Bose-metal Phase Research Articles

Bosonic topological insulators at the superconductor-to-superinsulator transition

We review the topological gauge theory of the superconductor-to-superinsulator transition. The possible intermediate Bose metal phase intervening between these two states is a bosonic topological insulator. We point out that the correct treatment of a bosonic topological insulator requires a normally neglected, additional dimensionless parameter, which arises because of the non-commutativity between the infinite gap limit and phase space reduction. We show that the bosonic topological insulator is a functional first Landau level. The additional parameter drives two Berezinskii–Kosterlitz–Thouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. The two BKT correlation scales account for the emergent granularity observed around the transition. Finally, we derive the ground state wave function for a system of charges and vortices in the Bose metal phase.

Superconductor-Insulator Transition in a Non-Fermi Liquid.

We present a model of a strongly correlated system with a non-Fermi liquid high temperature phase. Its ground state undergoes an insulator to superconductor quantum phase transition (QPT) as a function of a pairing interaction strength. Both the insulator and the superconductor are originating from the same interaction mechanism. The resistivity in the insulating phase exhibits the activation behavior with the activation energy, which goes to zero at the QPT. This leads to a wide quantum critical regime with an algebraic temperature dependence of the resistivity. Upon raising the temperature in the superconducting phase, the model exhibits a finite temperature phase transition to a Bose metal phase, which separates the superconductor from the non-Fermi liquid metal.

Geometric frustration produces long-sought Bose metal phase of quantum matter

Two of the most prominent phases of bosonic matter are the superfluid with perfect flow and the insulator with no flow. A now decades-old mystery unexpectedly arose when experimental observations indicated that bosons could organize into the formation of an entirely different intervening third phase: the Bose metal with dissipative flow. The most viable theory for such a Bose metal to date invokes the use of the extrinsic property of impurity-based disorder; however, a generic intrinsic quantum Bose metal state is still lacking. We propose a universal homogeneous theory for a Bose metal in which geometric frustration confines the essential quantum coherence to a lower dimension. The result is a gapless insulator characterized by dissipative flow that vanishes in the low-energy limit. This failed insulator exemplifies a frustration-dominated regime that is only enhanced by additional scattering sources at low energy and therefore produces a Bose metal that thrives under realistic experimental conditions.

Wave-function positivization via automatic differentiation

We introduce a procedure to systematically search for a local unitary transformation that maps a wavefunction with a non-trivial sign structure into a positive-real form. The transformation is parametrized as a quantum circuit compiled into a set of one and two qubit gates. We design a cost function that maximizes the average sign of the output state and removes its complex phases. The optimization of the gates is performed through automatic differentiation algorithms, widely used in the machine learning community. We provide numerical evidence for significant improvements in the average sign for a two-leg triangular Heisenberg ladder with next-to-nearest neighbour and ring-exchange interactions. This model exhibits phases where the sign structure can be removed by simple local one-qubit unitaries, but also an exotic Bose-metal phase whose sign structure induces "Bose surfaces" with a fermionic character and a higher entanglement that requires deeper circuits.

Two-dimensional superconductivity and magnetotransport from topological surface states in AuSn4 semimetal

Topological materials such as Dirac or Weyl semimetals are new states of matter characterized by symmetry-protected surface states responsible for exotic low-temperature magnetotransport properties. Here, transport measurements on AuSn4 single crystals, a topological nodal-line semimetal candidate, reveal the presence of two-dimensional superconductivity with a transition temperature Tc ~ 2.40 K. The two-dimensional nature of superconductivity is verified by a Berezinsky–Kosterlitz–Thouless transition, Bose-metal phase, and vortex dynamics interpreted in terms of thermally-assisted flux motion in two dimensions. The normal-state magnetoconductivity at low temperatures is found to be well described by the weak-antilocalization transport formula, which has been commonly observed in topological materials, strongly supporting the scenario that normal-state magnetotransport in AuSn4 is dominated by the surface electrons of topological Dirac-cone states. The entire results are summarized in a phase diagram in the temperature–magnetic field plane, which displays different regimes of transport. The combination of two-dimensional superconductivity and surface-driven magnetotransport suggests the topological nature of superconductivity in AuSn4.

Restoring Superconductivity in the Quantum Metal Phase of NbSe2 Using Dissipative Coupling.

Localization arguments forbid the appearance of a metallic ground state in two dimensions. Yet, a large variety of disordered superconductors are known to manifest an anomalous metal phase in the zero temperature limit. While previous observations were confined to noncrystalline "dirty" superconductors, the recent observation of the so-called Bose metal phase in crystalline thin flakes of NbSe2 has sparked off intense debate. While the exact nature of this phase remains unknown, it is thought that quantum fluctuations play a decisive role in Bose metal physics. In this work, we study the response of the anomalous metal phase in thin flakes of NbSe2 to dissipative coupling. We evince a dramatic quenching of the Bose metal phase when dissipative coupling is strong, fully restoring a zero resistance superconducting state in the entire region of the magnetic field (H)-temperature (T) phase diagram where the Bose metal phase is otherwise observed. The suppression of the Bose metal phase by dissipative coupling is possible only in a quantum system where dissipation can directly affect system thermodynamics. Our observation of a dissipative phase transition in two-dimensional NbSe2 firmly establishes the quantum nature of the anomalous metal phase in this class of "clean" superconductors.

2D superconductivity and vortex dynamics in 1T-MoS2

The Berezinskii-Kosterlitz-Thouless phase transition and Bose metal phase, driven by vortices and their dynamics are the hallmark features of a clean two-dimensional superconductor. Materials with a minimal structural disorder and high conductivity are essential for the observation of these features. 1T-MoS2, a relatively unexplored metallic van der Waals material, is a promising candidate in this regard. Here, we report the observation of two-dimensional superconductivity in a few-layer 1T-MoS2 device. The electrical characterisation reveals a transition temperature Tc ~920 mK. Berezinskii-Kosterlitz-Thouless transition and anisotropy in the magneto-transport confirm the dimensionality of the superconductivity. In addition, we observe an enhancement in the parallel upper-critical-field and emergence of the Bose metal state in our sample. The observation of 2D superconductivity in 1T-MoS2 and the capability to scalably engineer this phase on the semiconducting 2H-MoS2 phase opens up a new route for the realisation and study of monolithic hybrid quantum circuits.

P-Wave superfluidity by spin-nematic Fermi surface deformation.

We study attractively interacting fermions on a square lattice with dispersion relations exhibiting strong spin-dependent anisotropy. The resulting Fermi surface mismatch suppresses the s-wave BCS-type instability, clearing the way for unconventional types of order. Unbiased sampling of the Feynman diagrammatic series using diagrammatic Monte Carlo methods reveals a rich phase diagram in the regime of intermediate coupling strength. Instead of a proposed Cooper-pair Bose metal phase [A. E. Feiguin and M. P. A. Fisher, Phys. Rev. Lett. 103, 025303 (2009)], we find an incommensurate density wave at strong anisotropy and two different p-wave superfluid states with unconventional symmetry at intermediate anisotropy.

Quantum phases of hard-core bosons in a frustrated honeycomb lattice

Using exact diagonalization calculations, we investigate the ground-state phase diagram of the hard-core Bose–Hubbard–Haldane model on the honeycomb lattice. This allows us to probe the stability of the Bose-metal phase proposed in Varney et al (2011 Phys. Rev. Lett.107 077201), against various changes in the originally studied Hamiltonian.

Spin Bose-Metal and Valence Bond Solid Phases in a Spin-1/2Model with Ring Exchanges on a Four-Leg Triangular Ladder

We study a spin-1/2 system with Heisenberg plus ring exchanges on a four-leg triangular ladder using the density matrix renormalization group and Gutzwiller variational wave functions. Near an isotropic lattice regime, for moderate to large ring exchanges we find a spin Bose-metal phase with a spinon Fermi sea consisting of three partially filled bands. Going away from the triangular towards the square lattice regime, we find a staggered dimer phase with dimers in the transverse direction, while for small ring exchanges the system is in a featureless rung phase. We also discuss parent states and a possible phase diagram in two dimensions.

Exotic paired phases in ladders with spin-dependent hopping

Fermions in two-dimensions (2D) when subject to anisotropic spin-dependent hopping can potentially give rise to unusual paired states in {\it unpolarized} mixtures that can behave as non-Fermi liquids. One possibility is a fully paired state with a gap for fermion excitations in which the Cooper pairs remain uncondensed. Such a "Cooper-pair Bose-metal" phase would be expected to have a singular Bose-surface in momentum space. As demonstrated in the context of 2D bosons hopping with a frustrating ring-exchange interaction, an analogous Bose-metal phase has a set of quasi-1D descendent states when put on a ladder geometry. Here we present a density matrix renormalization group (DMRG) study of the attractive Hubbard model with spin-dependent hopping on a two-leg ladder geometry. In our setup, one spin species moves preferentially along the leg direction, while the other does so along the rung direction. We find compelling evidence for the existence of a novel Cooper-pair Bose-metal phase in a region of the phase diagram at intermediate coupling. We further explore the phase diagram of this model as a function of hopping anisotropy, density, and interaction strength, finding a conventional superfluid phase, as well as a phase of paired Cooper pairs with d-wave symmetry, similar to the one found in models of hard-core bosons with ring-exchange. We argue that simulating this model with cold Fermi gases on spin dependent optical lattices is a promising direction for realizing exotic quantum states.

Effects of Zeeman field on a spin Bose-metal phase

We consider Zeeman field effects on a spin Bose-metal (SBM) phase on a two-leg triangular ladder. This phase was found in a spin-1/2 model with ring exchanges [D. N. Sheng, O. I. Motrunich, and M. P. A. Fisher, Phys. Rev. B 79, 205112 (2009)] and was also proposed to appear in an interacting electronic model with longer-ranged repulsion [H.-H. Lai and O. I. Motrunich, Phys. Rev. B 81, 045105 (2010)]. Using bosonization of a spinon-gauge theory, we study the stability of the SBM phase and its properties under the field. We also explore phases arising from potential instabilities of the SBM; in all cases, we find a gap to spin-1 excitations while spin-nematic correlations are power law. We discuss two-dimensional analogues of these phases where spinons can pair with their own species.

Effects of impurities in spin Bose-metal phase on a two-leg triangular strip

We study effects of nonmagnetic impurities in a Spin Bose-Metal (SBM) phase discovered in a two-leg triangular strip spin-1/2 model with ring exchanges (D. N. Shenget al, arXiv:0902.4210). This phase is a quasi-1D descendant of a 2D spin liquid with spinon Fermi sea, and the present study aims at interpolating between the 1D and 2D cases. Different types of defects can be treated as local energy perturbations, which we find are always relevant. As a result, a nonmagnetic impurity generically cuts the system into two decoupled parts. We calculate bond energy and local spin susceptibility near the defect, both of which can be measured in experiments. The Spin Bose-Metal has dominant correlations at characteristic incommensurate wavevectors that are revealed near the defect. Thus, the bond energy shows a static texture oscillating as a function of distance from the defect and decaying as a slow power law. The local spin susceptibility also oscillates and actually {\it increases} as a function of distance from the defect, similar to the effect found in the 1D chain [S. Eggert and I. Affleck, Phys. Rev. Lett. {\bf 75}, 934 (1995)]. We calculate the corresponding power law exponents for the textures as a function of one Luttinger parameter of the SBM theory.

Spin Bose-metal phase in a spin-12model with ring exchange on a two-leg triangular strip

Recent experiments on triangular lattice organic Mott insulators have found evidence for a two-dimensional (2D) spin liquid in close proximity to the metal-insulator transition. A Gutzwiller wave function study of the triangular lattice Heisenberg model with a four-spin ring exchange term appropriate in this regime has found that the projected spinon Fermi sea state has a low variational energy. This wave function, together with a slave particle-gauge theory analysis, suggests that this putative spin liquid possesses spin correlations that are singular along surfaces in momentum space, i.e., ``Bose surfaces.'' Signatures of this state, which we will refer to as a ``spin Bose metal'' (SBM), are expected to manifest in quasi-one-dimensional (quasi-1D) ladder systems: the discrete transverse momenta cut through the 2D Bose surface leading to a distinct pattern of 1D gapless modes. Here, we search for a quasi-1D descendant of the triangular lattice SBM state by exploring the Heisenberg plus ring model on a two-leg triangular strip (zigzag chain). Using density matrix renormalization group (DMRG) supplemented by variational wave functions and a bosonization analysis, we map out the full phase diagram. In the absence of ring exchange the model is equivalent to the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg chain, and we find the expected Bethe-chain and dimerized phases. Remarkably, moderate ring exchange reveals a new gapless phase over a large swath of the phase diagram. Spin and dimer correlations possess singular wave vectors at particular ``Bose points'' (remnants of the 2D Bose surface) and allow us to identify this phase as the hoped for quasi-1D descendant of the triangular lattice SBM state. We use bosonization to derive a low-energy effective theory for the zigzag spin Bose metal and find three gapless modes and one Luttinger parameter controlling all power law correlations. Potential instabilities out of the zigzag SBM give rise to other interesting phases such as a period-3 valence bond solid or a period-4 chirality order, which we discover in the DMRG. Another interesting instability is into a spin Bose-metal phase with partial ferromagnetism (spin polarization of one spinon band), which we also find numerically using the DMRG.

Short-range interactions and a Bose metal phase in two dimensions

We show here based on a 1-loop scaling analysis that short-range interactions are strongly irrelevant perturbations near the insulator-superconductor (IST) quantum critical point. The lack of any proof that short-range interactions mediate physics which is present only in strong coupling leads us to conclude that short-range interactions are strictly irrelevant near the IST quantum critical point. Hence, we argue that no new physics, such as the formation of a uniform Bose metal phase can arise from an interplay between on-site and nearest-neighbour interactions.

Renormalized Bose condensation in the presence of fermions.

Bose condensation of a dilute charged Bose gas in contact with a dense Fermi liquid is examined. The particles have hard cores and hop on a lattice. It is argued that a ``Bose metal phase,'' i.e., a phase with vanishing condensate fraction, is unlikely to exist in this problem at zero temperature. However very strong renormalizations of the properties of the Bose system occur when the boson band is narrower than the fermion band. We find that the condensate fraction at zero temperature is suppressed by a factor 4(W/${\mathit{w}}_{\mathit{b}}$${)}^{2}$ exp(-W/${\mathit{w}}_{\mathit{b}}$) in two dimensions over Gutzwiller-type variational estimates. Here, ${\mathit{w}}_{\mathit{b}}$ and W are the boson and fermion half-band-widths, respectively. There is a similar reduction in the transition temperature. Thus the possibility that high-${\mathit{T}}_{\mathit{c}}$ superconductors are Bose metals in their normal states cannot be excluded on the basis of present experimental or theoretical evidence.