Shao-Kai Jian | Tsinghua University (original) (raw)

Papers by Shao-Kai Jian

We study collective modes near the quantum critical point of a pair-density-wave (PDW) supercondu... more We study collective modes near the quantum critical point of a pair-density-wave (PDW) superconductor in 2+1 dimensions. The fate of gaps of various collective modes is investigated by functional renormalization. For incommensurate PDW superconductors, we show that the gapless Leggett mode, protected by the emergent U(1) symmetry, can induce an exponentially small Higgs mass compared to the superconducting gap. Further, for commensurate PDW superconductors, we find an emergent mass hierarchy in the collective modes, i.e. the masses of Leggett boson, Higgs boson, and the superconducting gap can differ by several magnitudes in the infrared. This may shed light to a mechanism underlying the hierarchy problem in the Standard Model of particle physics.

Exotic physics often emerges around quantum criticality in metallic systems. Here we explore the ... more Exotic physics often emerges around quantum criticality in metallic systems. Here we explore the nature of topological phase transitions between 3D double-Weyl semimetals and insulators (through annihilating double-Weyl nodes with opposite chiralities) in the presence of Coulomb interactions. From renormalization-group (RG) analysis, we find a non-Fermi-liquid quantum critical point (QCP) between the double-Weyl semimetals and insulators when artificially neglecting short-range interactions. However, it is shown that this non-Fermi-liquid QCP is actually unstable against nematic ordering when short-range interactions are correctly included in the RG analysis. In other words, the putative QCP between the semimetals and insulators is preempted by emergence of nematic phases when Coulomb interactions are present. We further discuss possible experimental relevance of the nematicity-preempted QCP to double-Weyl candidate materials HgCr2Se4 and SrSi2.

We study the coupled quantum Hall bilayers each at half-filled first excited Landau levels with v... more We study the coupled quantum Hall bilayers each at half-filled first excited Landau levels with varying the layer distance. Based on numerical exact diagonalization on torus, we identify two distinct phases separated by a critical layer distance dc. From dc to infinite layer distance, the topological phase is smoothly connected to a direct tensor product of two Moore-Read states, while the interlayer coherence emerges at d < dc characterized by the xy easy-plane ferromagnetic energy spectra, gapless pseudospin excitations and the finite exciton super-fluid stiffness, corresponding to the exciton superfluid state. More interestingly, the results of the ground state fidelity, the evolution of energy spectra, and the superfluid stiffness indicate a possible continuous transition. Theoretically it can be interpreted as a topological phase transition which simultaneously changes the topology of ground state and breaks symmetry, providing an interesting example of transitions beyond Landau paradigm.

Quantum chaos in many-body systems may be characterized by the Lyapunov exponent defined as the e... more Quantum chaos in many-body systems may be characterized by the Lyapunov exponent defined as the exponential growth rate of out-of-time-order correlators (OTOC). So far Lyaponov exponents around various quantum critical points (QCP) remain largely unexplored. Here, we investigate the Lyapunov exponent around QCPs of the Gross-Neveu (GN) model with N flavors of Dirac fermions in (2+1) dimensions. Around the GN quantum phase transition between a Dirac semimetal and a gapped insulator breaking Z2 symmetry (e.g., inversion symmetry of the honeycomb lattice), we find that the Lyaponov exponent λL≈3.5T/N at temperature T and to the leading order of 1/N in the large-N expansion. We also obtain the quantum scattering rate of an excitation with energy ϵ, which is proportional to (ϵT)^(1/2)/N at low energy. We further discuss possible experimental relevances of the GN model in many-body systems.

We study the generalized Sachdev-Ye-Kitaev (SYK) chain consisting of N (complex or Majorana) ferm... more We study the generalized Sachdev-Ye-Kitaev (SYK) chain consisting of N (complex or Majorana) fermions per site with random interactions and hoppings between neighboring sites. In the limit of vanishing SYK interactions, from both supersymmetric field theory analysis and numerical calculations we find that the random-hopping model exhibits Anderson localization at finite N, irrespective of the parity of N. Moreover, the localization length scales linearly with N, implying the absence of Anderson localization only at N=∞. For finite SYK interactions, by performing the exact diagonalization we show that there is a dynamic phase transition from many-body localization to thermal diffusion as interaction strength exceeds a critical value Jc. In addition, we find that the critical interaction strength Jc decreases with the increase of N, consistent with the analytical result of Jc/t∝1/(N^(5/2)*logN) derived from the weakly interacting limit.

Phys. Rev. Lett. 120, 215702, 2018

Tricriticality, as a sister of criticality, is a fundamental and absorbing issue in condensed mat... more Tricriticality, as a sister of criticality, is a fundamental and absorbing issue in condensed matter physics. It has been verified that the bosonic Wilson-Fisher universality class can be changed by gapless fermionic modes at criticality. However, the counterpart phenomena at tricriticality have rarely been explored. In this paper, we study a model in which a tricritical Ising model is coupled to massless Dirac fermions. We find that the massless Dirac fermions result in the emergence of a new tricritical point, which we refer to as the chiral tricritical point (CTP), at the phase boundary between the Dirac semimetal and the charge-density-wave insulator. From functional renormalization group analysis of the effective action, we obtain the critical behaviors of the CTP, which are qualitatively distinct from both the tricritical Ising universality and the chiral Ising universality. We further extend the calculations of the chiral tricritical behaviors of Ising spins to the case of Heisenberg spins. The experimental relevance of the CTP in two-dimensional Dirac semimetals is also discussed.

Phys. Rev. B 97, 205141, 2018

We show that the quantum critical point (QCP) between a diffusive metal and ferromagnetic (or ant... more We show that the quantum critical point (QCP) between a diffusive metal and ferromagnetic (or antiferromagnetic) phases in the SYK chain has a gravitational description corresponding to the double-trace deformation in an AdS2 chain. Specifically, by studying a double-trace deformation of a Z2 scalar in an AdS2 chain where the Z2 scalar is dual to the order parameter in the SYK chain, we find that the susceptibility and renormalization group equation describing the QCP in the SYK chain can be exactly reproduced in the holographic model. Our results suggest that the infrared geometry in the gravity theory dual to the diffusive metal of the SYK chain is also an AdS2 chain. We further show that the transition in SYK model captures universal information about double-trace deformation in generic black holes with near horizon AdS2 spacetime.

Phys. Rev. B 97, 115162, 2018

We investigate novel topological magnon band crossings of pyrochlore antiferromagnets with all-in... more We investigate novel topological magnon band crossings of pyrochlore antiferromagnets with all-in-all-out (AIAO) magnetic order. By general symmetry analysis and spin-wave theory, we show that pyrochlore materials with AIAO orders can host Weyl magnons under external magnetic fields or uniaxial strains. Under a small magnetic field, the magnon bands of the pyrochlore with AIAO background can feature two opposite-charged Weyl points, which is the minimal number of Weyl points realizable in quantum materials and has not be experimentally observed so far. We further show that breathing pyrochlores with AIAO orders can exhibit Weyl magnons upon uniaxial strains. These findings apply to any pyrochlore material supporting AIAO orders, irrespective of the forms of interactions. Specifically, we show that the Weyl magnons are robust against direct (positive) Dzyaloshinskii-Moriya interactions. Because of the ubiquitous AIAO orders in pyrochlore magnets including R2Ir2O7, and experimentally achievable external strain and magnetic field, our predictions provide promising arena to witness the Weyl magnons in quantum magnets.

The study of spin-orbit coupling of photons has attracted much attention in recent years, and lea... more The study of spin-orbit coupling of photons has attracted much attention in recent years, and leads to many potential applications in optics. In the recently discovered metamaterial -- photonic crystals with Weyl points, the pseudospin-orbit coupling of photons bears a resemblance to the spin-orbit coupling. We study the pseudospin Hall effect of light in such metamaterials and find that during total reflection, the light beam experiences a transverse shift that is proportional to the pseudospin (or the monopole charge) of the Weyl point. As the spin Hall effect has inspired many works to explore the applications in optics, exploring the coupling between the orbital and pseudospin degrees of freedom of photons can also be fruitful in the field of optics, as well as in other fields where Weyl points can be realized.

Phys. Rev. B 96, 115448, 2017

The Imbert-Fedorov (IF) shift in optics describes the transverse shift of light beams at the refl... more The Imbert-Fedorov (IF) shift in optics describes the transverse shift of light beams at the reflection interface. Recently, the IF shift of Weyl fermions at the interface between Weyl semimetals (WSMs) with single monopole charge has been studied. Here, we study the IF shift at the interface between two WSMs, each of which is carrying an arbitrary integer monopole charge. We find a general relation between the monopole charges of the two WSMs and the IF shift. In particular, the IF shift is proportional to the monopole charge if both WSMs have the same one. Our results can be used to infer the topology of the materials by experimentally measuring their IF shift. Furthermore, we consider the possibility that the Weyl fermions are scattered to other Weyl cones during the reflection, which results in qualitatively different behavior of the IF shift. While we use a quantum mechanical approach to solve the problem, semiclassical equations of motion and the conservation of total angular momentum can help us intuitively interpret our results in special cases.

Phys. Rev. Lett. 119, 206602, 2017

Many aspects of many-body localization (MBL) transitions remain elusive so far. Here, we propose ... more Many aspects of many-body localization (MBL) transitions remain elusive so far. Here, we propose a higher-dimensional generalization of the Sachdev-Ye-Kitaev (SYK) model and show that it exhibits a MBL transition. The model on a bipartite lattice has N Majorana fermions with SYK interactions on each site of the A sublattice and M free Majorana fermions on each site the of B sublattice, where N and M are large and finite. For r≡M/N<rc=1, it describes a diffusive metal exhibiting maximal chaos. Remarkably, its diffusive constant D vanishes [D∝(rc−r)1/2] as r→rc, implying a dynamical transition to a MBL phase. It is further supported by numerical calculations of level statistics which changes from Wigner-Dyson (r<rc) to Poisson (r>rc) distributions. Note that no subdiffusive phase intervenes between diffusive and MBL phases. Moreover, the critical exponent ν=0, violating the Harris criterion. Our higher-dimensional SYK model may provide a promising arena to explore exotic MBL transitions.

Phys. Rev. B 96, 075110, 2017

It was recently shown that nonsymmorphic space group symmetries can protect novel surface states ... more It was recently shown that nonsymmorphic space group symmetries can protect novel surface states with hourglass-like dispersions. In this paper, we show that such dispersions can also appear in the bulk of three-dimensional (3D) systems which respect nonsymmorphic symmetries. Specifically, we construct 3D lattice models featuring hourglass-like dispersions in the bulk, which are protected by nonsymmorphic and time-reversal symmetries. We call such systems hourglass semimetals, as they have point or line nodes associated with hourglass-like dispersions. Hourglass nodal lines appear in glide-invariant planes, while hourglass Weyl points can occur on screw-invariant axes. The Weyl points and surface Fermi arcs in hourglass Weyl semimetals are stable against weak perturbations breaking those nonsymmorphic symmetries. Our results may shed light on searching for exotic Weyl semimetals in nonsymmorphic materials.

Phys. Rev. B 96, 241111, 2017

We study interaction effects, including both long-ranged Coulomb and short-range interactions, in... more We study interaction effects, including both long-ranged Coulomb and short-range interactions, in three-dimensional topological triple-Weyl semimetals whose triple-Weyl points are protected by crystal symmetries. By performing Wilsonian renormalization group analysis of the low-energy effective field theory of the minimal model with triple-Weyl nodes, we find that the fixed point of noninteracting triple-Weyl fermions is unstable in the presence of Coulomb interactions and flows to a nontrivial stable fixed point representing marginal Fermi liquids with anisotropic screening effects. We further discuss relevant unusual physical consequences due to the novel behavior of correlation effects in this system.

Phys. Rev. B 96, 195162, 2017

In this paper we investigate the nature of quantum phase transitions between two-dimensional Dira... more In this paper we investigate the nature of quantum phase transitions between two-dimensional Dirac semimetals and Z3-ordered phases (e.g. Kekule valence-bond solid), where cubic terms of the order parameter are allowed in the quantum Landau-Ginzberg theory and the transitions are putatively first-order. From large-N renormalization group (RG) analysis, we find that fermion-induced quantum critical points (FIQCPs) [Z.-X. Li et al., Nature Communications 8, 314 (2017)] occur when N (the number of flavors of four-component Dirac fermions) is larger than a critical value Nc. Remarkably, from the knowledge of spacetime supersymmetry, we obtain an exact lower bound for Nc, i.e., Nc>1/2. (Here the "1/2" flavor of four-component Dirac fermions is equivalent to one flavor of four-component Majorana fermions). Moreover, we show that the emergence of two length scales is a typical phenomenon of FIQCPs and obtain two different critical exponents, i.e., ν≠ν′, by large-N RG calculations. We further give a brief discussion on possible experimental realizations of FIQCPs.

Phys. Rev. B 96, 155112, 2017

Fermion-induced quantum critical points (FIQCPs) were recently discovered at the putatively first... more Fermion-induced quantum critical points (FIQCPs) were recently discovered at the putatively first-order transitions between two-dimensional (2D) Dirac semimetals and the Kekule valence bond solids on the honeycomb lattice by sign-free quantum Monte Carlo simulations [Nature Communications 8, 314, (2017)]. Here, we investigate possible FIQCP in 3D topological Weyl semimetals at a Z3 symmetry-breaking transition that is putatively first-order according to the Landau criterion. We construct a lattice model featuring 3D double-Weyl fermions (monopole charges ±2) and we show that Z3 nodal-nematic transitions occur under finite Hubbard interaction. Furthermore, using renormalization-group analysis, we identify such a transition as a genuine FIQCP where the cubic terms are irrelevant and an enlarged U(1) symmetry emerges at low energy. We further discuss quantum critical behaviors and experimental signatures of such FIQCPs in 3D double-Weyl semimetals.

Phys. Rev. Lett. 118, 166802, 2017

Supersymmetric (SUSY) gauge theories such as the Minimal Supersymmetric Standard Model play a fun... more Supersymmetric (SUSY) gauge theories such as the Minimal Supersymmetric Standard Model play a fundamental role in modern particle physics, but have not been verified so far in nature. Here, we show that a SUSY gauge theory with dynamical gauge bosons and fermionic gauginos emerges naturally at the pair-density-wave (PDW) quantum phase transition on the surface of a correlated topological insulator (TI) hosting three Dirac cones, such as the topological Kondo insulator SmB6. At the quantum tricritical point between the surface Dirac semimetal and nematic PDW phases, three massless bosonic Cooper pair fields emerge as the superpartners of three massless surface Dirac fermions. The resulting low-energy effective theory is the supersymmetric XYZ model, which is dual by mirror symmetry to N =2 supersymmetric quantum electrodynamics (SQED) in 2+1 dimensions, providing a first example of emergent supersymmetric gauge theory in condensed matter systems. Supersymmetry allows us to determine exactly certain critical exponents and the optical conductivity of the surface states at the strongly coupled tricritical point, which may be measured in future experiments.

Phys. Rev. Lett. 116, 226801, 2016

Weyl semimetals are new states of matter which feature novel Fermi arcs and exotic transport phen... more Weyl semimetals are new states of matter which feature novel Fermi arcs and exotic transport phenomena. Based on first-principles calculations, we report that the chalcopyrites CuTlSe2, AgTlTe2, AuTlTe2 and ZnPbAs2 are ideal Weyl semimetals, having largely separated Weyl points (∼ 0.05Å −1) and uncovered Fermi arcs that are amenable to experimental detections. We also construct a minimal effective model to capture the low-energy physics of this class of Weyl semimetals. Our discovery is a major step toward a perfect playground of intriguing Weyl semimetals and potential applications for low-power and high-speed electronics.

Nature Communications 8, 314, 2017

A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradi... more A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group (RG) analysis we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points (FIQCP). We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a FIQCP for N = 2, 3, 4, 5, 6, consistent with the RG analysis. We finally discuss possible experimental realizations of the FIQCP in graphene and graphene-like materials.

Phys. Rev. A, 93, 061801, 2016

Weyl points in three-dimensional photonic crystals behave as monopoles of Berry flux in momentum ... more Weyl points in three-dimensional photonic crystals behave as monopoles of Berry flux in momentum space. Here, based on general symmetry analysis, we show that a minimal number of four symmetry-related (consequently equifrequency) Weyl points can be realized in time-reversal invariant photonic crystals. We further propose an experimentally-feasible way to modify double-gyroid photonic crystals to realize four equifrequency Weyl points, which is explicitly confirmed by our first-principle photonic band-structure calculations. Remarkably, photonic crystals with equifrequency Weyl points are qualitatively advantageous in applications including angular selectivity, frequency selectivity, invisibility cloaking, and three dimensional imaging.

Nature Communications, 7, 11136, 2016

Ideal Weyl semimetals with all Weyl nodes exactly at the Fermi level and no coexisting trivial Fe... more Ideal Weyl semimetals with all Weyl nodes exactly at the Fermi level and no coexisting trivial Fermi surfaces in the bulk, similar to graphene, could feature deep physics such as exotic transport phenomena induced by the chiral anomaly. Here, we show that HgTe and half-Heusler compounds, under a broad range of in-plane compressive strain, could be materials in nature realizing ideal Weyl semimetals with four pairs of Weyl nodes and topological surface Fermi arcs. Generically, we find that the HgTe-class materials with nontrivial band inversion and noncentrosymmetry provide a promising arena to realize ideal Weyl semimetals. Such ideal Weyl semimetals could further provide a unique platform to study emergent phenomena such as the interplay between ideal Weyl fermions and superconductivity in the half-Heusler compound LaPtBi.