Phase Diagram ◽  
Low Temperature ◽  
Temperature Region ◽  
Chemical Potential ◽  
Phase Diagram Of Qcd ◽  
Baryon Density ◽  
Polyakov Loop ◽  
High Chemical ◽  
Pion Condensation

We study the phase diagram of QCD at finite isospin density using two flavors of staggered quarks. We investigate the low temperature region of the phase diagram where we find a pion condensation phase at high chemical potential. We started a basic analysis of the spectrum at finite isospin density. In particular, we measured pion, rho and nucleon masses inside and outside of the pion condensation phase. In agreement with previous studies in two-color QCD at finite baryon density we find that the Polyakov loop does not depend on the density in the staggered formulation.

Chemical potential, Gibbs–Duhem equation and quantum gases

2017 ◽  
Vol 31 (13) ◽  
pp. 1750104
Author(s):  
M. Howard Lee
Keyword(s):  
Low Temperature ◽  
Thermodynamic Functions ◽  
Chemical Potential ◽  
Quantum Gases ◽  
Temperature Behavior ◽  
Bose Gases ◽  
Duhem Equation ◽  
Temperature Form ◽  
Specific Temperature ◽  
The Ideal

Thermodynamic relations like the Gibbs–Duhem are valid from the lowest to the highest temperatures. But they cannot by themselves provide any specific temperature behavior of thermodynamic functions like the chemical potential. In this work, we show that if some general conditions are attached to the Gibbs–Duhem equation, it is possible to obtain the low temperature form of the chemical potential for the ideal Fermi and Bose gases very directly.

The influence of Coulomb interaction of localized charges on low-temperature scanning tunnelling spectra of surface nanodefects

2001 ◽  
Vol 13 (18) ◽  
pp. 3941-3948 ◽  
Author(s):  
N S Maslova ◽  
A I Oreshkin ◽  
S I Oreshkin ◽  
V I Panov ◽  
S V Savinov ◽  
...  
Keyword(s):  
Low Temperature ◽  
Coulomb Interaction ◽  
Scanning Tunnelling ◽  
Temperature Scanning

Growth of Cu Films on Si(111)-7×7 Surfaces at Low Temperature: A Scanning Tunnelling Microscopy Study

2007 ◽  
Vol 24 (11) ◽  
pp. 3214-3217
Author(s):  
Shen Quan-Tong ◽  
Sun Guo-Feng ◽  
Li Wen-Juan ◽  
Dong Guo-Cai ◽  
Han Tie-Zhu ◽  
...  
Keyword(s):  
Low Temperature ◽  
Microscopy Study ◽  
Scanning Tunnelling Microscopy ◽  
Cu Films ◽  
Scanning Tunnelling ◽  
Tunnelling Microscopy

LOW-TEMPERATURE THERMODYNAMIC PROPERTIES OF A ONE-DIMENSIONAL GENERALIZED WIGNER CRYSTAL

2005 ◽  
Vol 19 (26) ◽  
pp. 4009-4019
Author(s):  
V. SLAVIN
Keyword(s):  
Low Temperature ◽  
Thermodynamic Properties ◽  
Electron Density ◽  
Lattice Site ◽  
Chemical Potential ◽  
Thermodynamic Characteristics ◽  
Host Lattice ◽  
Wigner Crystal ◽  
One Dimensional ◽  
Interacting Electrons

The low-temperature thermodynamic properties of a one-dimensional generalized Wigner crystal at arbitrary values of electron density and arbitrary number of interacting electrons are studied. The modified transfer-matrixes method is applied. It is shown that increasing the number of interacting electrons leads to the appearance of more and more fine "stairs" in low-temperature dependence of chemical potential against electron density. An influence of the disorder in host-lattice site positions on thermodynamic characteristics of the system is considered. It is established that the disorder destroys the "stairs".

scholarly journals THE SAWTOOTH CHAIN: FROM HEISENBERG SPINS TO HUBBARD ELECTRONS

2008 ◽  
Vol 22 (25n26) ◽  
pp. 4418-4433 ◽  
Author(s):  
J. RICHTER ◽  
O. DERZHKO ◽  
A. HONECKER
Keyword(s):  
Low Temperature ◽  
Hubbard Model ◽  
Heisenberg Model ◽  
Chemical Potential ◽  
Ground States ◽  
High Magnetic Fields ◽  
Thermodynamic Quantities ◽  
Saturation Field ◽  
Ground State Degeneracy ◽  
Characteristic Features

We report on recent studies of the spin-half Heisenberg and the Hubbard model on the sawtooth chain. For both models we construct a class of exact eigenstates which are localized due to the frustrating geometry of the lattice for a certain relation of the exchange (hopping) integrals. Although these eigenstates differ in details for the two models because of the different statistics, they share some characteristic features. The localized eigenstates are highly degenerate and become ground states in high magnetic fields (Heisenberg model) or at certain electron fillings (Hubbard model), respectively. They may dominate the low-temperature thermodynamics and lead to an extra low-temperature maximum in the specific heat. The ground-state degeneracy can be calculated exactly by a mapping of the manifold of localized ground states onto a classical hard-dimer problem, and explicit expressions for thermodynamic quantities can be derived which are valid at low temperatures near the saturation field for the Heisenberg model or around a certain value of the chemical potential for the Hubbard model, respectively.

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