arXiv subjects

Guo-Zhu Liu

Publications and source records attributed to Guo-Zhu Liu.

At least 55 records · Page 3Linked to original sources

arXiv2015

Influence of Coulomb interaction on the anisotropic Dirac cone in graphene

Anisotropic Dirac cones can appear in a number of correlated electron systems, such as cuprate superconductors and deformed graphene. We study the influence of long-range Coulomb interaction on the physical properties of an anisotropic graphene by using the renormalization group method and 1/N expansion, where N is the flavor of Dirac fermions. Our explicit calculations reveal that the anisotropic fermion velocities flow monotonously to an isotropic fixed point in the lowest energy limit in clean graphene. We then incorporate three sorts of disorders, including random chemical potential, random gauge potential, and random mass, and show that the interplay of Coulomb interaction and disorders can lead to rich and unusual behaviors. In the presence of strong Coulomb interaction and a random chemical potential, the fermion velocities are driven to vanish at low energies and the system turns out to be an exotic anisotropic insulator. In the presence of Coulomb interaction and other two types of disorders, the system flows to an isotropic low-energy fixed point more rapidly than the clean case, and exhibits non-Fermi liquid behaviors. We also investigate the nonperturbative effects of Coulomb interaction, focusing on how the dynamical gap is affected by the velocity anisotropy. It is found that the dynamical gap is enhanced (suppressed) as the fermion velocities decrease (increase), but is suppressed as the velocity anisotropy increases.

cond-mat.str-el↗

arXiv2015

Infrared behavior of dynamical fermion mass generation in QED$_{3}$

Extensive investigations show that QED$_{3}$ exhibits dynamical fermion mass generation at zero temperature when the fermion flavor $N$ is sufficiently small. However, it seems difficult to extend the theoretical analysis to finite temperature. We study this problem by means of Dyson-Schwinger equation approach after considering the effect of finite temperature or disorder-induced fermion damping. Under the widely used instantaneous approximation, the dynamical mass displays an infrared divergence in both cases. We then adopt a new approximation that includes an energy-dependent gauge boson propagator and obtain results for dynamical fermion mass that do not contain infrared divergence. The validity of the new approximation is examined by comparing to the well-established results obtained at zero temperature.

hep-th↗

arXiv2014

Renormalization group analysis of competition between distinct order parameters

We perform a detailed renormalization group analysis to study a (2+1)-dimensional quantum field theory that is composed of two interacting scalar bosons, which represent the order parameters for two continuous phase transitions. This sort of field theory can describe the competition and coexistence between distinct long-range orders, and therefore plays a vital role in statistical physics and condensed matter physics. We first derive and solve the renormalization group equations of all the relevant physical parameters, and then show that the system does not have any stable fixed point in the lowest energy limit. Interestingly, this conclusion holds in both the ordered and disordered phases, and also at the quantum critical point. Therefore, the originally continuous transitions are unavoidably turned to first-order due to ordering competition. Moreover, we examine the impacts of massless Goldstone boson generated by continuous symmetry breaking on ordering competition, and briefly discuss the physical implications of our results.

cond-mat.str-el↗

arXiv2013

Novel behavior of upper critical field due to nematic order in $d$-wave superconductors

In recent years, there have been increasing experimental evidence suggesting the existence of an electronic nematic state in a number of unconventional $d$-wave superconductors. Interestingly, it is expected that the long-range nematic order can coexist with $d$-wave superconductivity. We analyze the in-plane upper critical field $H_{c2}$ after taking the influence of nematic state into account, and find that the four-fold oscillation of angle-dependent $H_{c2}$ in a pure $d$-wave superconducting state is turned into a novel two-fold oscillation pattern by a weak nematic order. Moreover, such effect is much more significant at higher temperatures. These behaviors are measurable and may be used to probe the predicted coexisting nematic order in $d$-wave superconductors. In addition, we show that the concrete angular dependence of $H_{c2}$ and the positions of its maximum can be strongly affected by several parameters, including temperature and $T_c$.

cond-mat.supr-con↗

arXiv2013

Additional electron pairing in a d-wave superconductor driven by nematic order

We perform a non-perturbative analysis of the strong interaction between gapless nodal fermions and the nematic order parameter in two-dimensional d_{x^2-y^2} superconductors. We predict that the critical nematic fluctuation can generate a dynamical nodal gap if the fermion flavor N is smaller than a threshold N_c. Such gap generation leads to an additional is-wave Cooper pairing instability, which induces a fully gapped d_{x^2-y^2}+is superconducting dome in the vicinity of the nematic quantum critical point. The opening of a dynamical gap has important consequences, including the saturation of fermion velocity renormalization, a weak confinement of fermions and the suppression of observable quantities.

cond-mat.supr-con↗

arXiv2013

Competition between superconductivity and nematic order in high-$T_c$ superconductor

We investigate the competition between d-wave superconductivity and nematic order in high-$T_c$ superconductor, and examine the role played by gapless fermionic degrees of freedom. Apart from the competitive interaction with the superconducting order parameter, the nematic order parameter couples strongly to gapless nodal quasiparticles. The interplay of these two kinds of interactions is analyzed by means of renormalization group method. In case the fermionic degree of freedom are entirely neglected, the competitive interaction between two bosonic order parameters is strongly relevant, and can lead to runaway behavior. However, these properties are fundamentally changed once the dynamics of fermions are taken into account. At the nematic quantum critical point where an extreme fermion velocity anisotropy occurs, the superconducting and nematic order parameters are decoupled from each other. Consequently, the phase transitions are continuous, and d-wave superconductivity can coexist with nematic order homogeneously. These results indicate that the gapless fermions can play an important role and should be carefully included in the theoretical description of competing orders.

cond-mat.supr-con↗

arXiv2012

Suppression of superconductivity at nematic critical point in underdoped cuprates

A nematic quantum critical point is anticipated to exist in the superconducting dome of some high-temperature superconductors. The nematic order competes with the superconducting order and hence reduces the superconducting condensate at $T = 0$. Moreover, the critical fluctuations of nematic order can excite more nodal quasiparticles out of the condensate. We address these two effects within an effective field theory and show that superfluid density $ρ^s(T)$ and superconducting temperature $T_c$ are both suppressed strongly by the critical fluctuations. The strong suppression of superconductivity provides a possible way to determine the nematic quantum critical point.

cond-mat.supr-con↗

arXiv2012

Unconventional behavior of Dirac fermions in three-dimensional gauge theory

We study the unconventional behavior of massless Dirac fermions due to interaction with a U(1) gauge field in two spatial dimensions. At zero chemical potential, the longitudinal and transverse components of gauge interaction are both long-ranged. There is no fermion velocity renormalization since the system respects Lorentz invariance. At finite chemical potential, the Lorentz invariance is explicitly broken by the finite Fermi surface. The longitudinal gauge interaction is statically screened and becomes unimportant, whereas the transverse gauge interaction remains long-ranged and leads to singular renormalization of fermion velocity. The anomalous dimension of fermion velocity is calculated by means of the renormalization group method. We then examine the influence of singular velocity renormalization on several physical quantities, and show that they exhibit different behavior at zero and finite chemical potential.

cond-mat.str-el↗

arXiv2012

Absence of dynamical gap generation in suspended graphene

There is an interesting proposal that the long-range Coulomb interaction in suspended graphene can generate a dynamical gap, which leads to a semimetal-insulator phase transition. We revisit this problem by solving the self-consistent Dyson-Schwinger equations of wave function renormalization and fermion gap. In order to satisfy the Ward identity, a suitable vertex function is introduced. The impacts of singular velocity renormalization and dynamical screening on gap generation are both included in this formalism, and prove to be very important. We obtain a critical interaction strength, $3.2 < α_{c} < 3.3$, which is larger than the physical value $α= 2.16$ for suspended graphene. It therefore turns out that suspended graphene is a semimetal, rather than insulator, at zero temperature.

cond-mat.str-el↗

arXiv2011

Nature of the antiferromagnetic quantum phase transition on the honeycomb lattice

We address the nature of the antiferromagnetic quantum phase transition that separates a semimetal from an antiferromagnet in the repulsive Hubbard model defined on the honeycomb lattice. At the critical point, the fermions acquire an anomalous dimension $η$ due to their strong coupling to the fluctuations of the order parameter $ϕ$. The finite $η$ in turn induces a singular $ϕ^{4}$ term and a non-analytical spin susceptibility signaling the breakdown of Hertz's $ϕ^{4}$ theory. As a result, the continuous antiferromagnetic quantum phase transition is internally unstable and turns into a first order transition.

cond-mat.str-el↗

arXiv2011

Disorder effects at a nematic quantum critical point in d-wave cuprate superconductor

A d-wave high temperature cuprate superconductor exhibits a nematic ordering transition at zero temperature. Near the quantum critical point, the coupling between gapless nodal quasiparticles and nematic order parameter fluctuation can result in unusual behaviors, such as extreme anisotropy of fermion velocities. We study the disorder effect on the nematic quantum critical behavior and especially on the flow of fermion velocities. The disorders that couple to nodal quasiparticles are divided into three types: random mass, random gauge field, and random chemical potential. A renormalization group analysis shows that random mass and random gauge field are both irrelevant and thus do not change the fixed point of extreme velocity anisotropy. However, the marginal interaction due to random chemical potential destroys this fixed point and makes the nematic phase transition unstable.

cond-mat.str-el↗

arXiv2011

Eliashberg theory of excitonic insulating transition in graphene

A sufficiently strong Coulomb interaction may open an excitonic fermion gap and thus drive a semimetal-insulator transition in graphene. In this paper, we study the Eliashberg theory of excitonic transition by coupling the fermion gap equation self-consistently to the equation of vacuum polarization function. Including the fermion gap into polarization function increases the effective strength of Coulomb interaction because it reduces the screening effects due to the collective particle-hole excitations. Although this procedure does not change the critical point, it leads to a significant enhancement of the dynamical fermion gap in the excitonic insulating phase. The validity of the Eliashberg theory is justified by showing that the vertex corrections are suppressed at large $N$ limit.

cond-mat.str-el↗

arXiv2011

Dynamical fermion mass generation and exciton spectra in graphene

The Coulomb interaction between massless Dirac fermions may induce dynamical chiral symmetry breaking by forming excitonic pairs in clean graphene, leading to semimetal-insulator transition. If the Dirac fermions have zero bare mass, an exact continuous chiral symmetry is dynamically broken and thus there are massless Goldstone excitons. If the Dirac fermions have a small bare mass, an approximate continuous chiral symmetry is dynamically broken and the resultant Goldstone type excitons become massive, which is analogous to what happens in QCD. In this paper, after solving Dyson-Schwinger gap equation in the presence of a small bare fermion mass, we found a remarkable reduction of the critical Coulomb interaction strength for excitonic pair formation and a strong enhancement of dynamical fermion mass. We then calculate the masses of Goldstone type excitons using the SVZ sum rule method and operator product expansion technique developed in QCD and find that the exciton masses are much larger than bare fermion mass but smaller than dynamical fermion mass gap. We also study the spin susceptibilities and estimate the masses of non-Goldstone type excitons using the same tools.

cond-mat.str-el↗

arXiv2011

Competition between excitonic gap generation and disorder scattering in graphene

We study the disorder effect on the excitonic gap generation caused by strong Coulomb interaction in graphene. By solving the self-consistently coupled equations of dynamical fermion gap $m$ and disorder scattering rate $Γ$, we found a critical line on the plane of interaction strength $λ$ and disorder strength $g$. The phase diagram is divided into two regions: in the region with large $λ$ and small $g$, $m \neq 0$ and $Γ= 0$; in the other region, $m = 0$ and $Γ\neq 0$ for nonzero $g$. In particular, there is no coexistence of finite fermion gap and finite scattering rate. These results imply a strong competition between excitonic gap generation and disorder scattering. This conclusion does not change when an additional contact four-fermion interaction is included. For sufficiently large $λ$, the growing disorder may drive a quantum phase transition from an excitonic insulator to a metal.

cond-mat.str-el↗

arXiv2010

Confinement induced by fermion damping in three-dimensional QED

The three-dimensional non-compact QED is known to exhibit weak confinement when fermions acquire a finite mass via the mechanism of dynamical chiral symmetry breaking. In this paper, we study the effect of fermion damping caused by elastic scattering on the classical potential between fermions. By calculating the vacuum polarization function that incorporates the fermion damping effect, we show that fermion damping can induce a weak confinement even when the fermions are massless and the chiral symmetry is not broken.

hep-th↗

arXiv2010

Fate of non-Fermi liquid behavior in QED$_{3}$ at finite chemical potential

The damping rate of two-dimensional massless Dirac fermions exhibit non-Fermi liquid behavior, $\propto ε^{1/2}$, due to gauge field at zero temperature and zero chemical potential. We study the fate of this behavior at finite chemical potential. We fist calculate explicitly the temporal and spatial components of vacuum polarization functions. The analytical expressions imply that the temporal component of gauge field develops a static screening length at finite chemical potential while the transverse component remains long-ranged owing to gauge invariance. We then calculate the fermion damping rate and show that the temporal gauge field leads to normal Fermi liquid behavior but the transverse gauge field leads to non-Fermi liquid behavior $\propto ε^{2/3}$ at zero temperature. This energy-dependence is more regular than $\propto ε^{1/2}$ and does not change as chemical potential varies.

cond-mat.str-el↗

arXiv2010

Coulomb interaction and semimetal-insulator transition in graphene

The strong Coulomb interaction between massless Dirac fermions can drive a semimetal-insulator transition in single-layer graphene by dynamically generating an excitonic fermion gap. There is a critical interaction strength $λ_c$ that separates the semimetal phase from the insulator phase. We calculate the specific heat and susceptibility of the system and show that they exhibit distinct behaviors in the semimetal and insulator phases.

cond-mat.str-el↗

arXiv2010

Unconventional Fermi surface in two-dimensional systems of Dirac fermions

At the low energy regime, the decay rate of two-dimensional massless Dirac fermions due to interactions can be written as $\mathrm{Im}Σ(ω) \propto |ω|^{x}$ at zero temperature. We find that the fermion system has: I) no sharp Fermi surface and no well-defined quasiparticle peak for $0 1$. In the presence of long-range gauge/Coulomb interaction or certain massless boson mode, the system exhibits unusual behavior belonging to class II.

cond-mat.str-el↗