Erez Berg | Weizmann Institute of Science (original) (raw)

Papers by Erez Berg

One of the most striking features of quantum mechanics is the appearance of phases of matter with... more One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems, the gapless surface states of topological insulators, and elementary excitations with non-abelian statistics in fractional quantum Hall systems and topological superconductors. Many of

Physical review letters, Jan 11, 2003

We apply the contractor renormalization (CORE) method to the spin half Heisenberg antiferromagnet... more We apply the contractor renormalization (CORE) method to the spin half Heisenberg antiferromagnet on the frustrated checkerboard and pyrochlore lattices. Their ground states are spin-gapped singlets which break lattice symmetry. Their effective Hamiltonians describe fluctuations of orthogonal singlet pairs on tetrahedral blocks, at an emergent low energy scale. We discuss low temperature thermodynamics and new interpretations of finite size numerical data. We argue that our results are common to many models of quantum frustration.

Physical Review B, 2015

ABSTRACT Bilayer graphene subjected to perpendicular magnetic and electric fields displays a subt... more ABSTRACT Bilayer graphene subjected to perpendicular magnetic and electric fields displays a subtle competition between different symmetry-broken phases, resulting from an interplay between the internal spin and valley degrees of freedom. The transition between different phases is often identified by an enhancement of the conductance. Here, we propose that the enhanced conductance at the transition is due to the appearance of robust conducting edge states at domain walls between the two phases. We formulate a criterion for the existence of such conducting edge states at the domain walls. For example, for a spontaneously layer polarized state at filling factor \nu${}=2$, domain walls between regions of opposite polarization carry conducting edge modes. A microscopic analysis shows that lattice-scale interactions can favor such a layer polarized state.

Physical review letters, Jan 24, 2015

We consider a normal lead coupled to a Majorana bound state. We show that the spin-resolved curre... more We consider a normal lead coupled to a Majorana bound state. We show that the spin-resolved current correlations exhibit unique features which distinguish Majorana bound states from other low-energy resonances. In particular, the spin-up and spin-down currents from a Majorana bound state are anticorrelated at low bias voltages, and become uncorrelated at higher voltages. This behavior is independent of the exact form of coupling to the lead, and of the direction of the spin polarization. In contrast, an ordinary low-energy Andreev bound state gives rise to a positive correlation between the spin-up and spin-down currents, and this spin-resolved current-current correlation approaches a nonzero constant at high bias voltages. We discuss experimental setups in which this effect can be measured.

Physical review letters, Jan 13, 2015

We describe a novel topological superfluid state, which forms in a one-dimensional Fermi gas with... more We describe a novel topological superfluid state, which forms in a one-dimensional Fermi gas with Rashba-like spin-orbit coupling, a Zeeman field, and intrinsic attractive interactions. In spite of total number conservation and the presence of gapless excitations, Majorana-like zero modes appear in this system and can be linked with interfaces between two distinct phases that naturally form at different regions of the harmonic trap. As a result, the low lying collective excitations of the system, including the dipole oscillations and the long-wavelength phonons are all doubly degenerate. While backscattering from point impurities can lead to a splitting of the degeneracies that scales algebraically with the system size, the smooth confining potential can only cause an exponentially small splitting. We show that the topological state can be uniquely probed by a pumping effect induced by a slow sweep of the Zeeman field from a high initial value down to zero. The effect is expected to...

Physical review letters, Jan 6, 2015

We show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_{2} a... more We show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_{2} and U(1) symmetry at the multicritical point where the Ising and Berezinskii-Kosterlitz-Thouless transitions coincide. To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations allowed by symmetry. This analysis reveals an intricate flow with a marginally irrelevant direction that preserves part of the supersymmetry of the fixed point. The slow flow along this special line has significant consequences on the physics of the multicritical point. In particular, we show that the scaling of the U(1) gap away from the multicritical point is different from the usual Berezinskii-Kosterlitz-Thouless exponential gap scaling.

Physical review letters, Jan 6, 2015

We consider a low T_{c} metallic superconductor weakly coupled to the soft fluctuations associate... more We consider a low T_{c} metallic superconductor weakly coupled to the soft fluctuations associated with proximity to a nematic quantum critical point (NQCP). We show that (1) a BCS-Eliashberg treatment remains valid outside of a parametrically narrow interval about the NQCP, (2) the symmetry of the superconducting state (d wave, s wave, p wave) is typically determined by the noncritical interactions, but T_{c} is enhanced by the nematic fluctuations in all channels, and (3) in 2D, this enhancement grows upon approach to criticality up to the point at which the weak coupling approach breaks down, but in 3D, the enhancement is much weaker.

Science (New York, N.Y.), Jan 7, 2014

Electrons have three quantized properties-charge, spin, and Fermi statistics-that are directly re... more Electrons have three quantized properties-charge, spin, and Fermi statistics-that are directly responsible for a vast array of phenomena. Here we show how these properties can be coherently and dynamically stripped from the electron as it enters a certain exotic state of matter known as a quantum spin liquid (QSL). In a QSL, electron spins collectively form a highly entangled quantum state that gives rise to the fractionalization of spin, charge, and statistics. We show that certain QSLs host distinct, topologically robust boundary types, some of which allow the electron to coherently enter the QSL as a fractionalized quasi-particle, leaving its spin, charge, or statistics behind. We use these ideas to propose a number of universal, conclusive experimental signatures that would establish fractionalization in QSLs.

By using ARPES interpretation for the origin of the collective spin and charge orderings in under... more By using ARPES interpretation for the origin of the collective spin and charge orderings in underdoped La-based cuprate superconductors is carefully examined. A Fermi surface nesting wave vector is identified which closely matches the collective ordering wave vector observed by ...

One of the most striking features of quantum mechanics is the appearance of phases of matter with... more One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems, the gapless surface states of topological insulators, and elementary excitations with non-abelian statistics in fractional quantum Hall systems and topological superconductors. Many of

Physical review letters, Jan 11, 2003

We apply the contractor renormalization (CORE) method to the spin half Heisenberg antiferromagnet... more We apply the contractor renormalization (CORE) method to the spin half Heisenberg antiferromagnet on the frustrated checkerboard and pyrochlore lattices. Their ground states are spin-gapped singlets which break lattice symmetry. Their effective Hamiltonians describe fluctuations of orthogonal singlet pairs on tetrahedral blocks, at an emergent low energy scale. We discuss low temperature thermodynamics and new interpretations of finite size numerical data. We argue that our results are common to many models of quantum frustration.

Physical Review B, 2015

ABSTRACT Bilayer graphene subjected to perpendicular magnetic and electric fields displays a subt... more ABSTRACT Bilayer graphene subjected to perpendicular magnetic and electric fields displays a subtle competition between different symmetry-broken phases, resulting from an interplay between the internal spin and valley degrees of freedom. The transition between different phases is often identified by an enhancement of the conductance. Here, we propose that the enhanced conductance at the transition is due to the appearance of robust conducting edge states at domain walls between the two phases. We formulate a criterion for the existence of such conducting edge states at the domain walls. For example, for a spontaneously layer polarized state at filling factor \nu${}=2$, domain walls between regions of opposite polarization carry conducting edge modes. A microscopic analysis shows that lattice-scale interactions can favor such a layer polarized state.

Physical review letters, Jan 24, 2015

We consider a normal lead coupled to a Majorana bound state. We show that the spin-resolved curre... more We consider a normal lead coupled to a Majorana bound state. We show that the spin-resolved current correlations exhibit unique features which distinguish Majorana bound states from other low-energy resonances. In particular, the spin-up and spin-down currents from a Majorana bound state are anticorrelated at low bias voltages, and become uncorrelated at higher voltages. This behavior is independent of the exact form of coupling to the lead, and of the direction of the spin polarization. In contrast, an ordinary low-energy Andreev bound state gives rise to a positive correlation between the spin-up and spin-down currents, and this spin-resolved current-current correlation approaches a nonzero constant at high bias voltages. We discuss experimental setups in which this effect can be measured.

Physical review letters, Jan 13, 2015

We describe a novel topological superfluid state, which forms in a one-dimensional Fermi gas with... more We describe a novel topological superfluid state, which forms in a one-dimensional Fermi gas with Rashba-like spin-orbit coupling, a Zeeman field, and intrinsic attractive interactions. In spite of total number conservation and the presence of gapless excitations, Majorana-like zero modes appear in this system and can be linked with interfaces between two distinct phases that naturally form at different regions of the harmonic trap. As a result, the low lying collective excitations of the system, including the dipole oscillations and the long-wavelength phonons are all doubly degenerate. While backscattering from point impurities can lead to a splitting of the degeneracies that scales algebraically with the system size, the smooth confining potential can only cause an exponentially small splitting. We show that the topological state can be uniquely probed by a pumping effect induced by a slow sweep of the Zeeman field from a high initial value down to zero. The effect is expected to...

Physical review letters, Jan 6, 2015

We show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_{2} a... more We show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_{2} and U(1) symmetry at the multicritical point where the Ising and Berezinskii-Kosterlitz-Thouless transitions coincide. To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations allowed by symmetry. This analysis reveals an intricate flow with a marginally irrelevant direction that preserves part of the supersymmetry of the fixed point. The slow flow along this special line has significant consequences on the physics of the multicritical point. In particular, we show that the scaling of the U(1) gap away from the multicritical point is different from the usual Berezinskii-Kosterlitz-Thouless exponential gap scaling.

Physical review letters, Jan 6, 2015

We consider a low T_{c} metallic superconductor weakly coupled to the soft fluctuations associate... more We consider a low T_{c} metallic superconductor weakly coupled to the soft fluctuations associated with proximity to a nematic quantum critical point (NQCP). We show that (1) a BCS-Eliashberg treatment remains valid outside of a parametrically narrow interval about the NQCP, (2) the symmetry of the superconducting state (d wave, s wave, p wave) is typically determined by the noncritical interactions, but T_{c} is enhanced by the nematic fluctuations in all channels, and (3) in 2D, this enhancement grows upon approach to criticality up to the point at which the weak coupling approach breaks down, but in 3D, the enhancement is much weaker.

Science (New York, N.Y.), Jan 7, 2014

Electrons have three quantized properties-charge, spin, and Fermi statistics-that are directly re... more Electrons have three quantized properties-charge, spin, and Fermi statistics-that are directly responsible for a vast array of phenomena. Here we show how these properties can be coherently and dynamically stripped from the electron as it enters a certain exotic state of matter known as a quantum spin liquid (QSL). In a QSL, electron spins collectively form a highly entangled quantum state that gives rise to the fractionalization of spin, charge, and statistics. We show that certain QSLs host distinct, topologically robust boundary types, some of which allow the electron to coherently enter the QSL as a fractionalized quasi-particle, leaving its spin, charge, or statistics behind. We use these ideas to propose a number of universal, conclusive experimental signatures that would establish fractionalization in QSLs.

By using ARPES interpretation for the origin of the collective spin and charge orderings in under... more By using ARPES interpretation for the origin of the collective spin and charge orderings in underdoped La-based cuprate superconductors is carefully examined. A Fermi surface nesting wave vector is identified which closely matches the collective ordering wave vector observed by ...