TKM Institutsseminar |
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Speaker: | Davide Valentinis |
Date: | 25/07/2024 12:30 |
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Where: | 10.01, Geb. 30.23, CS; and Zoom |
Affiliation: | TKM |

Host: | Jörg Schmalian |

## Abstract

Strange-metal phases, found in, e.g., heavy fermions, pnictides, and cuprates, defy

conventional theoretical descriptions based on Fermi-liquid (FL) theory [1,2]. Some

anomalous properties of such phases include: linear-in-temperature (T-linear) DC

resistivity [3-6], universal w/T scalings of the optical conductivity as a function of

frequency w [7], B/T scalings of the magnetoresistivity as a function of applied

magnetic field B [4,5,8], T2 behaviour of the Hall angle cotangent [9,10], and

interaction-dependent renormalizations of the cyclotron frequency [11]. In addition,

strange metals host partially coherent superconducting states, born out of incoherent,

non-Fermi liquid (NFL) normal-state spectra [12-14].

Constructing minimal exactly solvable models for NFL states might shed new light on

the electrodynamics and superconducting instabilities of strange metals. In this context,

the Sachdev-Ye-Kitaev (SYK) approach [1,15,16], based on all-to-all interactions

among N fermion species ("flavors") in 0-dimensional dots, is a promising route. A

superconducting instability emerges by coupling fermions to M bosonic flavors (the

Yukawa-SYK model), at once responsible for Cooper pairing and for normal-state

incoherence [17,18]. In this work, we generalize the Yukawa-SYK model to a lattice

with random hopping parameters. We exactly solve the model in the spin-singlet large-

N limit, at N=M and at particle-hole symmetry, we construct the phase diagram, and

we characterize the FL to NFL crossovers in the normal and superconducting states

[19,20]. Hopping exponentially decreases the critical temperature in FL regime, which

is maximal in the single-dot NFL limit at given coupling. However, the phase stiffness

and the condensation energy are maximal precisely at the NFL/FL crossover. Such

correlation is reminiscent of an analogous experimental evidence found in

superconducting cuprates [21].

We then generalize the theory to 2D dispersive fermions and bosons, coupled through

random interactions which are contact-like in real space. This model realizes a marginal

Fermi liquid (MFL) in the normal state [22-24], with T-linear DC resistivity down to

zero temperature, when the system is tuned to criticality by softening of the bosons.

Moreover, the optical scattering rate and effective mass of fermionic carriers, extracted

from the normal-state optical conductivity, display w/T scaling [25], in striking analogy

with recent optical experiments on the La2–xSrxCuO4 cuprate [7].

The phase diagram also includes a low-temperature superconducting phase, where swave pairing is mediated by the spatially random fermion-boson interactions [25]. We

find that this superconductor has finite phase stiffness [25], which in the low-T limit

increases with increasing detuning from the quantum critical point, thus anticorrelating

with Tc [19,25].

We apply this model to DC and AC strange-metal magnetotransport. Focusing on the

effects of orbital magnetism, we find that the cyclotron resonance frequency in the AC

conductivity shifts linearly with applied magnetic field and is renormalized by

disordered interactions [26], analogously to recent magnetoconductivity experiments on

cuprates [11]. Further work in preparation investigates the DC longitudinal and Hall

resistivities, which we analyze as a function of T and B.

References

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