Fermi liquid theory: a renormalization group approach

We show how Fermi liquid theory results can be systematically recovered using a renormalization group (RG) approach. Considering a two-dimensional system with a circular Fermi surface, we derive RG equations at one-loop order for the two-particle vertex function in the limit of small momentum () and energy () transfer and obtain the equation which determines the collective modes of a Fermi liquid. The density-density response function is also calculated. The Landau function (or, equivalently, the Landau parameters F _l ^s and F _l ^a ) is determined by the fixed point value of the -limit of the two-particle vertex function (). We show how the results obtained at one-loop order can be extended to all orders in a loop expansion. Calculating the quasi-particle life-time and renormalization factor at two-loop order, we reproduce the results obtained from two-dimensional bosonization or Ward Identities. We discuss the zero-temperature limit of the RG equations and the difference between the Field Theory and the Kadanoff-Wilson formulations of the RG. We point out the importance of n-body () interactions in the latter. Received: 27 June 1997 / Received in final form: 17 December 1997 / Accepted: 26 January 1998     

Influence of pressure effect on Fermi resonance in binary solution

The Fermi resonance behaviours of the two groups of binary solutions --- pyridine and methanol, benzene and carbon tetrachloride, under different pressures are investigated according to their Raman spectra. The effect of pressure on Fermi resonance in binary solution differs significantly from that in pure liquid. In a binary solution, with the intermolecular distance shortening, the intermolecular interaction potential increases, the shift rates of the Raman spectral lines increase, the spectral line splitting occurs ahead of that in pure liquid, and the wavenumber separation Δ₀ between the unperturbed harmonic levels shifts more quickly, too. The Fermi resonance parameters, the coupling coefficient W and the intensity ratio R of the two Raman bands, decrease rapidly with pressure increasing, and the pressure at which Fermi resonance phenomenon disappears is much lower than that in pure liquid, especially in the solution whose molecules are of the same polarity. This article is valuable in the identification and the assignment of spectral lines under high pressure, as well as the study of high pressure effect, intermolecular interaction, and solvent effects in different cases, etc.     

Instabilities of a Fermi Gas with Nested Fermi Surfaces

The nesting of the Fermi surfaces of an electron and a hole pocket separated by a vector Q commensurate with the lattice in conjunction with the interaction between the quasiparticles can give rise to a rich phase diagram. Of particular importance is itinerant antiferromagnetic order in the context of pnictides and heavy fermion compounds. By mismatching the nesting the order can gradually be suppressed and as the Néel temperature tends to zero a quantum critical point is obtained. A superconducting dome above the quantum critical point can be induced by the transfer of pairs of electrons between the pockets. The conditions under which such a dome arises are studied. In addition numerous other phases may arise, e.g. charge density waves, non‐Fermi liquid behavior, non‐s‐wave superconductivity, Pomeranchuk instabilities of the Fermi surface, nematic order, and phases with persistent orbital currents.     

Shubnikov-de Haas oscillations of massive Dirac fermions in a Dirac antiferromagnet SrMnSb2

We investigate the physical properties of massive Dirac fermions in SrMnSb₂ using transport, specific heat, electronic structure calculations, and Shubnikov-de Haas (SdH) oscillations. SrMnSb₂ is a candidate Dirac antiferromagnet, consisting of the MnSb layers and the distorted square net of Sb atoms with a zigzag chain structure. This structural distortion leads to gap opening at the band crossing point found in the square lattice of the sister compound SrMnBi₂ but leaves another Dirac band crossing near the Brillouin zone boundary. The small 2D Fermi surface with a light electron mass and a small Fermi energy is confirmed by the large resistivity anisotropy, the large Seebeck coefficient, and also the angle and temperature dependent SdH oscillations. The Berry phase obtained from the SdH oscillations is trivial, in contrast to the case of SrMnBi₂. The relatively large spin orbit coupling gap and the small Fermi energy in SrMnSb₂ is found to be essential to understand this contrasting behavior of the massive Dirac fermions as compared to SrMnBi₂. Our observations demonstrate that the Berry phase of the mobile electrons in SrMnSb₂ is sensitive to the Fermi level change and can be tuned by doping or deficiency.     

Fermi liquid breakdown and evidence for superconductivity in YFe2Ge2

In the d‐electron system YFe₂Ge₂, an unusually high and temperature dependent Sommerfeld ratio of the specific heat capacity C /T ～ 100 mJ/(mol K²) and an anomalous power law temperature dependence of the electrical resistivity signal Fermi liquid breakdown, probably connected to a close‐by quantum critical point. Full resistive transitions and DC diamagnetic screening fractions of up to 80% suggest that pure samples of YFe₂Ge₂ superconduct below 1.8 K. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Canonical Ensemble with Temperature Limitation

Ideal Bose and Fermi systems are studied on the basis of a canonical ensemble, subject to the condition that their temperature is less than a given temperature T_max. A single new parameter (the tau-parameter, τ) is needed to keep account of the new constraint. The parameter τ is shown to be the exponential of a pseudo-chemical potential that is linearly dependent on temperature. The inclusion of the τ- parameter leads to generalizations of usual thermodynamic quantities (internal energy, heat capacity and entropy) and various particular cases are discussed. The heat capacity of a Bose system can exhibit a maximum at a temperature less than the maximum temperature T_max. The number of micro-states in the canonical ensemble is found to increase with τ. The heat capacity c_V of a Fermi system of non-interacting spins exhibits a Schottky anomaly. The peak depends on τ, and for some cases c_V/k can significantly exceed unity. The influence of τ on the entropy of the Fermi system and on the number of micro-states in the canonical ensemble is significant but not spectacular.     

Direct observation of the hysteretic Fermi level modulation in monolayer MoS2 field effect transistors

The hysteresis in the transfer curve of MoS₂ has significant impact on the device performance. However, the hysteresis mechanism is still not clear. Here, we investigate the hysteresis of the monolayer MoS₂ by probing the local Fermi level variations as a function of the back gate voltage in different atmosphere using the Kelvin probe microscopy. While the Fermi level of the MoS₂ in air is much lower than that in vacuum, both the MoS₂ devices in vacuum and air show large Fermi level hysteresis. The Fermi level hysteresis direction is clock-wise, identical to that observed in the transfer curves. Both the hysteresis in Fermi level and transfer curve can be explained consistently by taking into account the charge trapping. Our findings confirm that carrier density modulation in MoS₂ plays a vital role in the hysteresis, and provide insight into the hysteresis mechanism for the optimization of the device performance.     

Electronic properties of a large quantum dot at a finite temperature

The physical properties of a two-dimensional parabolic quantum dot composed of large number of interacting electrons are numerically determined by the Thomas–Fermi (TF) method at a finite temperature. Analytical solutions are given for zero temperature for comparative purposes. The exact solution of the TF equation is obtained for the non-interacting system at finite temperatures. The effect of the number of particles and temperature on the properties are investigated both for interacting and non-interacting cases. The results indicate that the effect of e–e interaction on the density profile shows different temperature dependencies above and below a certain temperature T_c.     

Study of asymmetric wavenumber shift of the Fermi doublet ν1 − 2ν2 in the Raman spectrum of liquid carbon disulfide

The Raman spectra of liquid carbon disulfide (CS₂) diluted with benzene (C₆H₆) have been measured. By changing the CS₂, the concentration, we found an asymmetric wavenumber shift phenomenon. With decreasing concentration of CS₂, the position of the ν₁ (655 cm⁻¹) band remains practically unchanged, and the 2ν₂ (796 cm⁻¹) band shifts toward higher wavenumbers. To interpret this asymmetric wavenumber shift phenomenon of the Fermi doublet ν₁ − 2ν₂ in the Raman spectra satisfactorily, we propose a modified Bertran model. The values of the Fermi resonance (FR) parameters of CS₂ at different concentrations were calculated using the Bertran equations. In addition, we found the fundamental ν₂, which should be independent of the FR interaction, shifted to higher wavenumbers as the concentration decreased. This shift was probably driven by the tuning of the FR. Copyright © 2009 John Wiley & Sons, Ltd.     

Fermi surface,magnetic, and superconducting properties in actinide compounds

The de Haas–van Alphen effect, which is a powerful method to explore Fermi surface properties, has been observed in cerium, uranium, and nowadays even in neptunium and plutonium compounds. Here, we present the results of several studies concerning the Fermi surface properties of the heavy fermion superconductors UPt₃ and NpPd₅Al₂, and of the ferromagnetic pressure-induced superconductor UGe₂, together with those of some related compounds for which fascinating anisotropic superconductivity, magnetism, and heavy fermion behavior has been observed.     

Spontaneous breaking of four-fold rotational symmetry in two-dimensional electronic systems explained as a continuous topological transition

The Fermi liquid approach is applied to the problem of spontaneous violation of the C ₄ symmetry in strongly correlated two-dimensional electronic systems on a square lattice. The symmetry breaking is traced to the existence of a topological phase transition. This continuous transition is triggered when the Fermi line, driven by the quasiparticle interactions, reaches the van Hove saddle points, where the group velocity vanishes and the density of states becomes singular. An unconventional Fermi liquid emerges beyond the implicated quantum critical point.     

Oscillating Casimir force between two slabs in a Fermi sea

The Casimir effect for two parallel slabs immersed in an ideal Fermi sea is investigated at both zero and nonzero temperatures. It is found that the Casimir effect in a Fermi gas is distinctly different from that in an electromagnetic field or a massive Bose gas. In contrast to the familiar result that the Casimir force decreases monotonically with the increase of the separation L between two slabs in an electromagnetic field and a massive Bose gas, the Casimir force in a Fermi gas oscillates as a function of L. The Casimir force can be either attractive or repulsive, depending sensitively on the magnitude of L. In addition, it is found that the amplitude of the Casimir force in a Fermi gas decreases with the increase of the temperature, which also is contrary to the case in a Bose gas, since the bosonic Casimir force increases linearly with the increase of the temperature in the region T < T_c, where T_c is the critical temperature of the Bose-Einstein condensation.     

The instability conditions of a gas trapped in weak weakly interacting Fermi magnetic field

In this paper the analytical expression of free energy expressed by small parameter r of a weakly interacting Fermi gas trapped in weak magnetic field is derived by using `the maximum approximation' method and the ensemble theory. Based on the derived expression, the exact instability conditions of a weakly interacting Fermi gas trapped in weak magnetic field at both high and low temperatures are given. From the instability conditions we get the following two results. (1) At the whole low-temperature extent, whether the interactions are repulsive or attractive with (ɑn + 4\varepsilon_F/3) (n and \varepsilon _F denote the particle-number density and the Fermi energy respectively, ɑ= 4π a\hbar_F/ m, and a is s-wave scattering length) positive, there is a lower-limit magnetic field of instability; in addition, there is an upper-limit magnetic field for the system of attractive interactions with (ɑ n + \varepsilon_F/3) negative. (2) At the whole high-temperature extent, the system with repulsive interactions is always stable, but for the system with attractive interactions, the greater the scattering length of attractive interactions | a | is, the stronger the magnetic field is and the larger the particle-number density is, the bigger the possibility of instability in the system will be.     

Two-dimensionality of electronic structure and strong Fermi surface nesting in highly anisotropic iron-based superconductors

We perform first-principle calculations for a newly discovered iron-based superconductor, Sr₂ScFePO₃, whose blocking layer is a thick perovskite-based oxide (Sr₂ScO₃) and compare its result with those of other typical iron-based compounds, in order to make a strategy to explore iron-based compounds with higher superconducting transition temperature T_c. Consequently, we find that the thick blocking layer like Sr₂ScO₃ brings about perfectly cylindrical hole and electron Fermi surfaces. This can give much better nesting condition between disconnected Fermi surfaces compared to other types of iron-based superconductor compounds.     

Polarons in alkaline-earth-like atoms with multiple background Fermi surfaces

We study the impurity problem in a Fermi gas of ¹⁷³Yb atoms near an orbital Feshbach resonance (OFR), where a single moving particle in the ³P₀ state interacts with two background Fermi seas of particles in different nuclear states of the ground ¹S₀ manifold. By employing wave function ansatz to molecule and polaron states, we investigate various properties of the molecule, the attractive polaron, and the repulsive polaron states. In comparison to the case where only one Fermi sea is populated, we find that the presence of an additional Fermi sea acts as an energy shift between the two channels of the OFR. In addition, quantum fluctuations near the Fermi level can also induce sizable effects to various properties of the attractive and repulsive polarons.     

Asphericity in the Fermi Surface and Fermi Energy of Na-K, Na-Rb and Na-Cs Binary Alloys

Detailed theoretical investigations into asphericity in the Fermi surface (FS) and Fermi energy (FE) ofNa1_xKx, Na1_xRbx, and Na1_xCsx binary solid solutions are carried out for the first time. The alloying behavior ofthe K, Rb, and Cs with the Na generates the Fermi surface distortion (FSD) of bce simple metals. The FS of Na-K,Na-Rb, and Na-Cs solid solution is a distorted sphere with the largest deviation along [110]. We have found that theimpact of local-field correction function on FSD is maximun at [100] point and minimum at [111] point. The exchangeand correlation effect is found to suppress the value of FE.     

Unconventional superconductivity originating from disconnected Fermi surfaces in correlated superconductors : A case study for iron pnictides

We first generally summarize the effect of disconnected Fermi surfaces in spin fluctuation mediated superconductivity. We argue that disconnected Fermi surfaces are favorable in that the sign of the superconducting gap can be changed without nodal lines intersecting the Fermi surface. Then, as an example of actual materials that have disconnected Fermi surfaces, we focus on the iron-based high T_c superconductors. We construct a model that contains all of the five Fe d bands, and apply random-phase approximation. We find that multiple spin fluctuation modes develop due to the nesting between disconnected Fermi surfaces, and the superconductivity originating from the cooperation or competition between these multiple spin fluctuation modes depends on the lattice structure. In particular, the appearance of the Fermi surface around (π, π) in the unfolded Brillouin zone is sensitive to the pnictogen height h_Pn measured from the Fe plane, and the height can act as a switch between high T_c nodeless and low T_c nodal pairings. In the high T_c case, the superconducting gap is fully open on all of the five Fermi surfaces, but changes sign across the nesting vectors that bridge the disconnected Fermi surfaces.     

Magnetic quantum criticality in quasi‐one‐dimensional Heisenberg antiferromagnet

We analyze exciting recent measurements [Phys. Rev. Lett. 114 (2015) 037202] of the magnetization, differential susceptibility and specific heat on one dimensional Heisenberg antiferromagnet Cu(C₄H₄N₂)(NO₃)₂ (CuPzN) subjected to strong magnetic fields. Using the mapping between magnons (bosons) in CuPzN and fermions, we demonstrate that magnetic field tunes the insulator towards quantum critical point related to so‐called fermion condensation quantum phase transition (FCQPT) at which the resulting fermion effective mass diverges kinematically. We show that the FCQPT concept permits to reveal the scaling behavior of thermodynamic characteristics, describe the experimental results quantitatively, and derive for the first time the (temperature—magnetic field) phase diagram, that contains Landau‐Fermi‐liquid, crossover and non‐Fermi liquid parts, thus resembling that of heavy‐fermion compounds.     

Near EF electronic structure of heavily boron-doped superconducting diamond

We have performed soft X-ray angle-resolved photoemission spectroscopy (SXARPES) of a heavily boron-doped superconducting diamond film (T_c=7.2 K) in order to study the electronic structure near the Fermi level (E_F). Careful determination of measured momentum space that across Γ point in the Brillouin zone (BZ) and increase of an energy resolution provide further spectroscopic evidence that E_F is located at the highly dispersive diamond-like bands, indicating that holes at the top of the diamond-like valence band play an essential role for the conducting properties of the heavily boron-doped superconducting diamond for this boron-doping region (effective carrier concentration of 1.6%). The SXARPES intensities at E_F were also mapped out over BZ to obtain experimental Fermi surface sheets and compared with calculations.