The Casimir effect for rectangular boxes has been studied for several decades. But there are still some points unclear. Recently, there are new developments related to this topic, including the demonstration of the equivalence of the regularization m
ethods and the clarification of the ambiguity in the regularization of the temperature-dependent free energy. Also, the interesting quantum spring was raised stemming from the topological Casimir effect of the helix boundary conditions. We review these developments together with the general derivation of the Casimir energy of the $p$-dimensional cavity in ($D+1$)-dimensional spacetime, paying special attention to the sign of the Casimir force in a cavity with unequal edges. In addition, we also review the Casimir piston, which is a configuration related to rectangular cavity.
We investigate an unusual symmetry of Fe-based superconductors (FeSCs) and find novel superconducting pairing structures. FeSCs have a minimal translational unit cell composed of two Fe atoms due to the staggered positions of anions with respect to t
he Fe plane. We study the physical consequences of the additional glide symmetry that further reduces the unit cell to have only one Fe atoms. In the regular momentum space, it not only leads to a particular orbital parity separated spectral function but also dictates orbital parity distinct pairing structures. Furthermore, it produces accompanying Cooper pairs of $(pi,pi,0)$ momentum, which have a characteristic textit{odd} form factor and break time reversal symmetry. Such novel pairing structures explain the unusual angular modulations of the superconducting gaps on the hole pockets in recent ARPES and STS experiments.
We reconsider the thermal scalar Casimir effect for $p$-dimensional rectangular cavity inside $D+1$-dimensional Minkowski space-time. We derive rigorously the regularization of the temperature-dependent part of the free energy by making use of the Ab
el-Plana formula repeatedly and get the explicit expression of the terms to be subtracted. In the cases of $D$=3, $p$=1 and $D$=3, $p$=3, we precisely recover the results of parallel plates and three-dimensional box in the literature. Furthermore, for $D>p$ and $D=p$ cases with periodic, Dirichlet and Neumann boundary conditions, we give the explicit expressions of the Casimir free energy in both low temperature (small separations) and high temperature (large separations) regimes, through which the asymptotic behavior of the free energy changing with temperature and the side length is easy to see. We find that for $D>p$, with the side length going to infinity, the Casimir free energy tends to positive or negative constants or zero, depending on the boundary conditions. But for $D=p$, the leading term of the Casimir free energy for all three boundary conditions is a logarithmic function of the side length. We also discuss the thermal Casimir force changing with temperature and the side length in different cases and find with the side length going to infinity the force always tends to zero for different boundary conditions regardless of $D>p$ or $D=p$. The Casimir free energy and force at high temperature limit behave asymptotically alike in that they are proportional to the temperature, be they positive (repulsive) or negative (attractive) in different cases. Our study may be helpful in providing a comprehensive and complete understanding of this old problem.
The Fermi surface topology of $cI$16 Li at high pressures is studied using a recently developed first-principles unfolding method. We find the occurrence of a Lifshitz transition at $sim$43 GPa, which explains the experimentally observed anomalous on
set of the superconductivity enhancement toward lowered pressure. Furthermore we identify, in comparison with previous reports, additional nesting vectors that contribute to the $cI$16 structural stability. Our study highlights the importance of three-dimensional unfolding analyses for first-principles studies of Fermi surface topologies and instabilities in general.
Realization of conically linear dispersion, termed as Dirac cones, has recently opened up exciting opportunities for high-performance devices that make use of the peculiar transport properties of the massless carriers. A good example of current fashi
on is the heavily studied graphene, a single atomic layered graphite. It not only offers a prototype of Dirac physics in the field of condensed matter and materials science, but also provides a playground of various exotic phenomena. In the meantime, numerous routes have been attempted to search for the next graphene. Despite these efforts, to date there is still no simple guideline to predict and engineer such massless particles in materials. Here, we propose a theoretical recipe to create Dirac cones into anyones favorite materials. The method allows to tailor the properties, such as anisotropy and quantity, in any effective one-band two-dimensional lattice. We demonstrate the validity of our theory with two examples on the square lattice, an unlikely candidate hosting Dirac cones, and show that a graphene-like low-energy electronic structure can be realized. The proposed recipe can be applied in real materials via introduction of vacancy, substitution or intercalation, and also extended to photonic crystal, molecular array, and cold atoms systems.
We report a first-principles Wannier function study of the electronic structure of PdTe. Its electronic structure is found to be a broad three-dimensional Fermi surface with highly reduced correlations effects. In addition, the higher filling of the
Pd $d$-shell, its stronger covalency resulting from the closer energy of the Pd-$d$ and Te-$p$ shells, and the larger crystal field effects of the Pd ion due to its near octahedral coordination all serve to weaken significantly electronic correlations in the particle-hole (spin, charge, and orbital) channel. In comparison to the Fe Chalcogenide e.g., FeSe, we highlight the essential features (quasi-two-dimensionality, proximity to half-filling, weaker covalency, and higher orbital degeneracy) of Fe-based high-temperature superconductors.
In all iron pnictides, the positions of the ligand alternatively above and below the Fe plane create 2 inequivalent Fe sites. This results in 10 Fe 3d bands in the electronic structure. However, they do not all have the same status for an ARPES exper
iment. There are interference effects between the 2 Fe that modulate strongly the intensity of the bands and that can even switch their parity. We give a simple description of these effects, notably showing that ARPES polarization selection rules in these systems cannot be applied by reference to a single Fe ion. We show that ARPES data for the electron pockets in Ba(Fe0.92Co0.08)2As2 are in excellent agreement with this model. We observe both the total suppression of some bands and the parity switching of some other bands. Once these effects are properly taken into account, the structure of the electron pockets, as measured by ARPES, becomes very clear and simple. By combining ARPES measurements in different experimental configurations, we clearly isolate each band forming one of the electron pockets. We identify a deep electron band along one ellipse axis with the dxy orbital and a shallow electron band along the perpendicular axis with the dxz/dyz orbitals, in good agreement with band structure calculations. We show that the electron pockets are warped as a function of kz as expected theoretically, but that they are much smaller than predicted by the calculation.
We investigate the currently debated issue concerning whether transition metal substitutions dope carriers in iron based superconductors. From first-principles calculations of the configuration-averaged spectral function of BaFe$_2$As$_2$ with disord
ered Co/Zn substitutions of Fe, important doping effects are found beyond merely changing the carrier density. While the chemical potential shifts suggest doping of a large amount of carriers, a reduction of the coherent carrier density is found due to the loss of spectral weight. Therefore, none of the change in the Fermi surface, density of states, or charge distribution can be solely used for counting doped coherent carriers, let alone presenting the full effects of the disordered substitutions. Our study highlights the necessity of including disorder effects in the studies of doped materials in general.
We investigate the physical effects of translational symmetry breaking in Fe-based high-temperature superconductors due to alternating anion positions. In the representative parent compounds, including the newly discovered Fe-vacancy-ordered $mathrm{
K_{0.8}Fe_{1.6}Se_2}$, an unusual change of orbital character is found across the one-Fe Brillouin zone upon unfolding the first-principles band structure and Fermi surfaces, suggesting that covering a larger one-Fe Brillouin zone is necessary in experiments. Most significantly, the electron pockets (critical to the magnetism and superconductivity) are found only created with the broken symmetry, advocating strongly its full inclusion in future studies, particularly on the debated nodal structures of the superconducting order parameter.
