arXiv subjects

B. Andrei Bernevig

Publications and source records attributed to B. Andrei Bernevig.

At least 271 records · Page 15Linked to original sources

arXiv2011

Robustness of s-wave Pairing in Electron-Overdoped $\text{A}_{1-y}\text{Fe}_{2-x}\text{Se}_2$

Using self consistent mean field and functional renormalization group approaches we show that s-wave pairing symmetry is robust in the heavily electron-doped iron chalcogenides $(\text{K, Cs}) \text{Fe}_{2-x}\text{Se}_2 $. This is because in these materials the leading antiferromagnetic (AFM) exchange coupling is between next-nearest-neighbor (NNN) sites while the nearest neighbor (NN) magnetic exchange coupling is ferromagnetic (FM). This is different from the iron pnictides, where the NN magnetic exchange coupling is AFM and leads to strong competition between s-wave and d-wave pairing in the electron overdoped region. Our finding of a robust s-wave pairing in $(\text{K, Cs}) \text{Fe}_{2-x}\text{Se}_2$ differs from the d-wave pairing result obtained by other theories where non-local bare interaction terms and the NNN $J_2$ term are underestimated. Detecting the pairing symmetry in $(\text{K, Cs}) \text{Fe}_{2-x}\text{Se}_2 $ may hence provide important insights regarding the mechanism of superconducting pairing in iron based superconductors.

cond-mat.supr-con↗

arXiv2011

Dirac cone in iron-based high Tc superconductors

The band structure of iron-based superconductors gives rise to yet another scenario for the appearance of Dirac fermions. A viewpoint on "Observation of Dirac cone electronic dispersion in BaFe2As2" (Richard et.al., PRL 104, 137001 (2010)).

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arXiv2010

Decomposition of fractional quantum Hall states: New symmetries and approximations

We provide a detailed description of a new symmetry structure of the monomial (Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall states first obtained in Ref. 1, which we now extend to spin-singlet states. We show that the Haldane-Rezayi spin-singlet state can be obtained without exact diagonalization through a differential equation method that we conjecture to be generic to other FQH model states. The symmetry rules in Ref. 1 as well as the ones we obtain for the spin singlet states allow us to build approximations of FQH states that exhibit increasing overlap with the exact state (as a function of system size). We show that these overlaps reach unity in the thermodynamic limit even though our approximation omits more than half of the Hilbert space. We show that the product rule is valid for any FQH state which can be written as an expectation value of parafermionic operators.

cond-mat.str-el↗

arXiv2010

Inversion Symmetric Topological Insulators

We study translationally-invariant insulators with inversion symmetry that fall outside the established classification of topological insulators. These insulators are not required to have gapless boundary modes in the energy spectrum. However, they do exhibit protected modes in the entanglement spectrum localized on the cut between two entangled regions. Their entanglement entropy cannot be made to vanish adiabatically, and hence the insulators can be called topological. There is a direct connection between the inversion eigenvalues of the band structure and the mid-gap states in the entanglement spectrum. The classification of protected entanglement levels is given by an integer $n\in Z$, which is the difference between the negative inversion eigenvalues at inversion symmetric points in the Brillouin zone, taken in sets of two. When the Hamiltonian describes a Chern insulator or a non-trivial T-invariant topological insulator, the entanglement spectrum exhibits spectral flow. If the Chern number is zero for the former, or T is broken in the latter, the entanglement spectrum does \emph{not} have spectral flow, but, depending on the inversion eigenvalues, can still have protected midgap bands. Although spectral flow is broken, the mid-gap entanglement bands cannot be adiabatically removed, and the insulator is `topological.' In 1D, we establish a link between the product of the inversion eigenvalues of all occupied bands at all inversion momenta and charge polarization. In 2D, we prove a link between the product of the inversion eigenvalues and the parity of the Chern number. In 3D, we find a topological constraint on the product of the inversion eigenvalues indicating that some 3D materials are topological metals, and we show the link between the inversion eigenvalues and the 3D Quantum Hall Effect and the magnetoelectric polarization in the absence of T-symmetry.

cond-mat.mes-hall↗

arXiv2010

Entanglement Spectrum of a Disordered Topological Chern Insulator

How much information is stored in the ground-state of a system without \emph{any symmetry} and how can we extract it? This question is investigated by analyzing the behavior of a topological Chern Insulator (CI) in the presence of disorder, with a focus on its entanglement spectrum (EtS) constructed from the ground state. For systems with symmetries, the EtS was shown to contain explicit information revealed by sorting the EtS against the conserved quantum numbers. In the absence of any symmetry, we demonstrate that statistical methods such as the level statistics of the EtS can be equally insightful, allowing us to distinguish when an insulator is in a topological or trivial phase and to map the boundary between the two phases, where EtS becomes entirely delocalized. The phase diagram of a CI is explicitly computed as function of Fermi level ($E_F$) and disorder strength using the level statistics of the EtS and energy spectrum (EnS), together with a computation of the Chern number via an efficient real-space formula.

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arXiv2010

Non-local order in gapless systems: Entanglement Spectrum in Spin Chains

We show that the entanglement spectrum can be used to define non-local order in gapless spin systems. We find a gap that fully separates a series of generic, high `entanglement energy' levels, from a flat band of levels with specific multiplicities that uniquely define the ground-state, and remains finite in the thermodynamic limit. We pick the appropriate set of quantum numbers, and then partition the system in this space. This partition corresponds to a very non-local real-space cut. Despite the fact that the Laughlin state is bulk gapped while the antiferromagnetic spin chain state is bulk gapless, we show that the S=1/2 Heisenberg antiferromagnet in one dimension has an entanglement spectrum almost identical to that of the Laughlin Fractional Quantum Hall state in two dimensions, revealing the similar field theory of their low-energy edge and bulk excitations respectively.

cond-mat.str-el↗

arXiv2010

Electron-Quasihole Duality and Second Order Differential Equation for Read-Rezayi and Jacks Wavefunctions

We consider the quasihole wavefunctions of the non-abelian Read-Rezayi quantum Hall states which are given by the conformal blocks of the minimal model WA_{k-1}(k+1,k+2) of the WA_{k-1} algebra. By studying the degenerate representations of this conformal field theories, we derive a second order differential equation satisfied by a general many-quasihole wavefunction. We find a duality between the differential equations fixing the electron and quasihole wavefunctions. They both satisfy the Laplace-Beltrami equation. We use this equation to obtain an analytic expression for the generic wavefunction with one excess flux. These results also apply to the more general models WA_{k-1}(k+1,k+r) corresponding to the recently introduced Jack states.

cond-mat.str-el↗

arXiv2010

Leggett mode in a strong-coupling model of iron arsenide superconductors

Using a two-orbital model of the superconducting phase of the pnictides, we compute the spectrum of the Leggett mode -- a collective excitation of the phase of the superconducting gap known to exist in multi-gap superconductors -- for different possible symmetries of the superconducting order parameter. Specifically, we identify the small regions of parameter space where the Leggett mode lies below the two-particle continuum, and hence should be visible as a sharp resonance peak. We discuss the possible utility of the Leggett mode in distinguishing different momentum dependencies of the superconducting gap. We argue that the observation of a sharp Leggett mode would be consistent with the presence of strong electron-electron correlations in iron-based superconductors. We also emphasize the importance of the orbital character of the Leggett mode, which can result in an experimental observation of the mode in channels other than $A_{1g}$.

cond-mat.supr-con↗

arXiv2010

Why some Iron-based superconductors are nodal while others are nodeless

The symmetry of the order parameter in iron-based superconductors, especially the presence or absence of nodes, is still a question of debate. While contradictory experiments can be explained by appropriately tuned theories of nodeless superconductivity in the iron-arsenide compounds, for LaOFeP all experiments clearly point to a nodal order parameter. We put forward a scenario that naturally explains the difference between the order-parameter character in these two sets of compounds, and use functional renormalization group (fRG) techniques to analyze it in detail. Our results show that, due to the orbital content of the electron and hole bands, nodal superconductivity on the electron pockets (hole pocket gaps are always nodeless) can naturally appear when the third hole pocket which lies at wavevector (pi,pi) in the unfolded Brillouin zone is absent, as is the case in LaOFeP. When present, the third hole pocket has overwhelming d_{xy} orbital character, and the intra-orbital interaction with the d_{xy} dominated part of the electron Fermi surface is enough to drive the superconductivity nodeless (of s^+- form). However, in its absence, pair hopping, inter-orbital, and electron-electron intra-orbital interactions render the gap on the electron pockets softly nodal.

cond-mat.supr-con↗

arXiv2009

The entanglement gap and a new principle of adiabatic continuity

We give a complete definition of the entanglement gap separating low-energy, topological levels, from high-energy, generic ones, in the "entanglement spectrum" of Fractional Quantum Hall (FQH) states. By removing the magnetic length inherent in the FQH problem - a procedure which we call taking the "conformal limit", we find that the entanglement spectrum of an incompressible ground-state of a generic (i.e. Coulomb) lowest Landau Level Hamiltonian re-arranges into a low-(entanglement) energy part separated by a full gap from the high energy entanglement levels. As previously observed, the counting of these levels starts off as the counting of modes of the edge theory of the FQH state, but quickly develops finite-size effects which we show can also serve as a fingerprint of the FQH state. As the sphere manifold where the FQH resides grows, the level spacing of the states at the same angular momentum goes to zero, suggestive of the presence of relativistic gapless edge-states. By using the adiabatic continuity of the low entanglement energy levels, we investigate whether two states are topologically connected.

cond-mat.str-el↗

arXiv2009

Novel properties in Josephson junctions involving the cos(kx)cos(ky)-pairing state in iron-pnictides

We propose a trilayer $π$-junction that takes advantage of the unconventional $s_{x^2 y^2}=\cos k_x \cos k_y$ pairing symmetry which changes sign between electron and hole Fermi pockets in the iron pnictides. In addition, we also present theoretical results for Andreev bound states in thin superconductor-normal metal (or insulator) iron-pnictide junctions. The presence of nontrivial in-gap states, which uniquely appear in this unconventional pairing state, is a distinct feature in comparison to other singlet pairing states.

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arXiv2009

Doping-dependent pairing symmetry in the Iron-Pnictides

We use the functional renormalization group method to analyze the phase diagram of a 4-band model for the iron-pnictides subject to band interactions with certain A_{1g} momentum dependence. We determine the parameter regimes where an extended s-wave pairing instability with and without nodes emerges. On the electron-doped side, the parameter regime in which a nodal gap appears is found to be much narrower than recently predicted in arXiv:0903.5547. On the hole-doped side, the extended s-wave pairing never becomes nodal: above a critical strength of the intra-band repulsion, the system favors an exotic extended d-wave instability on the enlarged hole pockets at much lower T_c. At half filling, we find that a strong momentum dependence of inter-band pair hopping yields an extended s-wave instability instead of spin-density wave (SDW) ordering. These results demonstrate that an interaction anisotropy around the Fermi surfaces generally leads to a pronounced sensitivity of the pairing state on the system parameters.

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arXiv2009

Magnetic Properties of the Superconducting State of Iron-Based Superconductors

We show that features of the dynamical spin susceptibility can unambiguously distinguish between different pairing symmetries of the superconducting state in iron-based superconductors. A magnetic resonance is a unique feature for the extended $s_{x^2y^2}$-wave $\cos k_x\cos k_y$ pairing symmetry. It is present in the pure superconducting (SC) state, but weakens in the mixed SC and magnetically ordered state. We calculate the the RPA correction to the NMR spin relaxation rate $1/T_1$ and the Knight shift in the above states and show a good agreement with experimental results. Moreover, we argue that the energy dispersion of the magnetic resonance along c axis observed in neutron scattering experiments is also an indirect evidence supporting the $s_{x^2y^2}$ pairing symmetry.

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arXiv2009

Quasiparticle Scattering Interference in Superconducting Iron-pnictides

Using both two orbital and five orbital models, we investigate the quasiparticle interference (QPI) patterns in the superconducting (SC) state of iron-based superconductors. We compare the results for nonmagnetic and magnetic impurities in sign-changed s-wave $\cos(k_x)\cdot\cos(k_y)$ and sign-unchanged $|\cos(k_x)\cdot\cos(k_y)|$ SC states. While the patterns strongly depend on the chosen band structures, the sensitivity of peaks around $(\pmπ,0)$ and $(0,\pmπ)$ wavevectors on magnetic or non-magnetic impurity, and sign change or sign unchanged SC orders is common in two models. Our results strongly suggest that QPI may provide direct information of band structures and evidence of the pairing symmetry in the SC states.

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arXiv2009

Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras

We present a general method to obtain the central charge and quasihole scaling dimension directly from groundstate and quasihole wavefunctions. Our method applies to wavefunctions satisfying specific clustering properties. We then use our method to examine the relation between Jack symmetric functions and certain W-algebras. We add substantially to the evidence that the (k,r) admissible Jack functions correspond to correlators of the conformal field theory W_k(k+1,k+r), by calculating the central charge and scaling dimensions of some of the fields in both cases and showing that they match. For the Jacks described by unitary W-models, the central charge and quasihole exponents match the ones previously obtained from analyzing the physics of the edge excitations. For the Jacks described by non-unitary W-models the central charge and quasihole scaling dimensions obtained from the wavefunctions differ from the ones obtained from the edge physics, which instead agree with the "effective" central charge of the corresponding W-model.

cond-mat.mes-hall↗

arXiv2009

The Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States

We deduce a new set of symmetries and relations between the coefficients of the expansion of Abelian and Non-Abelian Fractional Quantum Hall (FQH) states in free (bosonic or fermionic) many-body states. Our rules allow to build an approximation of a FQH model state with an overlap increasing with growing system size (that may sometimes reach unity!) while using a fraction of the original Hilbert space. We prove these symmetries by deriving a previously unknown recursion formula for all the coefficients of the Slater expansion of the Laughlin, Read Rezayi and many other states (all Jacks multiplied by Vandermonde determinants), which completely removes the current need for diagonalization procedures.

cond-mat.mes-hall↗

arXiv2009

Topological Entanglement and Clustering of Jain Hierarchy States

We obtain the clustering properties and part of the structure of zeroes of the Jain states at filling $\frac{k}{2k+1}$: they are a direct product of a Vandermonde determinant (which has to exist for any fermionic state) and a bosonic polynomial at filling $\frac{k}{k+1}$ which vanishes when $k+1$ particles cluster together. We show that all Jain states satisfy a "squeezing rule" (they are "squeezed polynomials") which severely reduces the dimension of the Hilbert space necessary to generate them. The squeezing rule also proves the clustering conditions that these states satisfy. We compute the topological entanglement spectrum of the Jain $ν={2/5}$ state and compare it to both the Coulomb ground-state and the non-unitary Gaffnian state. All three states have very similar "low energy" structure. However, the Jain state entanglement "edge" state counting matches both the Coulomb counting as well as two decoupled U(1) free bosons, whereas the Gaffnian edge counting misses some of the "edge" states of the Coulomb spectrum. The spectral decomposition as well as the edge structure is evidence that the Jain state is universally equivalent to the ground state of the Coulomb Hamiltonian at $ν={2/5}$. The evidence is much stronger than usual overlap studies which cannot meaningfully differentiate between the Jain and Gaffnian states. We compute the entanglement gap and present evidence that it remains constant in the thermodynamic limit. We also analyze the dependence of the entanglement gap and overlap as we drive the composite fermion system through a phase transition.

cond-mat.mes-hall↗

arXiv2008

Theory of Magnetic Order in $ Fe_{1+y}Te_{1-x}Se_x$

We develop a local spin model to explain the rich magnetic structures in the iron-based superconductors $Fe_{1+y}Te_{1-x}Se_x$. We show that our model exhibits both commensurate antiferromagnetic and incommensurate magnetic order along the crystal a-axis. The transition from the commensurate to the incommensurate phase is induced when the concentration of excess $Fe$ atoms is larger than a critical value. Experimentally measurable spin-wave features are calculated, and the mean-field phase diagram of the model is obtained. Our model also suggests the existence of a large quantum critical region due to strong spin frustration upon increasing $Se$ concentration.

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