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arXiv:1802.04293 · Physical review. B./Physical review. B

Candidate theory for the strange metal phase at a finite-energy window

Xiao-Chuan Wu, Xiao Chen, Chao‐Ming Jian, Yi‐Zhuang You, Cenke Xu

Published Oct 11, 2018• 26 citations
arXivHTMLPDF

Abstract

We propose a lattice model for strongly interacting electrons with the potential to explain the main phenomenology of the strange metal phase in the cuprate high-temperature superconductors. Our model is motivated by the recently developed ``tetrahedron'' rank-3 tensor model that mimics much of the physics of the better-known Sachdev-Ye-Kitaev (SYK) model. Our electron model has the following advantageous properties: (1) it needs only one orbital per site on the square lattice. (2) It does not require any quenched random interaction. (3) It has local interactions and respects all the symmetries of the system. (4) The soluble limit of this model has a longitudinal dc resistivity that scales linearly with temperature within a finite temperature window. (5) Again, the soluble limit of this model has a fermion pairing instability in the infrared, which can lead to either superconductivity or a ``pseudogap'' phase. The linear-$T$ longitudinal resistivity and the pairing instability originate from the generic scaling feature of the SYK model and the tetrahedron tensor model.

DOI
10.1103/physrevb.98.165117

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We propose a lattice model for strongly interacting electrons with the potential to explain the main phenomenology of the strange metal phase in the cuprate high-temperature superconductors. Our model is motivated by the recently developed tetrahedron'' rank-3 tensor model that mimics much of the physics of the better-known Sachdev-Ye-Kitaev (SYK) model. Our electron model has the following advantageous properties: (1) it needs only one orbital per site on the square lattice. (2) It does not require any quenched random interaction. (3) It has local interactions and respects all the symmetries of the system. (4) The soluble limit of this model has a longitudinal dc resistivity that scales linearly with temperature within a finite temperature window. (5) Again, the soluble limit of this model has a fermion pairing instability in the infrared, which can lead to either superconductivity or a pseudogap'' phase. The linear-TTT longitudinal resistivity and the pairing instability originate from the generic scaling feature of the SYK model and the tetrahedron tensor model.
Abstract A lattice model for strongly interacting electrons motivated by a rank-3 tensor model provides a tool for understanding the pairing mechanism of high-temperature superconductivity. This Sachdev–Ye–Kitaev-like model describes the strange metal phase in the cuprate high temperature superconductors. Our calculation indicates that the superconducting gap ratio in this model is higher than the ratio in the BCS theory due to the coupling term and the spin operator. Under certain conditions, the ratio also agrees with the BCS theory. Our results relate to the case of strong coupling, so it may pave the way to gaining insight into the cuprate high temperature superconductors.
Models for strongly interacting fermions in disordered clusters forming an array, with electron hopping between sites, reproduce the linear dependence on temperature of the resistivity, typical of the strange metal phase of High Temperature Superconducting materials (Extended Sachdev-Ye-Kitaev (SYK) models). Our hydrodynamical approach to the marginal Fermi liquid emerging out of the interaction, identifies the low energy collective excitations of the system in its coherent phase. These neutral excitations diffuse in the lattice, but the diffusion is heavily hindered by coupling to the pseudo Goldstone modes of the conformal broken symmetry SYK phase, which are local in space. A critical temperature for superconductivity arises in the electron liquid,in case these excitations are assumed to mediate an attractive Cooper-pairing, in the electron liquid, which is not BCS-like.
Models for strongly interacting fermions in disordered clusters forming an array, with electron hopping between sites, reproduce the linear dependence on temperature of the resistivity, typical of the strange metal phase of high temperature superconducting materials [extended Sachdev-Ye-Kitaev (SYK) models]. We identify the low energy collective excitations as neutral energy excitations, diffusing in the lattice of the thermalized non-Fermi liquid phase. However, the diffusion is heavily hindered by coupling to the pseudo-Goldstone modes of the conformal broken symmetry SYK phase, which are local in space. The imaginary time evolution of the extended model in the strong interaction and 1/N1/N1/N expansion limit is presented in the incoherent nonchaotic regime. On the other hand, a Fermi electronic liquid at low energy becomes marginal when perturbed by the SYK dots. A critical temperature for superconductivity is derived, which is not BCS-like, in case the collective excitations are assumed to mediate an attractive Cooper pairing.
We study a two-flavor fermion model where each of the flavors form a Sachdev-Ye-Kitaev (SYK) system with arbitrary qqq-body interactions. The crucial new element is an all-to-all rrr-body interaction between the two flavors. At high temperatures, the model shows a strange metal phase where both flavors are gapless, similar to the usual single-flavor SYK model. Upon reducing temperature, the coupled system undergoes transitions to previously unseen phases in the SYK framework---first, a strange half-metal phase where one flavor remains a strange metal while the other is gapped, and second, an insulating phase of the Mott kind where both flavors are gapped. At a fixed low temperature, we obtain transitions between these phases by tuning the relative fraction of sites for each flavor. We discuss the physics of these phases and the nature of transitions between them. This work provides an example of an instability of the strange metal with potential to provide new routes to study strongly correlated systems through the rich physics contained in SYK-like models.
"Strange metals" with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-[Formula: see text] fermions interacting via onsite Hubbard interaction and random infinite-ranged spin-spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of [Formula: see text] symmetric models to models with physical [Formula: see text] spin-[Formula: see text] electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.
Despite considerable theoretical effort, there has been no consensus on the description of the strange metal state seen in high temperature superconductors and its linear in T resistivity. Here, we construct a simple solvable model of itinerant electrons interacting through random couplings on a honeycomb lattice composed of Sachdev-Ye-Kitaev quantum dots which describes electrons without quasiparticle excitations. This model is solvable in the large-N limit and displays a temperature dependant crossover between two regimes. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite T crossover to a fully incoherent regime that also has a linear in T resistivity. In the non-Fermi liquid regime, the dc resistivityincreases linearly with temperature over a broad range of temperatures. The self energy has a singular frequency dependence but lacks momentum dependence which is reminiscent of a dynamical mean-field-theory-like behavior but in dimensions d < ∞ . In the low-temperature and strong-coupling limit, the behaviour parallels that of Dirac fermions. We discuss the implications of theseresults and further possibilities in such studies.