Reply to "Comment on `Fluctuation-induced first-order transition in p-wave superconductors'"
This is a Reply to the Comment posted as arXiv:1207.1261.
cond-mat.supr-con↗
arXiv subjects
D. Belitz
Publications and source records attributed to D. Belitz.
Quantum Phase Transition in a Clean Two-Dimensional Electron System
A quantum phase transition that was recently observed in a high-mobility silicon MOSFET is analyzed in terms of a scaling theory. The most striking characteristic of the transition is a divergence of the thermopower, according to an inverse linear law, as a critical value of the electron density is approached. A scaling description of this transition yields predictions about the critical behavior of other observables, e.g., the specific heat. We also explore the possibility that this transition realizes a recently predicted transition from a Fermi liquid to a non-Fermi-liquid state.
cond-mat.str-el↗
A compilation of metallic systems that show a quantum ferromagnetic transition
We provide a compilation of metallic systems in which a low-temperature ferromagnetic or similar transition is observed. Our objective is to demonstrate the universal first-order nature of such transitions in clean systems in two or three spatial dimensions. Please contact the authors with information about omissions, corrections, or any other information.
cond-mat.str-el↗
Universal low-temperature tricritical point in metallic ferromagnets and ferrimagnets
An earlier theory of the quantum phase transition in metallic ferromagnets is revisited and generalized in three ways. It is shown that the mechanism that leads to a fluctuation-induced first-order transition in metallic ferromagnets with a low Curie temperature is valid, (1) irrespective of whether the magnetic moments are supplied by the conduction electrons or by electrons in another band, (2) for ferromagnets in the XY and Ising universality classes as well as for Heisenberg ferromagnets, and (3) for ferrimagnets as well as for ferromagnets. This vastly expands the class of materials for which a first-order transition at low temperatures is expected, and it explains why strongly anisotropic ferromagnets, such as UGe2, display a first-order transition as well as Heisenberg magnets.
cond-mat.str-el↗
Effective Soft-Mode Theory of Strongly Interacting Fermions
An effective field theory for clean electron systems is developed in analogy to the generalized nonlinear sigma-model for disordered interacting electrons. The physical goal is to separate the soft or massless electronic degrees of freedom from the massive ones and integrate out the latter to obtain a field theory in terms of the soft degrees of freedom only. The resulting theory is not perturbative with respect to the electron-electron interaction. It is controlled by means of a systematic loop expansion and allows for a renormalization-group analysis in a natural way. It is applicable to universal phenomena within phases, and to transitions between phases, with order parameters in arbitrary angular-momentum channels, and in the spin-singlet, spin-triplet, particle-hole, and particle-particle channels. Applications include ferromagnetic and ferrimagnetic ordering, non-s-wave ferromagnetic order (magnetic nematics), Fermi-liquid to non-Fermi-liquid transitions, and universal phenomena within a Fermi-liquid phase.
cond-mat.str-el↗
Theory of a Fermi-Liquid-to-Non-Fermi-Liquid Quantum Phase Transition in Dimensions d>1
We develop a theory for a generic instability of a Fermi liquid in dimension d>1 against the formation of a Luttinger-liquid-like state. The density of states at the Fermi level is the order parameter for the ensuing quantum phase transition, which is driven by the effective interaction strength. A scaling theory in conjunction with an effective field theoy for clean electrons is used to obtain the critical behavior of observables. In the Fermi-liquid phase the order-parameter susceptibility, which is measurable by tunneling, is predicted to diverge for 1<d<3.
cond-mat.str-el↗
Nature of the quantum phase transition to a spin-nematic phase
It is shown that the quantum phase transition in metallic non-s-wave ferromagnets, or spin nematics, is generically of first order. This is due to a coupling of the order parameter to soft electronic modes that play a role analogous to that of the electromagnetic vector potential in a superconductor, which leads to a fluctuation-induced first-order transition. A generalized mean-field theory for the p-wave case is constructed that explicitly shows this effect. Tricritical wings are predicted to appear in the phase diagram in a spatially varying magnetic field, but not in a homogeneous one.
cond-mat.str-el↗
Ordered Phases of Itinerant Dzyaloshinsky-Moriya Magnets and Their Electronic Properties
A field theory appropriate for magnets that display helical order due to the Dzyaloshinsky-Moriya mechanism, a class that includes MnSi and FeGe, is used to derive the phase diagram in a mean-field approximation. The helical phase, the conical phase in an external magnetic field, and recent proposals for the structure of the A-phase and the non-Fermi-liquid region in the paramagnetic phase are discussed. It is shown that the orientation of the helical pitch vector along an external magnetic field within the conical phase occurs via two distinct phase transitions. The Goldstone modes that result from the long-range order in the various phases are determined, and their consequences for electronic properties, in particular the specific heat, the single-particle relaxation time, and the electrical and thermal conductivities, are derived. Various aspects of the ferromagnetic limit, and qualitative differences between the transport properties of helimagnets and ferromagnets, are also discussed.
cond-mat.str-el↗
Columnar Fluctuations as a Source of Non-Fermi-Liquid Behavior in Weak Metallic Magnets
It is shown that columnar fluctuations, in conjunction with weak quenched disorder, lead to a T^{3/2} temperature dependence of the electrical resistivity. This is proposed as an explanation of the observed non-Fermi-liquid behavior in the helimagnet MnSi, with one possible realization of the columnar fluctuations provided by skyrmion lines that have independently been proposed to be present in this material.
cond-mat.str-el↗
Quantum Electrodynamics and the Origins of the Exchange, Dipole-Dipole, and Dzyaloshinsky-Moriya Interactions in Itinerant Fermion Systems
It is shown how the exchange interaction, the dipole-dipole interaction, and the Dzyaloshinsky-Moriya interaction between electronic spin-density fluctuations emerge naturally from a field-theoretic framework that couples electrons to the fluctuating electromagnetic potential. Semi-quantitative estimates are given to determine when the dipole-dipole interaction, which is often neglected, needs to be considered, and various applications are discussed, with an emphasis on weak ferromagnets and on helimagnets.
cond-mat.str-el↗
Anomalous Pinning Fields in Helical Magnets: Screening of the Quasiparticle Interaction
The spin-orbit interaction strength g_so in helical magnets determines both the pitch wave number q and the critical field H_c1 where the helix aligns with an external magnetic field. Within a standard Landau-Ginzburg-Wilson (LGW) theory, a determination of g_so in MnSi and FeGe from these two observables yields values that differ by a factor of 20. This discrepancy is remedied by considering the fermionic theory underlying the LGW theory, and in particular the effects of screening on the effective electron-electron interaction that results from an exchange of helical fluctuations.
cond-mat.str-el↗
Smectons: Soft modes in electronic stripe phases, and their consequences for thermodynamics and transport
The Goldstone mode due to stripe or unidirectional charge-density-wave order in electron systems is found to have the same functional form as the one in classical smectic liquid crystals. It is very similar to the Goldstone mode that results from helical magnetic order. This allows for an effective theory that provides a quasiparticle description of either stripe phases or helimagnets in the low-energy regime. The most remarkable observable consequence is an electronic relaxation rate in d=2 that is 1/τ~ T\ln T in clean systems and 1/τ~ \sqrt{T} in weakly disordered ones. The corresponding results in d=3 are 1/τ~ T^{3/2} and 1/τ~ T, respectively.
cond-mat.str-el↗
Electronic Transport at Low Temperatures: Diagrammatic Approach
We prove that a diagrammatic evaluation of the Kubo formula for the electronic transport conductivity due the exchange of bosonic excitations, in the usual conserving ladder approximation, yields a result consistent with the Boltzmann equation. In particular, we show that an uncontrolled approximation that has been used to solve the integral equation for the vertex function is unnecessary. An exact solution of the integral equation yields the same asymptotic low-temperature behavior as the approximate one, albeit with a different prefactor, and agrees with the temperature dependence of the Boltzmann solution. Examples considered are electron scattering from acoustic phonons, and from helimagnons in helimagnets.
cond-mat.stat-mech↗
Fluctuation-induced first-order transition in $p $-wave superconductors
The problem of a fluctuation-induced first-order transition is considered for $p $-wave superconductors. Both an $ε$-expansion about $d=4$ and a large-$n$ expansion conclude that the transition for the physical case $n=6$ in $d=3$ is of first order, as in the s-wave case.
cond-mat.supr-con↗
Theory of Helimagnons in Itinerant Quantum Systems III: Quasiparticle Description
In two previous papers we studied the problem of electronic properties in a system with long-ranged helimagnetic order caused by itinerant electrons. A standard many-fermion formalism was used. The calculations were quite tedious because different spin projections were coupled in the action, and because of the inhomogeneous nature of a system with long-ranged helimagnetic order. Here we introduce a canonical transformation that diagonalizes the action in spin space, and maps the problem onto a homogeneous fermion problem. This transformation to quasiparticle degrees of freedom greatly simplifies the calculations. We use the quasiparticle action to calculate single-particle properties, in particular the single-particle relaxation rate. We first reproduce our previous results for clean systems in a simpler fashion, and then study the much more complicated problem of three-dimensional itinerant helimagnets in the presence of an elastic relaxation rate 1/tau due to nonmagnetic quenched disorder. Our most important result involves the temperature dependence of the single-particle relaxation rate in the ballistic limit, tau^2 Tε_F > 1, for which we find a linear temperature dependence. We show how this result is related to a similar result found in nonmagnetic two-dimensional disordered metals.
cond-mat.str-el↗
Theory of Helimagnons in Itinerant Quantum Systems IV: Transport in the Weak-Disorder Regime
We apply a recent quasiparticle model for the electronic properties of metallic helimagnets to calculate the transport properties of three-dimensional systems in the helically ordered phase. We focus on the ballistic regime tau^2 T epsilon_F >> 1 at weak disorder (large elastic mean-free time tau) or intermediate temperature. In this regime, we find a leading temperature dependence of the electrical conductivity proportional to T. This is much stronger than either the Fermi-liquid contribution (T^2) or the contribution from helimagnon scattering in the clean limit (T^{5/2}). It is reminiscent of the behavior of non-magnetic two-dimensional metals, but the sign of the effect is opposite to that in the non-magnetic case. Experimental consequences of this result are discussed.
cond-mat.str-el↗
Analogy between Three-Dimensional Helimagnetic Metals and Two-Dimensional Nonmagnetic Metals: Transport in the Weak-Disorder Regime
We present a quasi-particle model that allows for a simple description of the electronic properties of metallic helimagnets. For weak quenched disorder, we find a leading linear temperature dependence of the electrical conductivity for 3-d materials. This is reminiscent of the behavior of nonmagnetic 2-d systems, and reflects a general tendency of certain properties of bulk helimagnets to appear effectively 2-d. The sign of the effect is opposite to that in nonmagnetic 2-d materials. These surprising predictions should be observable in weak helimagnets.
cond-mat.str-el↗
Skyrmion versus vortex flux lattices in p-wave superconductors
p-wave superconductors allow for topological defects known as skyrmions, in addition to the usual vortices that are possible in both s-wave and p-wave materials. In strongly type-II superconductors in a magnetic field, a skyrmion flux lattice yields a lower free energy than the Abrikosov flux lattice of vortices, and should thus be realized in p-wave superconductors. We analytically calculate the energy per skyrmion, which agrees very well with numerical results. From this, we obtain the magnetic induction B as a function of the external magnetic field H, and the elastic constants of the skyrmion lattice, near the lower critical field H_c1. Together with the Lindemann criterion, these results suffice to predict the melting curve of the skyrmion lattice. We find a striking difference in the melting curves of vortex lattices and skyrmion lattices: while the former is separated at all temperatures from the Meissner phase by a vortex liquid phase, the skyrmion lattice phase shares a direct boundary with the Meissner phase. That is, skyrmions lattices never melt near Hc1, while vortex lattices always melt sufficiently close to Hc1. This allows for a very simple test for the existence of a skyrmion lattice. Possible muSR experiments to detect skyrmion lattices are also discussed.
cond-mat.supr-con↗