Kondo enabled transmutation between spinons and superconducting vortices origin of magnetic memory in 4Hb- TaS 2 Shi-Zeng Lin1 2

2025-04-24 0 0 236.77KB 6 页 10玖币

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Kondo enabled transmutation between spinons and superconducting vortices: origin of magnetic

memory in 4Hb-TaS2

Shi-Zeng Lin1, 2

1Theoretical Division, T-4 and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

2Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

(Dated: October 14, 2022)

Recent experiments [Persky et al., Nature 607, 692 (2022)] demonstrate a magnetic memory eﬀect in 4Hb-

TaS2above its superconducting transition temperature, where Abriokosov vortices are generated spontaneously

by lowering temperature at zero magnetic ﬁeld after ﬁeld training the normal state. Motivated by the experiment,

we propose the chiral quantum spin liquid (QSL) stabilized in the constituent layers of 4Hb-TaS2as a mecha-

nism. We model 4Hb-TaS2as coupled layers of the chiral QSL and superconductor. Through the Kondo cou-

pling between the localized moments and conduction electrons, there is mutual transmutation between spinons

and vortices during the thermal cycling process, which yields magnetic memory eﬀect as observed in experi-

ments. We also propose a mechanism to stabilize the chiral and nematic superconductivity in 4Hb-TaS2through

the Kondo coupling of conduction electrons to the chiral QSL. Our results suggest 4Hb-TaS2as an exciting

platform to explore the interplay between QSL and superconductivity through the Kondo eﬀect.

Quantum spin liquid (QSL) is an exotic state of matter,

where electron spin fractionalizes into more elementary de-

gree of freedom that interacts through a dynamical gauge

ﬁeld. [1–4] The existence of QSL has been well established

by the exactly solvable models. Nevertheless, unambiguous

experimental identiﬁcation of the QSL remains a huge chal-

lenge despite many encouraging signs have been detected.

The QSL can serve as a mother state to induce other novel

quantum states. For instance, one can obtain unconventional

superconductivity by doping QSL [5] or by coupling QSL to

metals through the Kondo coupling. [6]

The recent observation of a magnetic memory and sponta-

neous vortices in a van der Waals superconductor 4Hb-TaS2

suggests the possible existence of QSL in this compound. [7]

4Hb-TaS2consists of two alternatingly stacked layers of octa-

hedral TaS2(1T-TaS2) and trigonal prismatic TaS2(1H-TaS2).

Both 1T-TaS2and 1H-TaS2can exist in a bulk form. The 1T-

TaS2bulk was argued to host QSL. [8] The 1T-TaS2undergoes

an incommensurate charge density wave (CDW) transition

around 350 K, followed by another transition to a commensu-

rate CDW around 200 K, forming a √13 ×√13 structure. [9]

The unit cell is enlarged to having 13 Ta ions, where each Ta

ions contributes one 5d electron. The unit cell forms a trian-

gular lattice. The observed insulating behavior implies a Mott

insulating state in 1T-TaS2below 200 K. Indeed, the lower and

upper Hubbard bands have been observed by scanning tunnel-

ing microscope. [10,11]. However, no magnetic order and

even the formation of localized moment has been observed

down to the lowest temperature that is much smaller than the

estimated exchange coupling between localized spins. [12–

15] These experiments support the existence of a QSL, either

a fully gapped Z2QSL or a Dirac QSL, in 1T-TaS2proposed

by Law et al. [8]. Later, a more reﬁned modeling calcula-

tions based a spin Hamiltonian that is appropriate for 1T-TaS2

concludes a QSL with spinon Fermi surface [16]. The QSL

picture is also supported by other measurements. [11,17,18]

On the other hand, 2H-TaS2(two layers of 1H-TaS2) is a

superconductor with Tc=0.7 K. [19] Therefore 4Hb-TaS2

oﬀers an exciting platform for studying the interplay between

superconductivity and QSL. One expects a Kondo coupling

between the metallic layer 1H-TaS2and the Mott insulator 1T-

TaS2, which has been conﬁrmed through the observation of

the Kondo resonance peak by scanning tunneling microscopy.

[11,18] [20] Several unusual superconducting behaviors in

4Hb-TaS2, which may have the origin from this interplay, are

observed in experiments. The Tcin 4Hb-TaS2is increased

to 2.7 K. The two-dimensional nature of the superconducting

state is conﬁrmed by the extracted coherence lengths from the

upper critical ﬁelds. Time-reversal symmetry (TRS) is found

to be broken in the superconducting state from muon spin

relaxation measurement and is interpreted as a signature for

chiral superconductivity. Both d+id and p+ip pairing sym-

metries that are constrained by the D3hcrystal structure are

proposed. [21] The two components superconducting order

parameter is further supported by the Little-Parks oscillation

and scanning tunneling microscopy and angle-resolved trans-

port experiment. [22] Furthermore, a crossover from the chiral

to the nematic state is also detected. [23]

Recent experiments report an unusual magnetic memory

eﬀect in 4Hb-TaS2single crystals between Tc=2.7 K and

TM=3.6 K. [7] Initially, the crystal is cooled below T=1.7

K below Tcin a small ﬁeld H=1.3 Oe to create a bunch

of randomly distributed vortices due to the pinning potential.

Then the crystal is warmed to Tf>Tcunder the same ﬁeld,

after which the crystal is zero-ﬁeld cooled to a target temper-

ature T<Tc. Surprisingly, there are randomly distributed

vortices despite zero-ﬁeld cooling. In experiments, this proto-

col is repeated, but at diﬀerent Tf. The density of the remnant

vortices decreases with Tfand disappears when Tf>TM.

The remnant vortice density increases linearly with the train-

ing magnetic ﬁeld, and there exists a weak hysteresis near the

zero ﬁeld. The authors of Ref. [7] also performed annealing

from T>TMto Tfwith Tc<Tf<TQin the training ﬁeld.

Then the crystal is cooled to T<Tcwithout a magnetic ﬁeld.

In this process, no ﬁeld is applied inside the superconducting

phase. However, remnant vortices are observed, which is in

arXiv:2210.06550v1 [cond-mat.str-el] 12 Oct 2022

sharp contrast to the case with zero-ﬁeld cooling directly from

T>TM. The experiments point to an anormalous mangetic

memory in Tc<T<TM. In this temperature window, a

small magnetization corresponding to one spin in an area of

40 nm×40 nm assuming a uniform distribution is observed.

This small magnetization is not enough to induce the observed

vortex density either due to Zeeman or orbital coupling to the

conduction electrons. The authors of Ref. [7] speculate on

the possibility of QSL with breaking TRS residing in the con-

stituting 1T-TaS2layers as the origin of the memory eﬀect,

without knowing the underlying mechanism. Recently, a Z2

QSL with TRS was proposed to explain the magnetic mem-

ory eﬀect, where Z2vortices or visons are transformed into

superconducting vortices at T<Tcupon cooling. [24]

Our starting point is based on the observation of the Kondo

resonance peak in the bilayer of 1T-TaS2/1H-TaS2. [11,18]

The presence of a Kondo peak suggests negligible charge

transfer between 1T-TaS2and 1H-TaS2, and a well-developed

localized magnetic moment in 1T-TaS2and the existence of

itinerant electrons in 1H-TaS2. Our physical picture is based

on the observation that, in the conventional heavy fermion liq-

uid, the Kondo eﬀect converts neutral spinons into charged

fermions and, therefore, forms a heavy fermion liquid with an

enlarged fermi volume. [25] (The charge here is deﬁned un-

der the gauge ﬁelds of the electromagnetic ﬁelds.) We model

4Hb-TaS2as a superconductor-Mott insulator layered struc-

ture with an interlayer Kondo coupling, see Fig. 1. The

Hamiltonian of 4Hb-TaS2can be schematically written as

H=HT+HK+HH(c†

i,ci), where HT(HH(c†

i,ci)) describes

1T-TaS2(1H-TaS2), and HKis the Kondo interaction. They

have the form (we set ~=e=c=1 below)

HT=X

<i j>

Ji jSi·Sj+X

<i jkl>

Ji jkl(Si·Sj)(Sk·Sl)+··· ,(1)

HK=JKX

c†

i,ασαβciβ·Si.(2)

We have included four spin interactions in HTand ··· repre-

sent higher-order interactions. The spin anisotropy in 1T-TaS2

is small [16] and is neglected here. Motivated by the experi-

mental observation [7] of TRS breaking between Tcand Tm,

and also the identiﬁcation of chiral QSL in triangular lattice

Hubbard model in the density matrix renormalization group

study [26,27], here we assume that 1T-TaS2is in a chiral QSL

below TQ. The spin chirality Si·(Sj×Sk) with i jk labeling

the sites in a smallest triangle has a nonzero expectation value

consistent with TRS breaking.

The chiral QSL and Kondo coupling can be treated us-

ing the parton construction, ψi=(fi↑,f†

i↓) with Si=

Pαβ f†

iασαβ fiβ/2 and f†

i↑fi↑+f†

i↓fi↓=1. In the mean-ﬁeld de-

scription, HT≈Pi j ψ†

jui,jψi. In this construction, HThas an

SU(2) gauge redundancy [28] and ui,jrelated by SU(2) gauge

rotation are equivalent, i.e. ψi→Wiψiand ui j →Wiui jW†

where Wiis a local SU(2) transformation. [29] We will dis-

cuss two ansatzes. In the ﬁrst case, the occupied fiαform a

Chern band with Chern number C=1, which can be obtained

1T-TaS2 : chiral quantum spin liquid

1H-TaS2: superconductor

vortex

spinon

vortex

Increase T

spinon

vortex

DecreaseT

FIG. 1. 4Hb-TaS2is modeled as a multilayer structure with alternat-

ing chiral QSL and superconductor layers. Through the interlayer

Kondo interaction, a superconducting vortex is dressed by a spinon.

Transmutation between spinons and vortices occurs during the ther-

mal cycling process, which results in a magnetic memory eﬀect in

the temperature window Tc<T<TQ.

by introducing ﬂux for fiαhopping in the triangular lattice, see

Fig. 2. The other ansatz corresponds to the state where fiαis

in the d+id superconducting state [30].

The Kondo coherence can also be described in terms of

the parton theory. [25] The Kondo term can be written as

c†

iασαβciβ·Si=−(f†

iαciα)(c†

iβfiβ)+···, where we have ne-

glected a shift in the local chemical potential for ciαfermion.

The Kondo coherence emerges when the composite bosons

Q=f†

iαciαcondense, hQi,0. As a consequence, the SU(2)

gauge redundancy in ψiis broken down to U(1). fαfermion

carries a charge associated with an emergent gauge ﬁeld a,

which is a subgroup of Wi. The cαfermion carries a physi-

cal charge associated with the physical gauge ﬁeld A(actual

electromagnetic ﬁelds). The condensation of Qlocks Ato a

as a result of the Higgs mechanism. In the conventional heavy

fermion liquid, the fαfermions become part of the fermi liq-

uid of cα, which enlarges the fermi volume. We ascribe the

observed memory eﬀect in 4Hb-TaS2to a consequence of the

coupling between Aand aas detailed below.

The total Lagrangian of the system can be written as

L=LT(fσ,a)−ρQ

2[∇θ−(a−A)]2−ρ∆

2(∇φ−A)2+···

(3)

where we have neglected other terms for simplicity (i.e.

quadratic and quartic terms in Qand ∆≡ hciαcjβi). We also

neglected the ﬂuctuations in the amplitude of Qand ∆, which

are gapped in the ordered state. The kinetic terms describe the

coupling between the phase ﬂuctuation of Q=|Q|exp(iθ) and

∆ = |∆|exp(iφ) to the gauge ﬁelds. The superconducting order

parameter ∆describes superconductivity in 1H-TaS2, which

can be intrinsic or induced by proximity to the chiral QSL. It

is shown that doping chiral QSL can stabilize the chiral d+id

superconductivity. [31,32] One may also argue that similar

superconductivity can emerge through the Kondo coupling.

In our picture, only the Higgs mechanics, which is universal

regardless of the pairing mechanism and symmetry, is impor-

tant for the current discussion. LTdescribes the quantum state

of 1T-TaS2. When fαform a Chern insulator with the occu-

pied up and down spin bands having a Chern number C=1,

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Kondoenabledtransmutationbetweenspinonsandsuperconductingvortices:originofmagneticmemoryin4Hb-TaS2Shi-ZengLin1,21TheoreticalDivision,T-4andCNLS,LosAlamosNationalLaboratory,LosAlamos,NewMexico87545,USA2CenterforIntegratedNanotechnologies(CINT),LosAlamosNationalLaboratory,LosAlamos,NewMexico87545,USA(...

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Kondo enabled transmutation between spinons and superconducting vortices origin of magnetic memory in 4Hb- TaS 2 Shi-Zeng Lin1 2

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