Finite-temperature Properties Research Articles

Non-equilibrium transport through a model quantum dot: Hartree–Fock approximation and beyond

The finite-temperature transport properties of the spinless interacting fermion model coupled to non-interacting leads are investigated. Employing the unrestricted time-dependent Hartree–Fock (HF) approximation, the transmission probability and the nonlinear I–V characteristics are calculated, and compared with available analytical results and with numerical data obtained from a Hubbard–Stratonovich decoupling of the interaction. In the weak interaction regime, the HF approximation reproduces the gross features of the exact I–V characteristics but fails to account for subtle properties like the particular power law for the reflected current in the interacting resonant level model.

Ground-state and finite-temperature properties of correlated ultracold bosons on optical lattices

We investigate the ground-state and finite-temperature properties of the Bose-Hubbard model using the standard basis operator method applied to the equation of motion for Green's functions. We show that by introducing the self-consistent approach, the theory goes significantly beyond the mean-field approximation, allowing more-precise description of quantum and thermal fluctuations. For optical lattice systems with ultracold bosons, we find relevant quantitative agreement with numerical and experimental data. In particular, the presented method reveals the importance of thermal fluctuations in time-of-flight experiments. For the most reliable fitting of the visibility analytical curve to the experimental data, the value of temperature is determined and proximity to the quantum regime is discussed. The problem of identification of the superfluid--Mott-insulator phase boundary from time-of-flight experiments is also considered.

Direct method for calculating temperature-dependent transport properties

We show how temperature-induced disorder can be combined in a direct way with first-principles scattering theory to study diffusive transport in real materials. Excellent (good) agreement with experiment is found for the resistivity of Cu, Pd, Pt (and Fe) when lattice (and spin) disorder are calculated from first principles. For Fe, the agreement with experiment is limited by how well the magnetization (of itinerant ferromagnets) can be calculated as a function of temperature. By introducing a simple Debye-like model of spin disorder parameterized to reproduce the experimental magnetization, the temperature dependence of the average resistivity, the anisotropic magnetoresistance and the spin polarization of a Ni$_{80}$Fe$_{20}$ alloy are calculated and found to be in good agreement with existing data. Extension of the method to complex, inhomogeneous materials as well as to the calculation of other finite-temperature physical properties within the adiabatic approximation is straightforward.

Crossover from conventional to inverse indirect magnetic exchange in the depleted Anderson lattice

We investigate the finite-temperature properties of an Anderson lattice with regularly depleted impurities. The physics of this model is ruled by two different magnetic exchange mechanisms: conventional Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction at weak hybridization strength V and a novel inverse indirect magnetic exchange (IIME) at strong V, both favoring a ferromagnetic ground state. The stability of ferromagnetic order against thermal fluctuations is systematically studied by static mean-field theory for an effective low-energy spin-only model emerging perturbatively in the strong-coupling limit as well as by dynamical mean-field theory for the full model. The Curie temperature is found at a maximum for a half-filled conduction band and at intermediate hybridization strengths in the crossover regime between RKKY and IIME.

Finite-temperature properties of antiferroelectricPbZrO3from atomistic simulations

Antiferroelectrics are under extensive reexamination owing to their unique properties and technological promise. Computationally, they pose a challenge for predictive modeling as they often do not possess well-defined localized electric moments and exhibit a delicate energetic balance between polar and antipolar phases. We propose a first-principles-based atomistic model for the prototype antiferroelectric ${\mathrm{PbZrO}}_{3}$ that captures accurately a wide range of its properties. Application of the model to study finite-temperature properties of ${\mathrm{PbZrO}}_{3}$ under external electric field and hydrostatic pressure aids in achieving a coherent picture of this intriguing material. In particular, our simulations predict (i) the existence of a strong coupling between the antiferrodistortive motion of oxygen octahedra and the antipolar distortion in a wide range of temperatures and electric fields; (ii) a linear temperature dependence for the critical field associated with the antiferroelectric to ferroelectric phase transition; and (iii) a stabilizing effect of the hydrostatic pressure on the phase transition in ${\mathrm{PbZrO}}_{3}$.

Low- and high-temperature magnetism of Cr and Fe nanoclusters in iron-chromium alloys

Low-energy magnetic states and finite-temperature properties of Cr nanoclusters in bulk bcc Fe and Fe nanoclusters in bulk Cr are investigated using density functional theory (DFT) and the Heisenberg-Landau Hamiltonian based magnetic cluster expansion (MCE). We show, by means of noncollinear magnetic DFT calculations, that magnetic frustration caused by competing ferromagnetic and antiferromagnetic interactions either strongly reduces local magnetic moments while keeping collinearity or generates noncollinear magnetic structures. Small Cr clusters generally exhibit collinear ground states. Noncollinear magnetic configurations form in the vicinity of small Fe clusters if antiferromagnetic Fe-Cr coupling dominates over ferromagnetic Fe-Fe interactions. MCE predictions broadly agree with DFT data on the low-energy magnetic structures, and extend the DFT analysis to larger systems. Nonvanishing cluster magnetization caused by the dominance of Fe-Cr over Cr-Cr antiferromagnetic coupling is found in Cr nanoclusters using both DFT and MCE. Temperature dependence of magnetic properties of Cr clusters is strongly influenced by the surrounding iron atoms. A Cr nanocluster remains magnetic until fairly high temperatures, close to the Curie temperature of pure Fe in the large cluster size limit. Cr-Cr magnetic moment correlations are retained at high temperatures due to the coupling of interfacial Cr atoms with the Fe environment. Variation of magnetization of Fe-Cr alloys as a function of temperature and Cr clusters size predicted by MCE is assessed against the available experimental data.

Mechanical instability at finite temperature.

Many physical systems including lattices near structural phase transitions, glasses, jammed solids and biopolymer gels have coordination numbers placing them at the edge of mechanical instability. Their properties are determined by an interplay between soft mechanical modes and thermal fluctuations. Here we report our investigation of the mechanical instability in a lattice model at finite temperature T. The model we used is a square lattice with a φ(4) potential between next-nearest-neighbour sites, whose quadratic coefficient κ can be tuned from positive to negative. Using analytical techniques and simulations, we obtain a phase diagram characterizing a first-order transition between the square and the rhombic phase and different regimes of elasticity, as well as an 'order-by-disorder' effect that favours the rhombic over other zigzagging configurations. We expect our study to provide a framework for the investigation of finite-T mechanical and phase behaviour of other systems with a large number of floppy modes.

Ab initio investigation of the intermetallics in the Nb–Sn binary system

The elastic and thermodynamic properties of the stable intermetallics in the Nb–Sn system were studied by the first-principles pseudo-potential plane-wave method based on density functional theory. The elastic constants, Debye temperatures, bulk, shear and Young’s moduli and Poisson’s ratios were calculated for all the phases. Nb3Sn has the highest bulk, shear and elastic moduli of the Nb–Sn intermetallics. The elastic properties at 0K and the Debye temperatures of the Nb6Sn5 and NbSn2 phases are reported for the first time. The enthalpies of formation were calculated for all the intermetallics. The finite-temperature elastic properties of the Nb and Nb3Sn were calculated using the quasi-static approximation. The thermal expansion coefficients of Nb and Nb3Sn were also obtained.

Finite-temperature properties of N two-level atoms in a single-mode optic cavity and phase transition

In this paper, we investigate the finite-temperature properties and phase transition of the Dicke model. Converting the atomic pseudo-spin operator to the two-mode Fermi operators, we obtain the partition function in terms of the imaginary-time path integral. The atomic population and average photon number as analytic functions of the atom-photon coupling strength are found from the thermodynamic equilibrium equation, which leads to the stationary state at a finite temperature and is determined by the variation in an extremum-condition of the Euclidean action with respect to the bosonic field. In particular we study the phase transition from normal to superradiation phase at a fixed low-temperature, in which the phase transition is dominated by quantum fluctuations. The phase transition induced by the variation of the atom-photon coupling strength indeed obeys the Landau continuous phase-transition theory, in which the average photon-number can serve as an order parameter with non-zero value that characterizes the superradiation phase. In the zero temperature limit our results recover exactly all those obtained from the quantum phase transition theory at zero temperature. In addition, we discuss the thermodynamic properties and compare the difference between finite-temperature phase transition and zero-temperature quantum phase transition. It is discovered that the average photon-number and mean energy in the low-temperature stationary state coincide with the corresponding values of zero-temperature in the strong coupling region. The entropy of the superradiation phase decays rapidly to zero with the increase of coupling strength.

Dynamic Stabilization of Cubic AuZn

A recently developed temperature-dependent effective potential method is employed to study the martensitic phase transformation in AuZn. This method is based on ab initio molecular dynamics and allows to obtain finite-temperature lattice vibrational properties. We show that the transversal acoustic TA2[110] mode associated with the phase transition is stabilized at 300K. Temperature evolution of single-phonon dynamic structure factor at the wave vector q=1/3[1,1,0], associated with phonon softening and Fermi surface nesting, was also studied.

On the scaling factor in Debye–Grüneisen model: A case study of the Mg–Zn binary system

The utility of the Debye–Grüneisen has been investigated with respect to a finite-temperature fitting parameter known as the scaling factor. This scaling factor is studied using bcc, fcc, hcp systems and the Mg–Zn binary system. Predicted Debye temperatures, using a calculated scaling factor, show good agreement with experiments and improvements over the scaling factor derived by Moruzzi et al. Finite-temperature thermodynamic properties of Mg, Zn, Mg4Zn7, MgZn2, and Mg2Zn11 are investigated to show the efficiency and improved accuracy of the calculated scaling factor. For the intermetallic compounds except Mg2Zn11, ΘD predictions are improved upon greatly by implementing a calculated scaling factor. Along the same line, heat capacity is also predicted, showing good agreement with experimental values for these compounds. For Mg2Zn11, the Debye–Grüneisen model cannot account for anomalous lattice dynamics at low temperatures.

Structural stability and thermodynamics of CrN magnetic phases fromab initiocalculations and experiment

The dynamical and thermodynamic phase stabilities of the stoichiometric compound CrN including different structural and magnetic configurations are comprehensively investigated using a first-principles density-functional-theory (DFT) plus U approach in conjunction with experimental measurements of the thermal expansion. Comparing DFT and DFT+U results with experimental data reveals that the treatment of electron correlations using methods beyond standard DFT is crucial. The non-magnetic face-centered cubic B1-CrN phase is both, elastically and dynamically unstable, even under high pressure, while CrN phases with non-zero local magnetic moments are predicted to be dynamically stable within the framework of the DFT+U scheme. Furthermore, the impact of different treatments for the exchange-correlation (xc)-functional is investigated by carrying out all computations employing the local density approximation and generalized gradient approximation. To address finite-temperature properties, both, magnetic and vibrational contributions to the free energy have been computed employing our recently developed spin-space averaging method. The calculated phase transition temperature between low-temperature antiferromagnetic and high-temperature paramagnetic (PM) CrN variants is in excellent agreement with experimental values and reveals the strong impact of the choice of the xc-functional. The temperature-dependent linear thermal expansion coefficient of CrN is experimentally determined by the wafer curvature method from a reactive magnetron sputter deposited single-phase B1-CrN thin film with dense film morphology. A good agreement is found between experimental and ab initio calculated linear thermal expansion coefficients of PM B1-CrN. Other thermodynamic properties, such as the specific heat capacity, have been computed as well and compared to previous experimental data.

First-principles investigation of the Cu–Ni, Cu–Pd, and Ni–Pd binary alloy systems

Phase diagrams of copper–nickel–palladium binary alloys were determined by density functional theory cluster expansion method. The system has both magnetic and non-magnetic binaries and subtle phase coexistence areas between similar and different kind of lattice types. Furthermore, the CuPd binary has several ordered structures. Cluster expansion models were constructed by heuristic cluster selection for all of the fcc structures and for the CuPdbcc structure. Both configurational and magnetic phase diagrams were determined. Small amount of nickel magnetize fcc palladium to 0.26 μB from which the magnetic moment rises almost linearly to that of pure Ni. In CuNi, 0.46 x-Ni is needed for the magnetic transition. In CuPd alloy in 0 K, configurational free energy difference between bcc and fcc lattice resulting to phase separation is only about 1.1 kJ/mol-atoms. Low temperature energetics and magnetic phase diagrams have good quantitative agreement with available experimental and theoretical results. Finite temperature properties of the alloys are in good qualitative agreement with experimental results.

First-principles calculations of finite-temperature thermodynamic properties of binary solid solutions in the Al–Cu–Mg system

Based on first-principles calculations in terms of the 16-atom special quasirandom structures (SQSs), enthalpy of mixing at 0K as well as thermodynamic properties, including Gibbs energy of mixing, enthalpy of mixing, and entropy of mixing (ΔG, ΔH, ΔS), have been investigated for the binary solid solutions in the Al–Cu–Mg system. The targeted binary solid solutions include fcc, bcc, hcp phases in the Al–Cu, Al–Mg, and Cu–Mg systems. For the Al–Cu system, the present first-principles predictions are in good agreement with the experimental data and the CALculation of PHAse Diagram (CALPHAD) modeling results. For the Al–Mg and Cu–Mg systems, where the reliable experimental information is not available, it is expected that the presently predicted thermodynamic properties could yield a helpful insight into the phase stabilities in these two systems, in particular for the metastable phases.

Transport properties of the one-dimensional Hubbard model at finite temperature

We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is twofold: First, we compute both the charge- and the spin-current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity ${\ensuremath{\sigma}}_{r}eg(\ensuremath{\omega})$ in the presence of small integrability-breaking next-nearest-neighbor interactions (the extended Hubbard model). The dc conductivity is finite and diverges as the temperature is decreased below the gap. Our results thus suggest that the half-filled, gapped Hubbard model is a normal charge conductor at finite temperatures. As a test bed for our numerics, we compute ${\ensuremath{\sigma}}_{r}eg(\ensuremath{\omega})$ for the integrable XXZ spin chain in its gapped phase.

Finite temperature superfluid transition of strongly correlated lattice bosons in various geometries

We study finite-temperature properties of the strongly interacting bosons in three-dimensional lattices by employing the combined Bogoliubov method and the quantum rotor approach. Based on the mapping of the Bose–Hubbard Hamiltonian of strongly interacting bosons onto U(1) phase action, we study their thermodynamic phase diagrams for several lattice geometries including simple cubic, body, as well as face-centered lattices. The quantitative values for the phase boundaries obtained here may be used as a reference for emulation of the Bose–Hubbard model on a variety of optical lattice structures in order to demonstrate experimental-theoretical consistency for the numerical values regarding the location of the critical points.

Ab-initio calculations of the elastic and finite-temperature thermodynamic properties of niobium- and magnesium hydrides

Density Functional Theory (DFT) calculations have been used for calculating the elastic and thermodynamic properties of Mg, Nb, and their hydrides. The study is motivated by a previous work that showed constraints arising from Mg/Nb layer interfaces de-stabilized the magnesium hydride and resulted in decomposition temperatures much lower than in the bulk state. The calculated mechanical properties and the difference in the volume expansion of Mg- and Nb-hydrides support the ideas of large, de-stabilizing mechanical stresses arising from significant volume expansion incompatibilities in Mg/Nb multilayers. The stress and corresponding formation of metastable phases result in significant destabilization of MgH2 and provide ultra-low hydrogen desorption temperature in Mg/Nb multilayers.

Matrix product state formulation of frequency-space dynamics at finite temperatures

We present a flexible density-matrix renormalization group approach to calculate finite-temperature spectral functions of one-dimensional strongly correlated quantum systems. The method combines the purification of the finite-temperature density operator with a moment expansion of the Green's function. Using this approach, we study finite-temperature properties of dynamical spectral functions of spin-1/2 XXZ chains with Dzyaloshinskii-Moriya interactions in magnetic fields and analyze the effect of these symmetry breaking interactions on the nature of the finite-temperature dynamic spin structure factor.

Temperature dependence of small harmonically trapped atom systems with Bose, Fermi, and Boltzmann statistics

While the zero-temperature properties of harmonically trapped cold few-atom systems have been discussed fairly extensively over the past decade, much less is known about the finite-temperature properties. Working in the canonical ensemble, we characterize small harmonically trapped atomic systems as a function of the temperature using analytical and numerical techniques. We present results for the energetics, structural properties, condensate fraction, superfluid fraction, and superfluid density. Our calculations for the two-body system underline that the condensate and superfluid fractions are distinctly different quantities. Our work demonstrates that the path integral Monte Carlo method yields reliable results for bosonic and fermionic systems over a wide temperature range, including the regime where the de Broglie wave length is large, i.e., where the statistics plays an important role. The regime where the Fermi sign problem leads to reasonably large signal to noise ratios is mapped out for selected parameter combinations. Our calculations for bosons focus on the unitary regime, where the physics is expected to be governed by the three-body parameter. If the three-body parameter is large compared to the inverse of the harmonic oscillator length, we find that the bosons form a droplet at low temperature and behave approximately like a non-interacting Bose and eventually Boltzmann gas at high temperature. The change of the behavior occurs over a fairly narrow temperature range. A simple model that reproduces the key aspects of the phase transition like feature, which can potentially be observed in cold atom Bose gas experiments, is presented.

Minimal model of the magnetically induced metal-insulator transition: Finite-temperature properties

An unconventional type of metal-insulator transition is realized in the FeSi${}_{1\ensuremath{-}x}$Ge${}_{x}$ alloys which is driven by the magnetic instability of the paramagnetic insulator. Recently, a minimal model for this type of transition has been introduced and studied in the limit of vanishing temperature. Here we explore the finite-temperature properties of the minimal model in the mean-field approximation. We show that the predictions of the model are in qualitative agreement with experimental data on FeSi${}_{1\ensuremath{-}x}$Ge${}_{x}$ and on FeGe under pressure.